Midterm II

---

Revised

22 Apr 2023

---

Programming Environment

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from fractions import Fraction

import numpy as np
import sympy as sp
from   sympy import init_printing,latex,solve,symbols
from   sympy.matrices import diag,eye,GramSchmidt,ones,Matrix,zeros
from   sympy.solvers.inequalities import reduce_inequalities

x1,x2,x3,x4=symbols('x1 x2 x3 x4')
init_printing(use_latex=True)

import matplotlib        as mpl
import matplotlib.pyplot as plt
plt.style.use('ggplot');
plt.rcParams.update({'text.usetex' : True});
%matplotlib inline

from IPython.display import display, Math

from   datetime import datetime as d
import locale                   as l
import platform                 as p
import sys                      as s

pad = 20
print(f"{'Executed'.upper():<{pad}}: {d.now()}")
print()
print(f"{'Platform'   :<{pad}}: "
      f"{p.mac_ver()[0]} | "
      f"{p.system()} | "
      f"{p.release()} | "
      f"{p.machine()}")
print(f"{''           :<{pad}}: {l.getpreferredencoding()}")
print()
print(f"{'Python'     :<{pad}}: {s.version}")
print(f"{''           :<{pad}}: {s.version_info}")
print(f"{''           :<{pad}}: {p.python_implementation()}")
print()
print(f"{'Matplotlib' :<{pad}}: {mpl.__version__}")
print(f"{'NumPy'      :<{pad}}: {np .__version__}")
print(f"{'SymPy'      :<{pad}}: {sp .__version__}")

def unitVector (vec : np.ndarray) -> np.ndarray:
  return vec/np.sqrt((vec[0]**2+vec[1]**2))

EXECUTED            : 2024-05-21 15:52:46.848447

Platform            : 14.4.1 | Darwin | 23.4.0 | arm64
                    : UTF-8

Python              : 3.11.9 | packaged by conda-forge | (main, Apr 19 2024, 18:34:54) [Clang 16.0.6 ]
                    : sys.version_info(major=3, minor=11, micro=9, releaselevel='final', serial=0)
                    : CPython

Matplotlib          : 3.8.4
NumPy               : 1.26.4
SymPy               : 1.12

---

Production Scenario

Product A [x1]
    $60.00   sale price
    1 hr     machining
    5 lb     material
    900 unit demand per week

Product B [x2]
    $90.00   sale price
    2 hr     machining
    4 lb     material
    700 unit demand per week

supply per week
    1000 hr machining
    3200 lb material

extra
    $28.00/hr machining [p1]
     $4.00/lb material  [p2]
    
initial cost D
    $40,800.00 = $28 .00/hr x 1000 hr + $4 .00/lb x 3200 lb

---

LP

\( \begin{aligned} \max z(\mathbf{x})&=60x_1+90x_2-40800 \\ g_1(\mathbf{x})&=x_1+2x_2\le1000=b_1 &&\text{machining constraint} \\ g_2(\mathbf{x})&=5x_1+4x_2\le3200=b_2 &&\text{material constraint} \\ g_3(\mathbf{x})&=x_1\le900=b_3 &&\text{Product A demand constaint} \\ g_4(\mathbf{x})&=x_2\le700=b_4 &&\text{Product B demand constraint} \\ \mathbf{x}&\ge\mathbf{0} &&\text{no negative production} \end{aligned} \)

LP          A       B
max z =  60x1 +  90x2  - 40800
   g1 =   1x1 +   2x2 <=  1000 = b1   machining constraint
   g2 =   5x1 +   4x2 <=  3200 = b2   material  constraint
   g3 =   1x1 +   0x2 <=   900 = b3   Product A demand constraint
   g4 =   0x1 +   1x2 <=   700 = b4   Product B demand constraint
                    x >= 0            no negative production

---

Gradients and directions

\( \begin{aligned} \nabla z&=\langle60,90\rangle \\ \nabla g_1&=\langle1,2\rangle &&\langle60,90\rangle\cdot\langle2,-1\rangle &&\gt0 &&\implies\langle2,-1\rangle \\ \nabla g_2&=\langle5,4\rangle &&\langle60,90\rangle\cdot\langle4,-5\rangle &&\lt0 &&\implies\langle-4,5\rangle \\ \nabla g_3&=\langle1,0\rangle &&\langle60,90\rangle\cdot\langle0,-1\rangle &&\lt0 &&\implies\langle0,1\rangle \\ \nabla g_4&=\langle0,1\rangle &&\langle60,90\rangle\cdot\langle1,0\rangle &&\gt0 &&\implies\langle1,0\rangle \end{aligned} \)

delz  = <60,90>
delg1 = < 1, 2>
delg2 = < 5, 4>
delg3 = < 1, 0>
delg4 = < 0, 1>

<60,90><2,-1> >0 => < 2,-1> g1
<60,90><4,-5> <0 => <-4, 5> g2
<60,90><0,-1> <0 => < 0, 1> g3
<60,90><1, 0> >0 => < 1, 0> g4

d =40800
b1= 1000
b2= 3200
b3=  900
b4=  700

z =60*x1+90*x2- d
g1= 1*x1+ 2*x2-b1
g2= 5*x1+ 4*x2-b2
g3= 1*x1+ 0*x2-b3
g4= 0*x1+ 1*x2-b4

# GRADIENTS & DIRECTIONS
delz =np.array([60,90])
delg1=np.array([ 1, 2]); dg1=np.array([ 2,-1])
delg2=np.array([ 5, 4]); dg2=np.array([-4, 5])
delg3=np.array([ 1, 0]); dg3=np.array([ 0, 1])
delg4=np.array([ 0, 1]); dg4=np.array([ 1, 0])

# UNIT DIRECTION VECTORS
udg1=dg1/np.sqrt(dg1[0]**2+dg1[1]**2)
udg2=dg2/np.sqrt(dg2[0]**2+dg2[1]**2)
udg3=dg3/np.sqrt(dg3[0]**2+dg3[1]**2)
udg4=dg4/np.sqrt(dg4[0]**2+dg4[1]**2)

print(f"{delz.dot(dg1):>3}")
print(f"{delz.dot(dg2):>3}")
print(f"{delz.dot(dg3):>3}")
print(f"{delz.dot(dg4):>3}")

# LINES & INTERSECTIONS
display(
'LINES',
'g1',solve(g1,x2,dict=True)[0],
'g2',solve(g2,x2,dict=True)[0],
#'g3',solve(g3,x2,dict=True)[0],
'g4',solve(g4,x2,dict=True)[0],
)

display(
reduce_inequalities(g1<=0,[x2]),
reduce_inequalities(g2<=0,[x2]),
reduce_inequalities(g3<=0,[x2]),
reduce_inequalities(g4<=0,[x2]),
)

display(
'INTERSECTIONS',
'g1=g2',   solve([g1,g2],  [x1,x2],dict=True)[0],
'g1=g3',   solve([g1,g3],  [x1,x2],dict=True)[0],
'g1=g4',   solve([g1,g4],  [x1,x2],dict=True)[0],
'g2=g3',   solve([g2,g3],  [x1,x2],dict=True)[0],
'g2=g4',   solve([g2,g4],  [x1,x2],dict=True)[0],
'g3=g4',   solve([g3,g4],  [x1,x2],dict=True)[0],
'g1[ 0,x2]',solve([g1,x1  ],[x1,x2],dict=True)[0],
'g2[x1, 0]',solve([g2,x2  ],[x1,x2],dict=True)[0],
'g2[ 0,x2]',solve([g2,x1  ],[x1,x2],dict=True)[0],
'g3[x1, 0]',solve([g3,x2  ],[x1,x2],dict=True)[0],
'g4[ 0,x2]',solve([g4,x1  ],[x1,x2],dict=True)[0],
)

