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3278 lines
119 KiB
3278 lines
119 KiB
5 months ago
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"""
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A Printer which converts an expression into its LaTeX equivalent.
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"""
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from __future__ import annotations
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from typing import Any, Callable, TYPE_CHECKING
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import itertools
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from sympy.core import Add, Float, Mod, Mul, Number, S, Symbol, Expr
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from sympy.core.alphabets import greeks
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from sympy.core.containers import Tuple
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from sympy.core.function import Function, AppliedUndef, Derivative
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from sympy.core.operations import AssocOp
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from sympy.core.power import Pow
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from sympy.core.sorting import default_sort_key
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from sympy.core.sympify import SympifyError
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from sympy.logic.boolalg import true, BooleanTrue, BooleanFalse
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from sympy.tensor.array import NDimArray
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# sympy.printing imports
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from sympy.printing.precedence import precedence_traditional
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from sympy.printing.printer import Printer, print_function
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from sympy.printing.conventions import split_super_sub, requires_partial
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from sympy.printing.precedence import precedence, PRECEDENCE
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from mpmath.libmp.libmpf import prec_to_dps, to_str as mlib_to_str
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from sympy.utilities.iterables import has_variety, sift
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import re
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if TYPE_CHECKING:
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from sympy.vector.basisdependent import BasisDependent
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# Hand-picked functions which can be used directly in both LaTeX and MathJax
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# Complete list at
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# https://docs.mathjax.org/en/latest/tex.html#supported-latex-commands
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# This variable only contains those functions which SymPy uses.
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accepted_latex_functions = ['arcsin', 'arccos', 'arctan', 'sin', 'cos', 'tan',
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'sinh', 'cosh', 'tanh', 'sqrt', 'ln', 'log', 'sec',
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'csc', 'cot', 'coth', 're', 'im', 'frac', 'root',
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'arg',
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]
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tex_greek_dictionary = {
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'Alpha': r'\mathrm{A}',
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'Beta': r'\mathrm{B}',
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'Gamma': r'\Gamma',
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'Delta': r'\Delta',
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'Epsilon': r'\mathrm{E}',
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'Zeta': r'\mathrm{Z}',
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'Eta': r'\mathrm{H}',
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'Theta': r'\Theta',
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'Iota': r'\mathrm{I}',
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'Kappa': r'\mathrm{K}',
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'Lambda': r'\Lambda',
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'Mu': r'\mathrm{M}',
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'Nu': r'\mathrm{N}',
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'Xi': r'\Xi',
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'omicron': 'o',
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'Omicron': r'\mathrm{O}',
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'Pi': r'\Pi',
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'Rho': r'\mathrm{P}',
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'Sigma': r'\Sigma',
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'Tau': r'\mathrm{T}',
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'Upsilon': r'\Upsilon',
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'Phi': r'\Phi',
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'Chi': r'\mathrm{X}',
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'Psi': r'\Psi',
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'Omega': r'\Omega',
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'lamda': r'\lambda',
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'Lamda': r'\Lambda',
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'khi': r'\chi',
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'Khi': r'\mathrm{X}',
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'varepsilon': r'\varepsilon',
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'varkappa': r'\varkappa',
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'varphi': r'\varphi',
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'varpi': r'\varpi',
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'varrho': r'\varrho',
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'varsigma': r'\varsigma',
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'vartheta': r'\vartheta',
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}
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other_symbols = {'aleph', 'beth', 'daleth', 'gimel', 'ell', 'eth', 'hbar',
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'hslash', 'mho', 'wp'}
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# Variable name modifiers
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modifier_dict: dict[str, Callable[[str], str]] = {
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# Accents
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'mathring': lambda s: r'\mathring{'+s+r'}',
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'ddddot': lambda s: r'\ddddot{'+s+r'}',
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'dddot': lambda s: r'\dddot{'+s+r'}',
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'ddot': lambda s: r'\ddot{'+s+r'}',
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'dot': lambda s: r'\dot{'+s+r'}',
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'check': lambda s: r'\check{'+s+r'}',
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'breve': lambda s: r'\breve{'+s+r'}',
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'acute': lambda s: r'\acute{'+s+r'}',
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'grave': lambda s: r'\grave{'+s+r'}',
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'tilde': lambda s: r'\tilde{'+s+r'}',
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'hat': lambda s: r'\hat{'+s+r'}',
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'bar': lambda s: r'\bar{'+s+r'}',
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'vec': lambda s: r'\vec{'+s+r'}',
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'prime': lambda s: "{"+s+"}'",
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'prm': lambda s: "{"+s+"}'",
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# Faces
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'bold': lambda s: r'\boldsymbol{'+s+r'}',
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'bm': lambda s: r'\boldsymbol{'+s+r'}',
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'cal': lambda s: r'\mathcal{'+s+r'}',
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'scr': lambda s: r'\mathscr{'+s+r'}',
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'frak': lambda s: r'\mathfrak{'+s+r'}',
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# Brackets
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'norm': lambda s: r'\left\|{'+s+r'}\right\|',
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'avg': lambda s: r'\left\langle{'+s+r'}\right\rangle',
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'abs': lambda s: r'\left|{'+s+r'}\right|',
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'mag': lambda s: r'\left|{'+s+r'}\right|',
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}
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greek_letters_set = frozenset(greeks)
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_between_two_numbers_p = (
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re.compile(r'[0-9][} ]*$'), # search
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re.compile(r'[0-9]'), # match
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)
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def latex_escape(s: str) -> str:
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"""
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Escape a string such that latex interprets it as plaintext.