 30
210
 90
 60

'LINES'

'g1'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{2} : 500 - \frac{x_{1}}{2}\right\}\]

'g2'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{2} : 800 - \frac{5 x_{1}}{4}\right\}\]

'g4'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{2} : 700\right\}\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle x_{2} \leq 500 - \frac{x_{1}}{2} \wedge -\infty < x_{2}\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle x_{2} \leq 800 - \frac{5 x_{1}}{4} \wedge -\infty < x_{2}\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle x_{1} \leq 900 \wedge -\infty < x_{1}\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle x_{2} \leq 700 \wedge -\infty < x_{2}\]

'INTERSECTIONS'

'g1=g2'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 400, \ x_{2} : 300\right\}\]

'g1=g3'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 900, \ x_{2} : 50\right\}\]

'g1=g4'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : -400, \ x_{2} : 700\right\}\]

'g2=g3'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 900, \ x_{2} : -325\right\}\]

'g2=g4'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 80, \ x_{2} : 700\right\}\]

'g3=g4'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 900, \ x_{2} : 700\right\}\]

'g1[ 0,x2]'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 0, \ x_{2} : 500\right\}\]

'g2[x1, 0]'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 640, \ x_{2} : 0\right\}\]

'g2[ 0,x2]'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 0, \ x_{2} : 800\right\}\]

'g3[x1, 0]'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 900, \ x_{2} : 0\right\}\]

'g4[ 0,x2]'

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 0, \ x_{2} : 700\right\}\]

---

Dual LP

\( \boxed{ \text{LP}= \begin{aligned} \max z(\mathbf{x})&=\mathbf{cx}+d \\ \mathbf{Ax}&\le\mathbf{b} \\ \mathbf{x}&\ge\mathbf{0} \end{aligned} \overset{\text{dual to}}{\iff} \begin{aligned} \min w(\mathbf{y})&=\mathbf{yb}+d \\ \mathbf{yA}&\ge\mathbf{c} \\ \mathbf{y}&\ge\mathbf{0} \end{aligned} =\text{LP}^* } \)

\( \text{LP}= \begin{aligned} \max z(\mathbf{x})&=60x_1+90x_2-40800 \\ g_1(\mathbf{x})&=x_1+2x_2\le1000=b_1 \\ g_2(\mathbf{x})&=5x_1+4x_2\le3200=b_2 \\ g_3(\mathbf{x})&=x_1\le900=b_3 \\ g_4(\mathbf{x})&=x_2\le700=b_4 \\ \mathbf{x}&\ge\mathbf{0} \end{aligned} \overset{\text{dual to}}{\iff} \begin{aligned} \min w(\mathbf{y})&=1000y_1+3200y_2+900y_3+700y_4-40800 \\ h_1(\mathbf{y})&= y_1+ 5y_2+ y_3 \ge60=c_1\\ h_2(\mathbf{y})&= 2y_1+ 4y_2+ y_4 \ge90=c_2\\ \mathbf{y}&\ge\mathbf{0} \end{aligned} =\text{LP}^* \)

---

Simplex Algorithm

Show code cell source Hide code cell source

def pivot (iStar,jStar,tab):
  nRows =tab.shape[0]-1
  nCols =tab.shape[1]-1
  newTab=tab[:,:]

  newTab[0,jStar]    =tab[iStar,nCols]
  newTab[iStar,nCols]=tab[0,jStar]
  newTab[iStar,0]    =-tab[nRows,jStar]
  newTab[nRows,jStar]=-tab[iStar,0]
  
  for i in range(1,nRows):
    for j in range(1,nCols):
      if   i==iStar and j==jStar:
        newTab[i,j]=1/tab[iStar,jStar]
      elif i==iStar and j!=jStar:
        newTab[i,j]=-tab[i,j]/tab[iStar,jStar]
      elif i!=iStar and j==jStar:
        newTab[i,j]= tab[i,j]/tab[iStar,jStar]
      elif i!=iStar and j!=jStar:
        newTab[i,j]= tab[i,j]-tab[iStar,j]*tab[i,jStar]/tab[iStar,jStar]
  return newTab

p1 =28
p2 = 4

db1=0
db2=0
db3=0
db4=0

rA = Matrix([
  [ 'c', 'x1',  'x2',     1, 'r'],
  ['y1',   -1,    -2,b1+db1,'s1'],
  ['y2',   -5,    -4,b2+db2,'s2'],
  ['y3',   -1,     0,b3+db3,'s3'],
  ['y4',    0,    -1,b4+db4,'s4'],
  [  -1,  -60,   -90,     d,'-z'],
  [ 'c','-v1', '-v2',   'w', 'r'],
])
rB = pivot(2,1,rA)
rC = pivot(1,2,rB)

cA = Matrix([
  [ 'c',  'y1',  'y2',  'y3',  'y4',   1, 'r'],
  ['x1',     1,     5,     1,     0, -60,'v1'],
  ['x2',     2,     4,     0,     1, -90,'v2'],
  [  -1,b1+db1,b2+db2,b3+db3,b4+db4,  -d, 'w'],
  [ 'c', '-s1', '-s2', '-s3', '-s4','-z', 'r'],
])
cB = pivot(2,1,cA)
cC = pivot(1,2,cB)

display(
  'ROW',
  Math(fr'rA = {latex(rA)}\,\,\,\,\,x_1=x_2=0'),
  Math(fr'rB = {latex(rB)}\,\,\,\,\,x_2=s_2=0'),
  Math(fr'rC = {latex(rC)}\,\,\,\,\,s_1=s_2=0'),
  'COLUMN',
  Math(fr'cA = {latex(cA)}\,\,\,\,\,x_1=x_2=0'),
  Math(fr'cB = {latex(cB)}\,\,\,\,\,x_1=s_1=0'),
  Math(fr'cC = {latex(cC)}\,\,\,\,\,s_1=s_2=0'),
)

'ROW'

\[\begin{split}\displaystyle rA = \left[\begin{matrix}c & x_{1} & x_{2} & 1 & r\\y_{1} & -1 & -2 & 1000 & s_{1}\\y_{2} & -5 & -4 & 3200 & s_{2}\\y_{3} & -1 & 0 & 900 & s_{3}\\y_{4} & 0 & -1 & 700 & s_{4}\\-1 & -60 & -90 & 40800 & - z\\c & - v_{1} & - v_{2} & w & r\end{matrix}\right]\,\,\,\,\,x_1=x_2=0\end{split}\]

\[\begin{split}\displaystyle rB = \left[\begin{matrix}c & s_{2} & x_{2} & 1 & r\\y_{1} & \frac{1}{5} & - \frac{6}{5} & 360 & s_{1}\\v_{1} & - \frac{1}{5} & - \frac{4}{5} & 640 & x_{1}\\y_{3} & \frac{1}{5} & \frac{4}{5} & 260 & s_{3}\\y_{4} & 0 & -1 & 700 & s_{4}\\-1 & 12 & -42 & 2400 & - z\\c & - y_{2} & - v_{2} & w & r\end{matrix}\right]\,\,\,\,\,x_2=s_2=0\end{split}\]

\[\begin{split}\displaystyle rC = \left[\begin{matrix}c & s_{2} & s_{1} & 1 & r\\v_{2} & \frac{1}{6} & - \frac{5}{6} & 300 & x_{2}\\v_{1} & - \frac{1}{3} & \frac{2}{3} & 400 & x_{1}\\y_{3} & \frac{1}{3} & - \frac{2}{3} & 500 & s_{3}\\y_{4} & - \frac{1}{6} & \frac{5}{6} & 400 & s_{4}\\-1 & 5 & 35 & -10200 & - z\\c & - y_{2} & - y_{1} & w & r\end{matrix}\right]\,\,\,\,\,s_1=s_2=0\end{split}\]

'COLUMN'

\[\begin{split}\displaystyle cA = \left[\begin{matrix}c & y_{1} & y_{2} & y_{3} & y_{4} & 1 & r\\x_{1} & 1 & 5 & 1 & 0 & -60 & v_{1}\\x_{2} & 2 & 4 & 0 & 1 & -90 & v_{2}\\-1 & 1000 & 3200 & 900 & 700 & -40800 & w\\c & - s_{1} & - s_{2} & - s_{3} & - s_{4} & - z & r\end{matrix}\right]\,\,\,\,\,x_1=x_2=0\end{split}\]

\[\begin{split}\displaystyle cB = \left[\begin{matrix}c & v_{2} & y_{2} & y_{3} & y_{4} & 1 & r\\x_{1} & \frac{1}{2} & 3 & 1 & - \frac{1}{2} & -15 & v_{1}\\s_{1} & \frac{1}{2} & -2 & 0 & - \frac{1}{2} & 45 & y_{1}\\-1 & 500 & 1200 & 900 & 200 & 4200 & w\\c & - x_{2} & - s_{2} & - s_{3} & - s_{4} & - z & r\end{matrix}\right]\,\,\,\,\,x_1=s_1=0\end{split}\]

\[\begin{split}\displaystyle cC = \left[\begin{matrix}c & v_{2} & v_{1} & y_{3} & y_{4} & 1 & r\\s_{2} & - \frac{1}{6} & \frac{1}{3} & - \frac{1}{3} & \frac{1}{6} & 5 & y_{2}\\s_{1} & \frac{5}{6} & - \frac{2}{3} & \frac{2}{3} & - \frac{5}{6} & 35 & y_{1}\\-1 & 300 & 400 & 500 & 400 & 10200 & w\\c & - x_{2} & - x_{1} & - s_{3} & - s_{4} & - z & r\end{matrix}\right]\,\,\,\,\,s_1=s_2=0\end{split}\]

xStar = (400,300)
zStar = z.subs([(x1,xStar[0]),(x2,xStar[1])])
yStar = (35,5,0,0)

print(f"xStar =  {xStar}")
print(f"zStar = ${int(zStar):,.2f} = wStar")
print(f"yStar =  {yStar}")

xStar =  (400, 300)
zStar = $10,200.00 = wStar
yStar =  (35, 5, 0, 0)

---

Graphical

Show code cell source Hide code cell source

s =1000
x =np.linspace(0,s,10001)

# LINES
y1=-(1/2)*x+500
y2=-(5/4)*x+800
#y3
y4= (  0)*x+700

fig=plt.figure(dpi=200);
ax =plt.subplot();
ax.set_aspect(1);

# LINES
ax.plot   (x,y1,label='g1=b1',linewidth=0.5,color='blue');
ax.plot   (x,y2,label='g2=b2',linewidth=0.5,color='yellow');
ax.axvline( 900,label='g3=b3',linewidth=0.5,color='green');
ax.plot   (x,y4,label='g4=b4',linewidth=0.5,color='red');

# delz
ax.arrow(200,200,*unitVector(  delz)*75,color='black', width=0.01,head_width=10,length_includes_head=True);
# FEASIBLE SIDES <=
ax.arrow(200,200,*unitVector(-delg1)*75,color='blue',  width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg2)*75,color='yellow',width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg3)*75,color='green', width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg4)*75,color='red',   width=0.01,head_width=10,length_includes_head=True);

# DIRECTIONS
ax.arrow(  0,500,*udg1*75,width=5,head_width=20,length_includes_head=True,color='blue');
ax.arrow(640,  0,*udg2*75,width=5,head_width=20,length_includes_head=True,color='yellow');
ax.arrow(900,  0,*udg3*75,width=5,head_width=20,length_includes_head=True,color='green');
ax.arrow(  0,700,*udg4*75,width=5,head_width=20,length_includes_head=True,color='red');

fx,fy=np.meshgrid(x,x)
plt.imshow(
  (
      (fy<=-(1/2)*fx+500)
    & (fy<=-(5/4)*fx+800)
    & (fy<= (  0)*fx+700)
  ).astype(int),
  extent=(fx.min(),fx.max(),fy.min(),fy.max()),
  origin='lower',
  cmap  ='Greys',
  alpha =0.3,
);

ax.set_xlim(0,s);
ax.set_ylim(0,s);
ax.legend();

# xStar
ax.scatter(400,300,s=1e2,color='purple');

sol=(
  r'\begin{eqnarray*}'
  r'x^*&=&(400,300)'
  r'\\'
  r'z^*&=&10200=w^*'
  r'\\'
  r'y^*&=&(35,5,0,0)'
  r'\end{eqnarray*}'
)
ax.text(400,600,sol,fontsize=10);

# SIMPLEX
dx,dy=20,20
ax.annotate( '$A$',(  0+dx,  0+dy));
ax.annotate('$rB$',(640+dx,  0+dy));
ax.annotate('$cB$',(  0+dx,500+dy));
ax.annotate( '$C$',(400+dx,300+dy));

Error in callback <function _draw_all_if_interactive at 0x136de8e00> (for post_execute), with arguments args (),kwargs {}:

---------------------------------------------------------------------------
PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/pyplot.py:197, in _draw_all_if_interactive()
    195 def _draw_all_if_interactive() -> None:
    196     if matplotlib.is_interactive():
--> 197         draw_all()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/_pylab_helpers.py:132, in Gcf.draw_all(cls, force)
    130 for manager in cls.get_all_fig_managers():
    131     if force or manager.canvas.figure.stale:
--> 132         manager.canvas.draw_idle()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:1893, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1891 if not self._is_idle_drawing:
   1892     with self._idle_draw_cntx():
-> 1893         self.draw(*args, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axes/_base.py:3070, in _AxesBase.draw(self, renderer)
   3067 if artists_rasterized:
   3068     _draw_rasterized(self.figure, artists_rasterized, renderer)
-> 3070 mimage._draw_list_compositing_images(
   3071     renderer, self, artists, self.figure.suppressComposite)
   3073 renderer.close_group('axes')
   3074 self.stale = False

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1388, in Axis.draw(self, renderer, *args, **kwargs)
   1385 renderer.open_group(__name__, gid=self.get_gid())
   1387 ticks_to_draw = self._update_ticks()
-> 1388 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
   1390 for tick in ticks_to_draw:
   1391     tick.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in <listcomp>(.0)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

---------------------------------------------------------------------------
PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2164, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2161     # we do this instead of `self.figure.draw_without_rendering`
   2162     # so that we can inject the orientation
   2163     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2164         self.figure.draw(renderer)
   2165 if bbox_inches:
   2166     if bbox_inches == "tight":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axes/_base.py:3070, in _AxesBase.draw(self, renderer)
   3067 if artists_rasterized:
   3068     _draw_rasterized(self.figure, artists_rasterized, renderer)
-> 3070 mimage._draw_list_compositing_images(
   3071     renderer, self, artists, self.figure.suppressComposite)
   3073 renderer.close_group('axes')
   3074 self.stale = False