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We cannot use verbatim easily with mathjax, so escaping is easier.
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Rules from https://tex.stackexchange.com/a/34586/41112.
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"""
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s = s.replace('\\', r'\textbackslash')
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for c in '&%$#_{}':
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s = s.replace(c, '\\' + c)
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s = s.replace('~', r'\textasciitilde')
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s = s.replace('^', r'\textasciicircum')
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return s
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class LatexPrinter(Printer):
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printmethod = "_latex"
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_default_settings: dict[str, Any] = {
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"full_prec": False,
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"fold_frac_powers": False,
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"fold_func_brackets": False,
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"fold_short_frac": None,
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"inv_trig_style": "abbreviated",
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"itex": False,
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"ln_notation": False,
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"long_frac_ratio": None,
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"mat_delim": "[",
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"mat_str": None,
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"mode": "plain",
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"mul_symbol": None,
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"order": None,
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"symbol_names": {},
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"root_notation": True,
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"mat_symbol_style": "plain",
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"imaginary_unit": "i",
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"gothic_re_im": False,
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"decimal_separator": "period",
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"perm_cyclic": True,
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"parenthesize_super": True,
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"min": None,
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"max": None,
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"diff_operator": "d",
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}
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def __init__(self, settings=None):
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Printer.__init__(self, settings)
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if 'mode' in self._settings:
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valid_modes = ['inline', 'plain', 'equation',
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'equation*']
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if self._settings['mode'] not in valid_modes:
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raise ValueError("'mode' must be one of 'inline', 'plain', "
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"'equation' or 'equation*'")
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if self._settings['fold_short_frac'] is None and \
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self._settings['mode'] == 'inline':
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self._settings['fold_short_frac'] = True
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mul_symbol_table = {
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None: r" ",
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"ldot": r" \,.\, ",
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"dot": r" \cdot ",
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"times": r" \times "
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}
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try:
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self._settings['mul_symbol_latex'] = \
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mul_symbol_table[self._settings['mul_symbol']]
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except KeyError:
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self._settings['mul_symbol_latex'] = \
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self._settings['mul_symbol']
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try:
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self._settings['mul_symbol_latex_numbers'] = \
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mul_symbol_table[self._settings['mul_symbol'] or 'dot']
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except KeyError:
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if (self._settings['mul_symbol'].strip() in
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['', ' ', '\\', '\\,', '\\:', '\\;', '\\quad']):
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self._settings['mul_symbol_latex_numbers'] = \
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mul_symbol_table['dot']
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else:
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self._settings['mul_symbol_latex_numbers'] = \
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self._settings['mul_symbol']
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self._delim_dict = {'(': ')', '[': ']'}
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imaginary_unit_table = {
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None: r"i",
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"i": r"i",
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"ri": r"\mathrm{i}",
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"ti": r"\text{i}",
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"j": r"j",
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"rj": r"\mathrm{j}",
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"tj": r"\text{j}",
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}
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imag_unit = self._settings['imaginary_unit']
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self._settings['imaginary_unit_latex'] = imaginary_unit_table.get(imag_unit, imag_unit)
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diff_operator_table = {
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None: r"d",
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"d": r"d",
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"rd": r"\mathrm{d}",
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"td": r"\text{d}",
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}
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diff_operator = self._settings['diff_operator']
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self._settings["diff_operator_latex"] = diff_operator_table.get(diff_operator, diff_operator)
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def _add_parens(self, s) -> str:
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return r"\left({}\right)".format(s)
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# TODO: merge this with the above, which requires a lot of test changes
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def _add_parens_lspace(self, s) -> str:
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return r"\left( {}\right)".format(s)
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def parenthesize(self, item, level, is_neg=False, strict=False) -> str:
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prec_val = precedence_traditional(item)
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if is_neg and strict:
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return self._add_parens(self._print(item))
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if (prec_val < level) or ((not strict) and prec_val <= level):
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return self._add_parens(self._print(item))
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else:
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return self._print(item)
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def parenthesize_super(self, s):
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"""
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Protect superscripts in s
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If the parenthesize_super option is set, protect with parentheses, else
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wrap in braces.