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1388, in Axis.draw(self, renderer, *args, **kwargs)
   1385 renderer.open_group(__name__, gid=self.get_gid())
   1387 ticks_to_draw = self._update_ticks()
-> 1388 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
   1390 for tick in ticks_to_draw:
   1391     tick.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in <listcomp>(.0)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

<Figure size 1280x960 with 1 Axes>

---

Should the company buy more material?

print(f"xStar =  {xStar}")
print(f"zStar = ${int(zStar):,.2f} = wStar")
print(f"yStar =  {yStar}")

xStar =  (400, 300)
zStar = $10,200.00 = wStar
yStar =  (35, 5, 0, 0)

ROI1=(yStar[0]-p1)/p1
ROI2=(yStar[1]-p2)/p2

db2   =g2.subs([(x1,900),(x2,50)])
dzStar=(yStar[1]-p2)*db2

r2cost=p2*db2

display(
  ROI1,
  ROI2,
  db2,
  dzStar,
  zStar+dzStar,
  r2cost,
)

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 0.25\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 0.25\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 1500\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 1500\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 11700\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 6000\]

Show code cell source Hide code cell source

def pivot (iStar,jStar,tab):
  nRows =tab.shape[0]-1
  nCols =tab.shape[1]-1
  newTab=tab[:,:]

  newTab[0,jStar]    =tab[iStar,nCols]
  newTab[iStar,nCols]=tab[0,jStar]
  newTab[iStar,0]    =-tab[nRows,jStar]
  newTab[nRows,jStar]=-tab[iStar,0]
  
  for i in range(1,nRows):
    for j in range(1,nCols):
      if   i==iStar and j==jStar:
        newTab[i,j]=1/tab[iStar,jStar]
      elif i==iStar and j!=jStar:
        newTab[i,j]=-tab[i,j]/tab[iStar,jStar]
      elif i!=iStar and j==jStar:
        newTab[i,j]= tab[i,j]/tab[iStar,jStar]
      elif i!=iStar and j!=jStar:
        newTab[i,j]= tab[i,j]-tab[iStar,j]*tab[i,jStar]/tab[iStar,jStar]
  return newTab

p1 =28
p2 = 4

rA = Matrix([
  [ 'c', 'x1',  'x2',       1, 'r'],
  ['y1',   -1,    -2,  b1+db1,'s1'],
  ['y2',   -5,    -4,  b2+db2,'s2'],
  ['y3',   -1,     0,  b3+db3,'s3'],
  ['y4',    0,    -1,  b4+db4,'s4'],
  [  -1,  -60,   -90,d+r2cost,'-z'],
  [ 'c','-v1', '-v2',     'w', 'r'],
])
rB = pivot(2,1,rA)
rC = pivot(1,2,rB)
rD = pivot(3,1,rC)

cA = Matrix([
  [ 'c',  'y1',  'y2',  'y3',  'y4',          1, 'r'],
  ['x1',     1,     5,     1,     0,        -60,'v1'],
  ['x2',     2,     4,     0,     1,        -90,'v2'],
  [  -1,b1+db1,b2+db2,b3+db3,b4+db4,-(d+r2cost), 'w'],
  [ 'c', '-s1', '-s2', '-s3', '-s4',       '-z', 'r'],
])
cB = pivot(2,1,cA)
cC = pivot(1,2,cB)
cD = pivot(1,3,cC)

display(
  'ROW',
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,rA = {latex(rA)}\,\,\,\,\,x_1=x_2=0'),
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,rB = {latex(rB)}\,\,\,\,\,x_2=s_2=0'),
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,rC = {latex(rC)}\,\,\,\,\,s_1=s_2=0'),
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,rD = {latex(rD)}\,\,\,\,\,s_1=s_3=0'),
  'COLUMN',
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,cA = {latex(cA)}\,\,\,\,\,x_1=x_2=0'),
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,cB = {latex(cB)}\,\,\,\,\,x_1=s_1=0'),
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,cC = {latex(cC)}\,\,\,\,\,s_1=s_2=0'),
  Math(fr'db = ({db1},{db2},{db3},{db4})\,\,\,cD = {latex(cD)}\,\,\,\,\,s_1=s_3=0'),
)

'ROW'

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,rA = \left[\begin{matrix}c & x_{1} & x_{2} & 1 & r\\y_{1} & -1 & -2 & 1000 & s_{1}\\y_{2} & -5 & -4 & 4700 & s_{2}\\y_{3} & -1 & 0 & 900 & s_{3}\\y_{4} & 0 & -1 & 700 & s_{4}\\-1 & -60 & -90 & 46800 & - z\\c & - v_{1} & - v_{2} & w & r\end{matrix}\right]\,\,\,\,\,x_1=x_2=0\end{split}\]

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,rB = \left[\begin{matrix}c & s_{2} & x_{2} & 1 & r\\y_{1} & \frac{1}{5} & - \frac{6}{5} & 60 & s_{1}\\v_{1} & - \frac{1}{5} & - \frac{4}{5} & 940 & x_{1}\\y_{3} & \frac{1}{5} & \frac{4}{5} & -40 & s_{3}\\y_{4} & 0 & -1 & 700 & s_{4}\\-1 & 12 & -42 & -9600 & - z\\c & - y_{2} & - v_{2} & w & r\end{matrix}\right]\,\,\,\,\,x_2=s_2=0\end{split}\]

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,rC = \left[\begin{matrix}c & s_{2} & s_{1} & 1 & r\\v_{2} & \frac{1}{6} & - \frac{5}{6} & 50 & x_{2}\\v_{1} & - \frac{1}{3} & \frac{2}{3} & 900 & x_{1}\\y_{3} & \frac{1}{3} & - \frac{2}{3} & 0 & s_{3}\\y_{4} & - \frac{1}{6} & \frac{5}{6} & 650 & s_{4}\\-1 & 5 & 35 & -11700 & - z\\c & - y_{2} & - y_{1} & w & r\end{matrix}\right]\,\,\,\,\,s_1=s_2=0\end{split}\]

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,rD = \left[\begin{matrix}c & s_{3} & s_{1} & 1 & r\\v_{2} & \frac{1}{2} & - \frac{1}{2} & 50 & x_{2}\\v_{1} & -1 & 0 & 900 & x_{1}\\y_{2} & 3 & 2 & 0 & s_{2}\\y_{4} & - \frac{1}{2} & \frac{1}{2} & 650 & s_{4}\\-1 & 15 & 45 & -11700 & - z\\c & - y_{3} & - y_{1} & w & r\end{matrix}\right]\,\,\,\,\,s_1=s_3=0\end{split}\]

'COLUMN'

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,cA = \left[\begin{matrix}c & y_{1} & y_{2} & y_{3} & y_{4} & 1 & r\\x_{1} & 1 & 5 & 1 & 0 & -60 & v_{1}\\x_{2} & 2 & 4 & 0 & 1 & -90 & v_{2}\\-1 & 1000 & 4700 & 900 & 700 & -46800 & w\\c & - s_{1} & - s_{2} & - s_{3} & - s_{4} & - z & r\end{matrix}\right]\,\,\,\,\,x_1=x_2=0\end{split}\]

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,cB = \left[\begin{matrix}c & v_{2} & y_{2} & y_{3} & y_{4} & 1 & r\\x_{1} & \frac{1}{2} & 3 & 1 & - \frac{1}{2} & -15 & v_{1}\\s_{1} & \frac{1}{2} & -2 & 0 & - \frac{1}{2} & 45 & y_{1}\\-1 & 500 & 2700 & 900 & 200 & -1800 & w\\c & - x_{2} & - s_{2} & - s_{3} & - s_{4} & - z & r\end{matrix}\right]\,\,\,\,\,x_1=s_1=0\end{split}\]

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,cC = \left[\begin{matrix}c & v_{2} & v_{1} & y_{3} & y_{4} & 1 & r\\s_{2} & - \frac{1}{6} & \frac{1}{3} & - \frac{1}{3} & \frac{1}{6} & 5 & y_{2}\\s_{1} & \frac{5}{6} & - \frac{2}{3} & \frac{2}{3} & - \frac{5}{6} & 35 & y_{1}\\-1 & 50 & 900 & 0 & 650 & 11700 & w\\c & - x_{2} & - x_{1} & - s_{3} & - s_{4} & - z & r\end{matrix}\right]\,\,\,\,\,s_1=s_2=0\end{split}\]

\[\begin{split}\displaystyle db = (0,1500,0,0)\,\,\,cD = \left[\begin{matrix}c & v_{2} & v_{1} & y_{2} & y_{4} & 1 & r\\s_{3} & - \frac{1}{2} & 1 & -3 & \frac{1}{2} & 15 & y_{3}\\s_{1} & \frac{1}{2} & 0 & -2 & - \frac{1}{2} & 45 & y_{1}\\-1 & 50 & 900 & 0 & 650 & 11700 & w\\c & - x_{2} & - x_{1} & - s_{2} & - s_{4} & - z & r\end{matrix}\right]\,\,\,\,\,s_1=s_3=0\end{split}\]

xStar1  = (900,50)
zStar1  = z.subs([(x1,xStar1[0]),(x2,xStar1[1])])
ycStar1 = (35,5, 0,0)
ydStar1 = (45,0,15,0)

print(f"xStar =  {xStar1}")
print(f"zStar = ${int(zStar1):,.2f} = wStar")
print(f"yStar =  {ycStar1}")
print(f"yStar =  {ydStar1}")

xStar =  (900, 50)
zStar = $17,700.00 = wStar
yStar =  (35, 5, 0, 0)
yStar =  (45, 0, 15, 0)

Show code cell source Hide code cell source

s =1000
x =np.linspace(0,s,10001)

# LINES
y1=-(1/2)*x+500
y2=-(5/4)*x+800
#y3
y4= (  0)*x+700

fig=plt.figure(dpi=300,figsize=(12,16));
ax =plt.subplot(131);
ax.set_aspect(1);

# LINES
ax.plot   (x,y1,label='g1=b1',linewidth=0.5,color='blue');
ax.plot   (x,y2,label='g2=b2',linewidth=0.5,color='yellow');
ax.axvline( 900,label='g3=b3',linewidth=0.5,color='green');
ax.plot   (x,y4,label='g4=b4',linewidth=0.5,color='red');

# delz
ax.arrow(200,200,*unitVector(  delz)*75,color='black', width=0.01,head_width=10,length_includes_head=True);
# FEASIBLE SIDES <=
ax.arrow(200,200,*unitVector(-delg1)*75,color='blue',  width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg2)*75,color='yellow',width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg3)*75,color='green', width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg4)*75,color='red',   width=0.01,head_width=10,length_includes_head=True);

# DIRECTIONS
ax.arrow(  0,500,*udg1*75,width=5,head_width=20,length_includes_head=True,color='blue');
ax.arrow(640,  0,*udg2*75,width=5,head_width=20,length_includes_head=True,color='yellow');
ax.arrow(900,  0,*udg3*75,width=5,head_width=20,length_includes_head=True,color='green');
ax.arrow(  0,700,*udg4*75,width=5,head_width=20,length_includes_head=True,color='red');

fx,fy=np.meshgrid(x,x)
plt.imshow(
  (
      (fy<=-(1/2)*fx+500)
    & (fy<=-(5/4)*fx+800)
    & (fy<= (  0)*fx+700)
  ).astype(int),
  extent=(fx.min(),fx.max(),fy.min(),fy.max()),
  origin='lower',
  cmap  ='Greys',
  alpha =0.3,
);

ax.set_xlim(0,s);
ax.set_ylim(0,s);
#ax.legend();

# xStar
ax.scatter(400,300,s=1e2,color='purple');

xStar=(
  r'\begin{eqnarray*}'
  r'x^*&=&(400,300)'
  r'\\'
  r'z^*&=&10200=w^*'
  r'\\'
  r'y^*&=&(35,5,0,0)'
  r'\end{eqnarray*}'
)
ax.text(400,600,xStar,fontsize=5);

# SIMPLEX
dx,dy=20,20
ax.annotate( '$A$',(  0+dx,  0+dy));
ax.annotate('$rB$',(640+dx,  0+dy));
ax.annotate('$cB$',(  0+dx,500+dy));
ax.annotate( '$C$',(400+dx,300+dy));

##########

ax2 =plt.subplot(132);
ax2.set_aspect(1);

# LINES
ax2.plot   (x,y1,label='g1=b1',linewidth=0.5,color='blue');
ax2.plot   (x,y2,label='g2=b2',linewidth=0.5,color='yellow',linestyle='--');
ax2.plot   (x,-(5/4)*(x-900)+50,label='g2=b2',linewidth=0.5,color='yellow');
ax2.axvline( 900,label='g3=b3',linewidth=0.5,color='green');
ax2.plot   (x,y4,label='g4=b4',linewidth=0.5,color='red');

# delz
ax2.arrow(200,200,*unitVector(  delz)*75,color='black', width=0.01,head_width=10,length_includes_head=True);
# FEASIBLE SIDES <=
ax2.arrow(200,200,*unitVector(-delg1)*75,color='blue',  width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg2)*75,color='yellow',width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg3)*75,color='green', width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg4)*75,color='red',   width=0.01,head_width=10,length_includes_head=True);

# DIRECTIONS
ax2.arrow(  0,500,*udg1*75,width=5,head_width=20,length_includes_head=True,color='blue');
ax2.arrow(640,  0,*udg2*75,width=5,head_width=20,length_includes_head=True,color='yellow');
ax2.arrow(900,  0,*udg3*75,width=5,head_width=20,length_includes_head=True,color='green');
ax2.arrow(  0,700,*udg4*75,width=5,head_width=20,length_includes_head=True,color='red');

fx,fy=np.meshgrid(x,x)
plt.imshow(
  (
      (fy<=-(1/2)* fx+500)
    & (fy<=-(5/4)*(fx-900)+50)
    & (fx<=900)
    & (fy<= (  0)* fx+700)
  ).astype(int),
  extent=(fx.min(),fx.max(),fy.min(),fy.max()),
  origin='lower',
  cmap  ='Greys',
  alpha =0.3,
);

ax2.set_xlim(0,s);
ax2.set_ylim(0,s);
#ax.legend();

# xStar
ax2.scatter(900, 50,s=1e2,color='purple');

xStar=(
  r'\begin{eqnarray*}'
  r'x^*&=&(900, 50)'
  r'\\'
  r'z^*&=&11700=w^*'
  r'\\'
  r'yc^*&=&(35,5,0,0)'
    r'\\'
  r'yd^*&=&(45,0,15,0)'
  r'\end{eqnarray*}'
)
ax2.text(400,600,xStar,fontsize=5);

# SIMPLEX
dx,dy=20,20
ax2.annotate( '$A$',(  0+dx,  0+dy));
ax2.annotate('$rB$',(640+dx,  0+dy));
ax2.annotate('$cB$',(  0+dx,500+dy));
ax2.annotate( '$C$',(400+dx,300+dy));