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"""
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if "^" in s:
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if self._settings['parenthesize_super']:
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return self._add_parens(s)
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else:
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return "{{{}}}".format(s)
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return s
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def doprint(self, expr) -> str:
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tex = Printer.doprint(self, expr)
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if self._settings['mode'] == 'plain':
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return tex
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elif self._settings['mode'] == 'inline':
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return r"$%s$" % tex
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elif self._settings['itex']:
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return r"$$%s$$" % tex
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else:
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env_str = self._settings['mode']
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return r"\begin{%s}%s\end{%s}" % (env_str, tex, env_str)
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def _needs_brackets(self, expr) -> bool:
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"""
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Returns True if the expression needs to be wrapped in brackets when
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printed, False otherwise. For example: a + b => True; a => False;
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10 => False; -10 => True.
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"""
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return not ((expr.is_Integer and expr.is_nonnegative)
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or (expr.is_Atom and (expr is not S.NegativeOne
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and expr.is_Rational is False)))
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def _needs_function_brackets(self, expr) -> bool:
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"""
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Returns True if the expression needs to be wrapped in brackets when
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passed as an argument to a function, False otherwise. This is a more
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liberal version of _needs_brackets, in that many expressions which need
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to be wrapped in brackets when added/subtracted/raised to a power do
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not need them when passed to a function. Such an example is a*b.
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"""
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if not self._needs_brackets(expr):
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return False
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else:
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# Muls of the form a*b*c... can be folded
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if expr.is_Mul and not self._mul_is_clean(expr):
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return True
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# Pows which don't need brackets can be folded
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||
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elif expr.is_Pow and not self._pow_is_clean(expr):
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return True
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# Add and Function always need brackets
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||
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elif expr.is_Add or expr.is_Function:
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return True
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else:
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return False
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def _needs_mul_brackets(self, expr, first=False, last=False) -> bool:
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"""
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Returns True if the expression needs to be wrapped in brackets when
|
||
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printed as part of a Mul, False otherwise. This is True for Add,
|
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but also for some container objects that would not need brackets
|
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when appearing last in a Mul, e.g. an Integral. ``last=True``
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||
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specifies that this expr is the last to appear in a Mul.
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``first=True`` specifies that this expr is the first to appear in
|
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a Mul.
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"""
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||
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from sympy.concrete.products import Product
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from sympy.concrete.summations import Sum
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||
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from sympy.integrals.integrals import Integral
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||
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if expr.is_Mul:
|
||
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if not first and expr.could_extract_minus_sign():
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||
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return True
|
||
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elif precedence_traditional(expr) < PRECEDENCE["Mul"]:
|
||
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return True
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||
|
|
elif expr.is_Relational:
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||
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return True
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||
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if expr.is_Piecewise:
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return True
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if any(expr.has(x) for x in (Mod,)):
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return True
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||
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if (not last and
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any(expr.has(x) for x in (Integral, Product, Sum))):
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||
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return True
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||
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return False
|
||
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def _needs_add_brackets(self, expr) -> bool:
|
||
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"""
|
||
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Returns True if the expression needs to be wrapped in brackets when
|
||
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printed as part of an Add, False otherwise. This is False for most
|
||
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|
things.
|
||
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"""
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||
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if expr.is_Relational:
|
||
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return True
|
||
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if any(expr.has(x) for x in (Mod,)):
|
||
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return True
|
||
|
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if expr.is_Add:
|
||
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return True
|
||
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return False
|
||
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|
||
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def _mul_is_clean(self, expr) -> bool:
|
||
|
|
for arg in expr.args:
|
||
|
|
if arg.is_Function:
|
||
|
|
return False
|
||
|
|
return True
|
||
|
|
|
||
|
|
def _pow_is_clean(self, expr) -> bool:
|
||
|
|
return not self._needs_brackets(expr.base)
|
||
|
|
|
||
|
|
def _do_exponent(self, expr: str, exp):
|
||
|
|
if exp is not None:
|
||
|
|
return r"\left(%s\right)^{%s}" % (expr, exp)
|
||
|
|
else:
|
||
|
|
return expr
|
||
|
|
|
||
|
|
def _print_Basic(self, expr):
|
||
|
|
name = self._deal_with_super_sub(expr.__class__.__name__)
|
||
|
|
if expr.args:
|
||
|
|
ls = [self._print(o) for o in expr.args]
|
||
|
|
s = r"\operatorname{{{}}}\left({}\right)"
|
||
|
|
return s.format(name, ", ".join(ls))
|
||
|
|
else:
|
||
|
|
return r"\text{{{}}}".format(name)
|
||
|
|
|
||
|
|
def _print_bool(self, e: bool | BooleanTrue | BooleanFalse):
|
||
|
|
return r"\text{%s}" % e
|
||
|
|
|
||
|
|
_print_BooleanTrue = _print_bool
|
||
|
|
_print_BooleanFalse = _print_bool
|
||
|
|
|
||
|
|
def _print_NoneType(self, e):
|
||
|
|
return r"\text{%s}" % e
|
||
|
|
|
||
|
|
def _print_Add(self, expr, order=None):
|
||
|
|
terms = self._as_ordered_terms(expr, order=order)
|
||
|
|
|
||
|
|
tex = ""
|
||
|
|
for i, term in enumerate(terms):
|
||
|
|
if i == 0:
|
||
|
|
pass
|
||
|
|
elif term.could_extract_minus_sign():
|
||
|
|
tex += " - "
|
||
|
|
term = -term
|
||
|
|
else:
|
||
|
|
tex += " + "
|
||
|
|
term_tex = self._print(term)
|
||
|
|
if self._needs_add_brackets(term):
|
||
|
|
term_tex = r"\left(%s\right)" % term_tex
|
||
|
|
tex += term_tex
|
||
|
|
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_Cycle(self, expr):
|
||
|
|
from sympy.combinatorics.permutations import Permutation
|
||
|
|
if expr.size == 0:
|
||
|
|
return r"\left( \right)"
|
||
|
|
expr = Permutation(expr)
|
||
|
|
expr_perm = expr.cyclic_form
|
||
|
|
siz = expr.size
|
||
|
|
if expr.array_form[-1] == siz - 1:
|
||
|
|
expr_perm = expr_perm + [[siz - 1]]
|
||
|
|
term_tex = ''
|
||
|
|
for i in expr_perm:
|
||
|
|
term_tex += str(i).replace(',', r"\;")
|
||
|
|
term_tex = term_tex.replace('[', r"\left( ")