Error in callback <function _draw_all_if_interactive at 0x136de8e00> (for post_execute), with arguments args (),kwargs {}:

---------------------------------------------------------------------------
PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/pyplot.py:197, in _draw_all_if_interactive()
    195 def _draw_all_if_interactive() -> None:
    196     if matplotlib.is_interactive():
--> 197         draw_all()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/_pylab_helpers.py:132, in Gcf.draw_all(cls, force)
    130 for manager in cls.get_all_fig_managers():
    131     if force or manager.canvas.figure.stale:
--> 132         manager.canvas.draw_idle()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:1893, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1891 if not self._is_idle_drawing:
   1892     with self._idle_draw_cntx():
-> 1893         self.draw(*args, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axes/_base.py:3070, in _AxesBase.draw(self, renderer)
   3067 if artists_rasterized:
   3068     _draw_rasterized(self.figure, artists_rasterized, renderer)
-> 3070 mimage._draw_list_compositing_images(
   3071     renderer, self, artists, self.figure.suppressComposite)
   3073 renderer.close_group('axes')
   3074 self.stale = False

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1388, in Axis.draw(self, renderer, *args, **kwargs)
   1385 renderer.open_group(__name__, gid=self.get_gid())
   1387 ticks_to_draw = self._update_ticks()
-> 1388 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
   1390 for tick in ticks_to_draw:
   1391     tick.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in <listcomp>(.0)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

---------------------------------------------------------------------------
PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2164, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2161     # we do this instead of `self.figure.draw_without_rendering`
   2162     # so that we can inject the orientation
   2163     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2164         self.figure.draw(renderer)
   2165 if bbox_inches:
   2166     if bbox_inches == "tight":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axes/_base.py:3070, in _AxesBase.draw(self, renderer)
   3067 if artists_rasterized:
   3068     _draw_rasterized(self.figure, artists_rasterized, renderer)
-> 3070 mimage._draw_list_compositing_images(
   3071     renderer, self, artists, self.figure.suppressComposite)
   3073 renderer.close_group('axes')
   3074 self.stale = False

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1388, in Axis.draw(self, renderer, *args, **kwargs)
   1385 renderer.open_group(__name__, gid=self.get_gid())
   1387 ticks_to_draw = self._update_ticks()
-> 1388 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
   1390 for tick in ticks_to_draw:
   1391     tick.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in <listcomp>(.0)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

<Figure size 3600x4800 with 2 Axes>

---

Show code cell source Hide code cell source

s =1000
x =np.linspace(0,s,10001)

# LINES
y1=-(1/2)*x+500
y2=-(5/4)*x+800
#y3
y4= (  0)*x+700

fig=plt.figure(figsize=(16,16));

##########

ax =plt.subplot(221);
ax.set_aspect(1);

# LINES
ax.plot   (x,y1,label='g1=b1',linewidth=0.5,color='blue');
ax.plot   (x,y2,label='g2=b2',linewidth=0.5,color='yellow');
ax.axvline( 900,label='g3=b3',linewidth=0.5,color='green');
ax.plot   (x,y4,label='g4=b4',linewidth=0.5,color='red');

# delz
ax.arrow(200,200,*unitVector(  delz)*75,color='black', width=0.01,head_width=10,length_includes_head=True);
# FEASIBLE SIDES <=
ax.arrow(200,200,*unitVector(-delg1)*75,color='blue',  width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg2)*75,color='yellow',width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg3)*75,color='green', width=0.01,head_width=10,length_includes_head=True);
ax.arrow(200,200,*unitVector(-delg4)*75,color='red',   width=0.01,head_width=10,length_includes_head=True);

# DIRECTIONS
ax.arrow(  0,500,*udg1*75,width=5,head_width=20,length_includes_head=True,color='blue');
ax.arrow(640,  0,*udg2*75,width=5,head_width=20,length_includes_head=True,color='yellow');
ax.arrow(900,  0,*udg3*75,width=5,head_width=20,length_includes_head=True,color='green');
ax.arrow(  0,700,*udg4*75,width=5,head_width=20,length_includes_head=True,color='red');

fx,fy=np.meshgrid(x,x)
plt.imshow(
  (
      (fy<=-(1/2)*fx+500)
    & (fy<=-(5/4)*fx+800)
    & (fy<= (  0)*fx+700)
  ).astype(int),
  extent=(fx.min(),fx.max(),fy.min(),fy.max()),
  origin='lower',
  cmap  ='Greys',
  alpha =0.3,
);

ax.set_xlim(0,s);
ax.set_ylim(0,s);
#ax.legend();

# xStar
ax.scatter(400,300,s=1e2,color='purple');

xStar=(
  r'\begin{eqnarray*}'
  r'x^*&=&(400,300)'
  r'\\'
  r'z^*&=&10200=w^*'
  r'\\'
  r'y^*&=&(35,5,0,0)'
  r'\end{eqnarray*}'
)
ax.text(400,600,xStar,fontsize=5);

# SIMPLEX
dx,dy=20,20
ax.annotate( '$A$',(  0+dx,  0+dy));
ax.annotate('$rB$',(640+dx,  0+dy));
ax.annotate('$cB$',(  0+dx,500+dy));
ax.annotate( '$C$',(400+dx,300+dy));

##########

ax2 =plt.subplot(222);
ax2.set_aspect(1);

# LINES
ax2.plot   (x,y1,label='g1=b1',linewidth=0.5,color='blue');
ax2.plot   (x,y2,label='g2=b2',linewidth=0.5,color='yellow',linestyle='--');
ax2.plot   (x,-(5/4)*(x-900)+50,label='g2=b2',linewidth=0.5,color='yellow');
ax2.axvline( 900,label='g3=b3',linewidth=0.5,color='green');
ax2.plot   (x,y4,label='g4=b4',linewidth=0.5,color='red');

# delz
ax2.arrow(200,200,*unitVector(  delz)*75,color='black', width=0.01,head_width=10,length_includes_head=True);
# FEASIBLE SIDES <=
ax2.arrow(200,200,*unitVector(-delg1)*75,color='blue',  width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg2)*75,color='yellow',width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg3)*75,color='green', width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg4)*75,color='red',   width=0.01,head_width=10,length_includes_head=True);

# DIRECTIONS
ax2.arrow(  0,500,*udg1*75,width=5,head_width=20,length_includes_head=True,color='blue');
ax2.arrow(640,  0,*udg2*75,width=5,head_width=20,length_includes_head=True,color='yellow');
ax2.arrow(900,  0,*udg3*75,width=5,head_width=20,length_includes_head=True,color='green');
ax2.arrow(  0,700,*udg4*75,width=5,head_width=20,length_includes_head=True,color='red');

fx,fy=np.meshgrid(x,x)
plt.imshow(
  (
      (fy<=-(1/2)* fx+500)
    & (fy<=-(5/4)*(fx-900)+50)
    & (fx<=900)
    & (fy<= (  0)* fx+700)
  ).astype(int),
  extent=(fx.min(),fx.max(),fy.min(),fy.max()),
  origin='lower',
  cmap  ='Greys',
  alpha =0.3,
);

ax2.set_xlim(0,s);
ax2.set_ylim(0,s);
#ax.legend();

# xStar
ax2.scatter(900, 50,s=1e2,color='purple');

xStar=(
  r'\begin{eqnarray*}'
  r'x^*&=&(900, 50)'
  r'\\'
  r'z^*&=&11700=w^*'
  r'\\'
  r'yc^*&=&(35,5,0,0)'
  r'\\'
  r'yd^*&=&(45,0,15,0)'
  r'\end{eqnarray*}'
)
ax2.text(400,600,xStar,fontsize=5);