|
||
|
|
term_tex = term_tex.replace(']', r"\right)")
|
||
|
|
return term_tex
|
||
|
|
|
||
|
|
def _print_Permutation(self, expr):
|
||
|
|
from sympy.combinatorics.permutations import Permutation
|
||
|
|
from sympy.utilities.exceptions import sympy_deprecation_warning
|
||
|
|
|
||
|
|
perm_cyclic = Permutation.print_cyclic
|
||
|
|
if perm_cyclic is not None:
|
||
|
|
sympy_deprecation_warning(
|
||
|
|
f"""
|
||
|
|
Setting Permutation.print_cyclic is deprecated. Instead use
|
||
|
|
init_printing(perm_cyclic={perm_cyclic}).
|
||
|
|
""",
|
||
|
|
deprecated_since_version="1.6",
|
||
|
|
active_deprecations_target="deprecated-permutation-print_cyclic",
|
||
|
|
stacklevel=8,
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
perm_cyclic = self._settings.get("perm_cyclic", True)
|
||
|
|
|
||
|
|
if perm_cyclic:
|
||
|
|
return self._print_Cycle(expr)
|
||
|
|
|
||
|
|
if expr.size == 0:
|
||
|
|
return r"\left( \right)"
|
||
|
|
|
||
|
|
lower = [self._print(arg) for arg in expr.array_form]
|
||
|
|
upper = [self._print(arg) for arg in range(len(lower))]
|
||
|
|
|
||
|
|
row1 = " & ".join(upper)
|
||
|
|
row2 = " & ".join(lower)
|
||
|
|
mat = r" \\ ".join((row1, row2))
|
||
|
|
return r"\begin{pmatrix} %s \end{pmatrix}" % mat
|
||
|
|
|
||
|
|
|
||
|
|
def _print_AppliedPermutation(self, expr):
|
||
|
|
perm, var = expr.args
|
||
|
|
return r"\sigma_{%s}(%s)" % (self._print(perm), self._print(var))
|
||
|
|
|
||
|
|
def _print_Float(self, expr):
|
||
|
|
# Based off of that in StrPrinter
|
||
|
|
dps = prec_to_dps(expr._prec)
|
||
|
|
strip = False if self._settings['full_prec'] else True
|
||
|
|
low = self._settings["min"] if "min" in self._settings else None
|
||
|
|
high = self._settings["max"] if "max" in self._settings else None
|
||
|
|
str_real = mlib_to_str(expr._mpf_, dps, strip_zeros=strip, min_fixed=low, max_fixed=high)
|
||
|
|
|
||
|
|
# Must always have a mul symbol (as 2.5 10^{20} just looks odd)
|
||
|
|
# thus we use the number separator
|
||
|
|
separator = self._settings['mul_symbol_latex_numbers']
|
||
|
|
|
||
|
|
if 'e' in str_real:
|
||
|
|
(mant, exp) = str_real.split('e')
|
||
|
|
|
||
|
|
if exp[0] == '+':
|
||
|
|
exp = exp[1:]
|
||
|
|
if self._settings['decimal_separator'] == 'comma':
|
||
|
|
mant = mant.replace('.','{,}')
|
||
|
|
|
||
|
|
return r"%s%s10^{%s}" % (mant, separator, exp)
|
||
|
|
elif str_real == "+inf":
|
||
|
|
return r"\infty"
|
||
|
|
elif str_real == "-inf":
|
||
|
|
return r"- \infty"
|
||
|
|
else:
|
||
|
|
if self._settings['decimal_separator'] == 'comma':
|
||
|
|
str_real = str_real.replace('.','{,}')
|
||
|
|
return str_real
|
||
|
|
|
||
|
|
def _print_Cross(self, expr):
|
||
|
|
vec1 = expr._expr1
|
||
|
|
vec2 = expr._expr2
|
||
|
|
return r"%s \times %s" % (self.parenthesize(vec1, PRECEDENCE['Mul']),
|
||
|
|
self.parenthesize(vec2, PRECEDENCE['Mul']))
|
||
|
|
|
||
|
|
def _print_Curl(self, expr):
|
||
|
|
vec = expr._expr
|
||
|
|
return r"\nabla\times %s" % self.parenthesize(vec, PRECEDENCE['Mul'])
|
||
|
|
|
||
|
|
def _print_Divergence(self, expr):
|
||
|
|
vec = expr._expr
|
||
|
|
return r"\nabla\cdot %s" % self.parenthesize(vec, PRECEDENCE['Mul'])
|
||
|
|
|
||
|
|
def _print_Dot(self, expr):
|
||
|
|
vec1 = expr._expr1
|
||
|
|
vec2 = expr._expr2
|
||
|
|
return r"%s \cdot %s" % (self.parenthesize(vec1, PRECEDENCE['Mul']),
|
||
|
|
self.parenthesize(vec2, PRECEDENCE['Mul']))
|
||
|
|
|
||
|
|
def _print_Gradient(self, expr):
|
||
|
|
func = expr._expr
|
||
|
|
return r"\nabla %s" % self.parenthesize(func, PRECEDENCE['Mul'])
|
||
|
|
|
||
|
|
def _print_Laplacian(self, expr):
|
||
|
|
func = expr._expr
|
||
|
|
return r"\Delta %s" % self.parenthesize(func, PRECEDENCE['Mul'])
|
||
|
|
|
||
|
|
def _print_Mul(self, expr: Expr):
|
||
|
|
from sympy.simplify import fraction
|
||
|
|
separator: str = self._settings['mul_symbol_latex']
|
||
|
|
numbersep: str = self._settings['mul_symbol_latex_numbers']
|
||
|
|
|
||
|
|
def convert(expr) -> str:
|
||
|
|
if not expr.is_Mul:
|
||
|
|
return str(self._print(expr))
|
||
|
|
else:
|
||
|
|
if self.order not in ('old', 'none'):
|
||
|
|
args = expr.as_ordered_factors()
|
||
|
|
else:
|
||
|
|
args = list(expr.args)
|
||
|
|
|
||
|
|
# If there are quantities or prefixes, append them at the back.
|
||
|
|
units, nonunits = sift(args, lambda x: (hasattr(x, "_scale_factor") or hasattr(x, "is_physical_constant")) or
|
||
|
|
(isinstance(x, Pow) and
|
||
|
|
hasattr(x.base, "is_physical_constant")), binary=True)
|
||
|
|
prefixes, units = sift(units, lambda x: hasattr(x, "_scale_factor"), binary=True)
|
||
|
|
return convert_args(nonunits + prefixes + units)
|
||
|
|
|
||
|
|
def convert_args(args) -> str:
|
||
|
|
_tex = last_term_tex = ""
|
||
|
|
|
||
|
|
for i, term in enumerate(args):
|
||
|
|
term_tex = self._print(term)
|
||
|
|
if not (hasattr(term, "_scale_factor") or hasattr(term, "is_physical_constant")):
|
||
|
|
if self._needs_mul_brackets(term, first=(i == 0),
|
||
|
|
last=(i == len(args) - 1)):
|
||
|
|
term_tex = r"\left(%s\right)" % term_tex
|
||
|
|
|
||
|
|
if _between_two_numbers_p[0].search(last_term_tex) and \
|
||
|
|
_between_two_numbers_p[1].match(str(term)):
|
||
|
|
# between two numbers
|
||
|
|
_tex += numbersep
|
||
|
|
elif _tex:
|
||
|
|
_tex += separator
|
||
|
|
elif _tex:
|
||
|
|
_tex += separator
|
||
|
|
|
||
|
|
_tex += term_tex
|
||
|
|
last_term_tex = term_tex
|
||
|
|
return _tex
|
||
|
|
|
||
|
|
# Check for unevaluated Mul. In this case we need to make sure the
|
||
|
|
# identities are visible, multiple Rational factors are not combined
|
||
|
|
# etc so we display in a straight-forward form that fully preserves all
|
||
|
|
# args and their order.
|
||
|
|
# XXX: _print_Pow calls this routine with instances of Pow...
|
||
|
|
if isinstance(expr, Mul):
|
||
|
|
args = expr.args
|
||
|
|
if args[0] is S.One or any(isinstance(arg, Number) for arg in args[1:]):
|
||
|
|
return convert_args(args)
|
||
|
|
|
||
|
|
include_parens = False
|
||
|
|
if expr.could_extract_minus_sign():
|
||
|
|
expr = -expr
|
||
|
|
tex = "- "
|
||
|
|
if expr.is_Add:
|
||
|
|
tex += "("
|
||
|
|
include_parens = True
|
||
|
|
else:
|
||
|
|
tex = ""
|
||
|
|
|
||
|
|
numer, denom = fraction(expr, exact=True)
|
||
|
|
|
||
|
|
if denom is S.One and Pow(1, -1, evaluate=False) not in expr.args:
|
||
|
|
# use the original expression here, since fraction() may have
|
||
|
|
# altered it when producing numer and denom
|
||
|
|
tex += convert(expr)
|
||
|
|
|
||
|
|
else:
|
||
|
|
snumer = convert(numer)
|
||
|
|
sdenom = convert(denom)
|
||
|
|
ldenom = len(sdenom.split())
|
||
|
|
ratio = self._settings['long_frac_ratio']
|
||
|
|
if self._settings['fold_short_frac'] and ldenom <= 2 and \
|
||
|
|
"^" not in sdenom:
|
||
|
|
# handle short fractions
|
||
|
|
if self._needs_mul_brackets(numer, last=False):
|
||
|
|
tex += r"\left(%s\right) / %s" % (snumer, sdenom)
|
||
|
|
else:
|
||
|
|
tex += r"%s / %s" % (snumer, sdenom)
|
||
|
|
elif ratio is not None and \
|
||
|
|
len(snumer.split()) > ratio*ldenom:
|
||
|
|
# handle long fractions
|
||
|
|
if self._needs_mul_brackets(numer, last=True):
|
||
|
|
tex += r"\frac{1}{%s}%s\left(%s\right)" \
|
||
|
|
% (sdenom, separator, snumer)
|
||
|
|
elif numer.is_Mul:
|
||
|
|
# split a long numerator
|
||
|
|
a = S.One
|
||
|
|
b = S.One
|
||
|
|
for x in numer.args:
|
||
|
|
if self._needs_mul_brackets(x, last=False) or \
|
||
|
|
len(convert(a*x).split()) > ratio*ldenom or \
|
||
|
|
(b.is_commutative is x.is_commutative is False):
|
||
|
|
b *= x
|
||
|
|
else:
|
||
|
|
a *= x
|
||
|
|
if self._needs_mul_brackets(b, last=True):
|
||
|
|
tex += r"\frac{%s}{%s}%s\left(%s\right)" \
|
||
|
|
% (convert(a), sdenom, separator, convert(b))
|
||
|
|
else:
|
||
|
|
tex += r"\frac{%s}{%s}%s%s" \
|
||
|
|
% (convert(a), sdenom, separator, convert(b))
|
||
|
|
else:
|
||
|
|
tex += r"\frac{1}{%s}%s%s" % (sdenom, separator, snumer)
|
||
|
|
else:
|
||
|
|
tex += r"\frac{%s}{%s}" % (snumer, sdenom)
|
||
|
|
|
||
|
|
if include_parens:
|
||
|
|
tex += ")"
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_AlgebraicNumber(self, expr):
|
||
|
|
if expr.is_aliased:
|
||
|
|
return self._print(expr.as_poly().as_expr())
|
||
|
|
else:
|
||
|
|
return self._print(expr.as_expr())
|
||
|
|
|
||
|
|
def _print_PrimeIdeal(self, expr):
|
||
|
|
p = self._print(expr.p)
|
||
|
|
if expr.is_inert:
|
||
|
|
return rf'\left({p}\right)'
|
||
|
|
alpha = self._print(expr.alpha.as_expr())
|
||
|
|
return rf'\left({p}, {alpha}\right)'
|
||
|
|
|
||
|
|
def _print_Pow(self, expr: Pow):
|
||
|
|
# Treat x**Rational(1,n) as special case
|
||
|
|
if expr.exp.is_Rational:
|
||
|
|
p: int = expr.exp.p # type: ignore
|
||
|
|
q: int = expr.exp.q # type: ignore
|
||
|
|
if abs(p) == 1 and q != 1 and self._settings['root_notation']:
|
||
|
|
base = self._print(expr.base)
|
||
|
|
if q == 2:
|
||
|
|
tex = r"\sqrt{%s}" % base
|
||
|
|
elif self._settings['itex']:
|
||
|
|
tex = r"\root{%d}{%s}" % (q, base)
|
||
|
|
else:
|
||
|
|
tex = r"\sqrt[%d]{%s}" % (q, base)
|
||
|
|
if expr.exp.is_negative:
|
||
|
|
return r"\frac{1}{%s}" % tex
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
elif self._settings['fold_frac_powers'] and q != 1:
|
||
|
|
base = self.parenthesize(expr.base, PRECEDENCE['Pow'])
|
||
|
|
# issue #12886: add parentheses for superscripts raised to powers
|
||
|
|
if expr.base.is_Symbol:
|
||
|
|
base = self.parenthesize_super(base)
|
||
|
|
if expr.base.is_Function:
|
||
|
|
return self._print(expr.base, exp="%s/%s" % (p, q))
|
||
|
|
return r"%s^{%s/%s}" % (base, p, q)
|
||
|
|
elif expr.exp.is_negative and expr.base.is_commutative:
|
||
|
|
# special case for 1^(-x), issue 9216
|
||
|
|
if expr.base == 1:
|
||
|
|
return r"%s^{%s}" % (expr.base, expr.exp)
|
||
|
|
# special case for (1/x)^(-y) and (-1/-x)^(-y), issue 20252
|
||
|
|
if expr.base.is_Rational:
|
||
|
|
base_p: int = expr.base.p # type: ignore
|
||
|
|
base_q: int = expr.base.q # type: ignore
|
||
|
|
if base_p * base_q == abs(base_q):
|
||
|
|
if expr.exp == -1:
|
||
|
|
return r"\frac{1}{\frac{%s}{%s}}" % (base_p, base_q)
|
||
|
|
else:
|
||
|
|
return r"\frac{1}{(\frac{%s}{%s})^{%s}}" % (base_p, base_q, abs(expr.exp))
|
||
|
|
# things like 1/x
|
||
|
|
return self._print_Mul(expr)
|
||
|
|
if expr.base.is_Function:
|
||
|
|
return self._print(expr.base, exp=self._print(expr.exp))
|
||
|
|
tex = r"%s^{%s}"
|
||
|
|
return self._helper_print_standard_power(expr, tex)
|
||
|
|
|
||
|
|
def _helper_print_standard_power(self, expr, template: str) -> str:
|
||
|
|
exp = self._print(expr.exp)
|
||
|
|
# issue #12886: add parentheses around superscripts raised
|
||
|
|
# to powers
|
||
|
|
base = self.parenthesize(expr.base, PRECEDENCE['Pow'])
|
||
|
|
if expr.base.is_Symbol:
|
||
|
|
base = self.parenthesize_super(base)
|
||
|
|
elif (isinstance(expr.base, Derivative)
|
||
|
|
and base.startswith(r'\left(')
|
||
|
|
and re.match(r'\\left\(\\d?d?dot', base)
|
||
|
|
and base.endswith(r'\right)')):
|
||
|
|
# don't use parentheses around dotted derivative
|
||
|
|
base = base[6: -7] # remove outermost added parens
|
||
|
|
return template % (base, exp)
|
||
|
|
|
||
|
|
def _print_UnevaluatedExpr(self, expr):
|
||
|
|
return self._print(expr.args[0])
|
||
|
|
|
||
|
|
def _print_Sum(self, expr):
|
||
|
|
if len(expr.limits) == 1:
|
||
|
|
tex = r"\sum_{%s=%s}^{%s} " % \
|
||
|
|
tuple([self._print(i) for i in expr.limits[0]])
|
||
|
|
else:
|
||
|
|
def _format_ineq(l):
|
||
|
|
return r"%s \leq %s \leq %s" % \
|
||
|
|
tuple([self._print(s) for s in (l[1], l[0], l[2])])
|
||
|
|
|
||
|
|
tex = r"\sum_{\substack{%s}} " % \
|
||
|
|
str.join('\\\\', [_format_ineq(l) for l in expr.limits])
|
||
|
|
|
||
|
|
if isinstance(expr.function, Add):
|
||
|
|
tex += r"\left(%s\right)" % self._print(expr.function)
|
||
|
|
else:
|
||
|
|
tex += self._print(expr.function)
|
||
|
|
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_Product(self, expr):
|
||
|
|
if len(expr.limits) == 1:
|
||
|
|
tex = r"\prod_{%s=%s}^{%s} " % \
|
||
|
|
tuple([self._print(i) for i in expr.limits[0]])
|
||
|
|
else:
|
||
|
|
def _format_ineq(l):
|
||
|
|
return r"%s \leq %s \leq %s" % \
|
||
|
|
tuple([self._print(s) for s in (l[1], l[0], l[2])])
|
||
|
|
|
||
|
|
tex = r"\prod_{\substack{%s}} " % \
|
||
|
|
str.join('\\\\', [_format_ineq(l) for l in expr.limits])
|
||
|
|
|
||
|
|
if isinstance(expr.function, Add):
|
||
|
|
tex += r"\left(%s\right)" % self._print(expr.function)
|
||
|
|
else:
|
||
|
|
tex += self._print(expr.function)
|
||
|
|
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_BasisDependent(self, expr: 'BasisDependent'):
|
||
|
|
from sympy.vector import Vector
|
||
|
|
|
||
|
|
o1: list[str] = []
|
||
|
|
if expr == expr.zero:
|
||
|
|
return expr.zero._latex_form
|
||
|
|
if isinstance(expr, Vector):
|
||
|
|