# SIMPLEX
dx,dy=20,20
ax2.annotate( '$A$',(  0+dx,  0+dy));
ax2.annotate('$rB$',(640+dx,  0+dy));
ax2.annotate('$cB$',(  0+dx,500+dy));
ax2.annotate( '$C$',(400+dx,300+dy));

##########

ax2 =plt.subplot(223);
ax2.set_aspect(1);

# LINES
ax2.plot   (x,y1,label='g1=b1',linewidth=0.8,color='blue',linestyle=(0,(5,10)));
ax2.plot   (x,-(1/2)*(x-380)+700,label='g1=b1',linewidth=0.8,color='blue');
ax2.plot   (x,y2,label='g2=b2',linewidth=0.8,color='yellow',linestyle=(0,(5,10)));
ax2.plot   (x,-(5/4)*(x-900)+50,label='g2=b2',linewidth=0.8,color='yellow');
ax2.axvline( 900,label='g3=b3',linewidth=0.5,color='green');
ax2.plot   (x,y4,label='g4=b4',linewidth=0.5,color='red');

# delz
ax2.arrow(200,200,*unitVector(  delz)*75,color='black', width=0.01,head_width=10,length_includes_head=True);
# FEASIBLE SIDES <=
ax2.arrow(200,200,*unitVector(-delg1)*75,color='blue',  width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg2)*75,color='yellow',width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg3)*75,color='green', width=0.01,head_width=10,length_includes_head=True);
ax2.arrow(200,200,*unitVector(-delg4)*75,color='red',   width=0.01,head_width=10,length_includes_head=True);

# DIRECTIONS
ax2.arrow(  0,500,*udg1*75,width=5,head_width=20,length_includes_head=True,color='blue');
ax2.arrow(640,  0,*udg2*75,width=5,head_width=20,length_includes_head=True,color='yellow');
ax2.arrow(900,  0,*udg3*75,width=5,head_width=20,length_includes_head=True,color='green');
ax2.arrow(  0,700,*udg4*75,width=5,head_width=20,length_includes_head=True,color='red');

fx,fy=np.meshgrid(x,x)
plt.imshow(
  (
      (fy<=-(1/2)*(fx-380)+700)
    & (fy<=-(5/4)*(fx-900)+50)
    & (fx<=900)
    & (fy<= (  0)* fx+700)
  ).astype(int),
  extent=(fx.min(),fx.max(),fy.min(),fy.max()),
  origin='lower',
  cmap  ='Greys',
  alpha =0.3,
);

ax2.set_xlim(0,s);
ax2.set_ylim(0,s);
#ax.legend();

# xStar
ax2.scatter(380,700,s=1e2,color='purple');

xStar=(
  r'\begin{eqnarray*}'
  r'x^*&=&(900, 50)'
  r'\\'
  r'z^*&=&11700=w^*'
  r'\\'
  r'yc^*&=&(35,5,0,0)'
  r'\\'
  r'yd^*&=&(45,0,15,0)'
  r'\end{eqnarray*}'
)
ax2.text(400,600,xStar,fontsize=5);

# SIMPLEX
dx,dy=20,20
ax2.annotate( '$A$',(  0+dx,  0+dy));
ax2.annotate('$rB$',(640+dx,  0+dy));
ax2.annotate('$cB$',(  0+dx,500+dy));
ax2.annotate( '$C$',(400+dx,300+dy));

Error in callback <function _draw_all_if_interactive at 0x136de8e00> (for post_execute), with arguments args (),kwargs {}:

---------------------------------------------------------------------------
PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/pyplot.py:197, in _draw_all_if_interactive()
    195 def _draw_all_if_interactive() -> None:
    196     if matplotlib.is_interactive():
--> 197         draw_all()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/_pylab_helpers.py:132, in Gcf.draw_all(cls, force)
    130 for manager in cls.get_all_fig_managers():
    131     if force or manager.canvas.figure.stale:
--> 132         manager.canvas.draw_idle()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:1893, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1891 if not self._is_idle_drawing:
   1892     with self._idle_draw_cntx():
-> 1893         self.draw(*args, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axes/_base.py:3070, in _AxesBase.draw(self, renderer)
   3067 if artists_rasterized:
   3068     _draw_rasterized(self.figure, artists_rasterized, renderer)
-> 3070 mimage._draw_list_compositing_images(
   3071     renderer, self, artists, self.figure.suppressComposite)
   3073 renderer.close_group('axes')
   3074 self.stale = False

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1388, in Axis.draw(self, renderer, *args, **kwargs)
   1385 renderer.open_group(__name__, gid=self.get_gid())
   1387 ticks_to_draw = self._update_ticks()
-> 1388 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
   1390 for tick in ticks_to_draw:
   1391     tick.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in <listcomp>(.0)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

---------------------------------------------------------------------------
PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2164, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2161     # we do this instead of `self.figure.draw_without_rendering`
   2162     # so that we can inject the orientation
   2163     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2164         self.figure.draw(renderer)
   2165 if bbox_inches:
   2166     if bbox_inches == "tight":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axes/_base.py:3070, in _AxesBase.draw(self, renderer)
   3067 if artists_rasterized:
   3068     _draw_rasterized(self.figure, artists_rasterized, renderer)
-> 3070 mimage._draw_list_compositing_images(
   3071     renderer, self, artists, self.figure.suppressComposite)
   3073 renderer.close_group('axes')
   3074 self.stale = False

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1388, in Axis.draw(self, renderer, *args, **kwargs)
   1385 renderer.open_group(__name__, gid=self.get_gid())
   1387 ticks_to_draw = self._update_ticks()
-> 1388 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
   1390 for tick in ticks_to_draw:
   1391     tick.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/axis.py:1315, in <listcomp>(.0)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

<Figure size 1600x1600 with 3 Axes>

y2p=-(5/4)*(x1-900)+50
g2p= (5/4)*x1+x2-1175

g1max=-(1/2)*(x1-380)+700

display(
y2p,
solve([g2p,g4])
)

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 1175.0 - 1.25 x_{1}\]

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:343, in BaseFormatter.__call__(self, obj)
    341     pass
    342 else:
--> 343     return printer(obj)
    344 # Finally look for special method names
    345 method = get_real_method(obj, self.print_method)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle \left\{ x_{1} : 380.0, \ x_{2} : 700.0\right\}\]

g1max

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:178, in _init_ipython_printing.<locals>._print_latex_png(o)
    177 try:
--> 178     return _preview_wrapper(s)
    179 except RuntimeError as e:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:89, in _init_ipython_printing.<locals>._preview_wrapper(o)
     88 try:
---> 89     preview(o, output='png', viewer='BytesIO', euler=euler,
     90             outputbuffer=exprbuffer, extra_preamble=extra_preamble,
     91             dvioptions=dvioptions, fontsize=fontsize)
     92 except Exception as e:
     93     # IPython swallows exceptions

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/printing/preview.py:308, in preview(expr, output, viewer, euler, packages, filename, outputbuffer, preamble, dvioptions, outputTexFile, extra_preamble, fontsize, **latex_settings)
    307 if not shutil.which('latex'):
--> 308     raise RuntimeError("latex program is not installed")
    310 try:

RuntimeError: latex program is not installed

During handling of the above exception, another exception occurred:

PermissionError                           Traceback (most recent call last)
File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/core/formatters.py:347, in BaseFormatter.__call__(self, obj)
    345     method = get_real_method(obj, self.print_method)
    346     if method is not None:
--> 347         return method()
    348     return None
    349 else:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:184, in _init_ipython_printing.<locals>._print_latex_png(o)
    182 if latex_mode != 'inline':
    183     s = latex(o, mode='inline', **settings)
--> 184 return _matplotlib_wrapper(s)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/sympy/interactive/printing.py:118, in _init_ipython_printing.<locals>._matplotlib_wrapper(o)
    116 try:
    117     try:
--> 118         return latex_to_png(o, color=forecolor, scale=scale)
    119     except TypeError: #  Old IPython version without color and scale
    120         return latex_to_png(o)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:105, in latex_to_png(s, encode, backend, wrap, color, scale)
    103 else:
    104     raise ValueError('No such backend {0}'.format(backend))
--> 105 bin_data = f(s, wrap, color, scale)
    106 if encode and bin_data:
    107     bin_data = encodebytes(bin_data)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/IPython/lib/latextools.py:135, in latex_to_png_mpl(s, wrap, color, scale)
    133     fig.text(0, depth / height, s, fontproperties=prop, color=color)
    134     backend_agg.FigureCanvasAgg(fig)
--> 135     fig.savefig(buffer, dpi=dpi, format="png", transparent=True)
    136     return buffer.getvalue()
    137 except (ValueError, RuntimeError, ParseFatalException):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3390, in Figure.savefig(self, fname, transparent, **kwargs)
   3388     for ax in self.axes:
   3389         _recursively_make_axes_transparent(stack, ax)
-> 3390 self.canvas.print_figure(fname, **kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2193, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2189 try:
   2190     # _get_renderer may change the figure dpi (as vector formats
   2191     # force the figure dpi to 72), so we need to set it again here.
   2192     with cbook._setattr_cm(self.figure, dpi=dpi):
-> 2193         result = print_method(
   2194             filename,
   2195             facecolor=facecolor,
   2196             edgecolor=edgecolor,
   2197             orientation=orientation,
   2198             bbox_inches_restore=_bbox_inches_restore,
   2199             **kwargs)
   2200 finally:
   2201     if bbox_inches and restore_bbox:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:2043, in FigureCanvasBase._switch_canvas_and_return_print_method.<locals>.<lambda>(*args, **kwargs)
   2039     optional_kws = {  # Passed by print_figure for other renderers.
   2040         "dpi", "facecolor", "edgecolor", "orientation",
   2041         "bbox_inches_restore"}
   2042     skip = optional_kws - {*inspect.signature(meth).parameters}
-> 2043     print_method = functools.wraps(meth)(lambda *args, **kwargs: meth(
   2044         *args, **{k: v for k, v in kwargs.items() if k not in skip}))
   2045 else:  # Let third-parties do as they see fit.
   2046     print_method = meth

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:497, in FigureCanvasAgg.print_png(self, filename_or_obj, metadata, pil_kwargs)
    450 def print_png(self, filename_or_obj, *, metadata=None, pil_kwargs=None):
    451     """
    452     Write the figure to a PNG file.
    453 
   (...)
    495         *metadata*, including the default 'Software' key.
    496     """
--> 497     self._print_pil(filename_or_obj, "png", pil_kwargs, metadata)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:445, in FigureCanvasAgg._print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata)
    440 def _print_pil(self, filename_or_obj, fmt, pil_kwargs, metadata=None):
    441     """
    442     Draw the canvas, then save it using `.image.imsave` (to which
    443     *pil_kwargs* and *metadata* are forwarded).
    444     """
--> 445     FigureCanvasAgg.draw(self)
    446     mpl.image.imsave(
    447         filename_or_obj, self.buffer_rgba(), format=fmt, origin="upper",
    448         dpi=self.figure.dpi, metadata=metadata, pil_kwargs=pil_kwargs)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:748, in Text.draw(self, renderer)
    745 renderer.open_group('text', self.get_gid())
    747 with self._cm_set(text=self._get_wrapped_text()):
--> 748     bbox, info, descent = self._get_layout(renderer)
    749     trans = self.get_transform()
    751     # don't use self.get_position here, which refers to text
    752     # position in Text:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/texmanager.py:366, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
--> 366     page, = dvi
    367 # A total height (including the descent) needs to be returned.
    368 return page.width, page.height + page.descent, page.descent

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:296, in Dvi.__iter__(self)
    280 def __iter__(self):
    281     """
    282     Iterate through the pages of the file.
    283 
   (...)
    294         integers.
    295     """
--> 296     while self._read():
    297         yield self._output()

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:375, in Dvi._read(self)
    373 while True:
    374     byte = self.file.read(1)[0]
--> 375     self._dtable[byte](self, byte)
    376     name = self._dtable[byte].__name__
    377     if name == "_push":

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:227, in _dispatch.<locals>.decorate.<locals>.wrapper(self, byte)
    225 if state is not None and self.state != state:
    226     raise ValueError("state precondition failed")
--> 227 return method(self, *[f(self, byte-min) for f in get_args])

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:526, in Dvi._fnt_def(self, k, c, s, d, a, l)
    524 @_dispatch(min=243, max=246, args=('olen1', 'u4', 'u4', 'u4', 'u1', 'u1'))
    525 def _fnt_def(self, k, c, s, d, a, l):
--> 526     self._fnt_def_real(k, c, s, d, a, l)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:531, in Dvi._fnt_def_real(self, k, c, s, d, a, l)
    529 n = self.file.read(a + l)
    530 fontname = n[-l:].decode('ascii')
--> 531 tfm = _tfmfile(fontname)
    532 if c != 0 and tfm.checksum != 0 and c != tfm.checksum:
    533     raise ValueError('tfm checksum mismatch: %s' % n)

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1116, in _fontfile(cls, suffix, texname)
   1114 @lru_cache
   1115 def _fontfile(cls, suffix, texname):
-> 1116     return cls(find_tex_file(texname + suffix))

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1082, in find_tex_file(filename)
   1079     filename = filename.decode('utf-8', errors='replace')
   1081 try:
-> 1082     lk = _LuatexKpsewhich()
   1083 except FileNotFoundError:
   1084     lk = None  # Fallback to directly calling kpsewhich, as below.

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1037, in _LuatexKpsewhich.__new__(cls)
   1034 @lru_cache  # A singleton.
   1035 def __new__(cls):
   1036     self = object.__new__(cls)
-> 1037     self._proc = self._new_proc()
   1038     return self

File ~/anaconda3/envs/ml/lib/python3.11/site-packages/matplotlib/dviread.py:1041, in _LuatexKpsewhich._new_proc(self)
   1040 def _new_proc(self):
-> 1041     return subprocess.Popen(
   1042         ["luatex", "--luaonly",
   1043          str(cbook._get_data_path("kpsewhich.lua"))],
   1044         stdin=subprocess.PIPE, stdout=subprocess.PIPE)

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1022         if self.text_mode:
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.
   1037     for f in filter(None, (self.stdin, self.stdout, self.stderr)):

File ~/anaconda3/envs/ml/lib/python3.11/subprocess.py:1955, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1953     err_msg = os.strerror(errno_num)
   1954 if err_filename is not None:
-> 1955     raise child_exception_type(errno_num, err_msg, err_filename)
   1956 else:
   1957     raise child_exception_type(errno_num, err_msg)

PermissionError: [Errno 13] Permission denied: 'luatex'

\[\displaystyle 890.0 - 0.5 x_{1}\]