items = expr.separate().items()
|
||
|
|
else:
|
||
|
|
items = [(0, expr)]
|
||
|
|
|
||
|
|
for system, vect in items:
|
||
|
|
inneritems = list(vect.components.items())
|
||
|
|
inneritems.sort(key=lambda x: x[0].__str__())
|
||
|
|
for k, v in inneritems:
|
||
|
|
if v == 1:
|
||
|
|
o1.append(' + ' + k._latex_form)
|
||
|
|
elif v == -1:
|
||
|
|
o1.append(' - ' + k._latex_form)
|
||
|
|
else:
|
||
|
|
arg_str = r'\left(' + self._print(v) + r'\right)'
|
||
|
|
o1.append(' + ' + arg_str + k._latex_form)
|
||
|
|
|
||
|
|
outstr = (''.join(o1))
|
||
|
|
if outstr[1] != '-':
|
||
|
|
outstr = outstr[3:]
|
||
|
|
else:
|
||
|
|
outstr = outstr[1:]
|
||
|
|
return outstr
|
||
|
|
|
||
|
|
def _print_Indexed(self, expr):
|
||
|
|
tex_base = self._print(expr.base)
|
||
|
|
tex = '{'+tex_base+'}'+'_{%s}' % ','.join(
|
||
|
|
map(self._print, expr.indices))
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_IndexedBase(self, expr):
|
||
|
|
return self._print(expr.label)
|
||
|
|
|
||
|
|
def _print_Idx(self, expr):
|
||
|
|
label = self._print(expr.label)
|
||
|
|
if expr.upper is not None:
|
||
|
|
upper = self._print(expr.upper)
|
||
|
|
if expr.lower is not None:
|
||
|
|
lower = self._print(expr.lower)
|
||
|
|
else:
|
||
|
|
lower = self._print(S.Zero)
|
||
|
|
interval = '{lower}\\mathrel{{..}}\\nobreak {upper}'.format(
|
||
|
|
lower = lower, upper = upper)
|
||
|
|
return '{{{label}}}_{{{interval}}}'.format(
|
||
|
|
label = label, interval = interval)
|
||
|
|
#if no bounds are defined this just prints the label
|
||
|
|
return label
|
||
|
|
|
||
|
|
def _print_Derivative(self, expr):
|
||
|
|
if requires_partial(expr.expr):
|
||
|
|
diff_symbol = r'\partial'
|
||
|
|
else:
|
||
|
|
diff_symbol = self._settings["diff_operator_latex"]
|
||
|
|
|
||
|
|
tex = ""
|
||
|
|
dim = 0
|
||
|
|
for x, num in reversed(expr.variable_count):
|
||
|
|
dim += num
|
||
|
|
if num == 1:
|
||
|
|
tex += r"%s %s" % (diff_symbol, self._print(x))
|
||
|
|
else:
|
||
|
|
tex += r"%s %s^{%s}" % (diff_symbol,
|
||
|
|
self.parenthesize_super(self._print(x)),
|
||
|
|
self._print(num))
|
||
|
|
|
||
|
|
if dim == 1:
|
||
|
|
tex = r"\frac{%s}{%s}" % (diff_symbol, tex)
|
||
|
|
else:
|
||
|
|
tex = r"\frac{%s^{%s}}{%s}" % (diff_symbol, self._print(dim), tex)
|
||
|
|
|
||
|
|
if any(i.could_extract_minus_sign() for i in expr.args):
|
||
|
|
return r"%s %s" % (tex, self.parenthesize(expr.expr,
|
||
|
|
PRECEDENCE["Mul"],
|
||
|
|
is_neg=True,
|
||
|
|
strict=True))
|
||
|
|
|
||
|
|
return r"%s %s" % (tex, self.parenthesize(expr.expr,
|
||
|
|
PRECEDENCE["Mul"],
|
||
|
|
is_neg=False,
|
||
|
|
strict=True))
|
||
|
|
|
||
|
|
def _print_Subs(self, subs):
|
||
|
|
expr, old, new = subs.args
|
||
|
|
latex_expr = self._print(expr)
|
||
|
|
latex_old = (self._print(e) for e in old)
|
||
|
|
latex_new = (self._print(e) for e in new)
|
||
|
|
latex_subs = r'\\ '.join(
|
||
|
|
e[0] + '=' + e[1] for e in zip(latex_old, latex_new))
|
||
|
|
return r'\left. %s \right|_{\substack{ %s }}' % (latex_expr,
|
||
|
|
latex_subs)
|
||
|
|
|
||
|
|
def _print_Integral(self, expr):
|
||
|
|
tex, symbols = "", []
|
||
|
|
diff_symbol = self._settings["diff_operator_latex"]
|
||
|
|
|
||
|
|
# Only up to \iiiint exists
|
||
|
|
if len(expr.limits) <= 4 and all(len(lim) == 1 for lim in expr.limits):
|
||
|
|
# Use len(expr.limits)-1 so that syntax highlighters don't think
|
||
|
|
# \" is an escaped quote
|
||
|
|
tex = r"\i" + "i"*(len(expr.limits) - 1) + "nt"
|
||
|
|
symbols = [r"\, %s%s" % (diff_symbol, self._print(symbol[0]))
|
||
|
|
for symbol in expr.limits]
|
||
|
|
|
||
|
|
else:
|
||
|
|
for lim in reversed(expr.limits):
|
||
|
|
symbol = lim[0]
|
||
|
|
tex += r"\int"
|
||
|
|
|
||
|
|
if len(lim) > 1:
|
||
|
|
if self._settings['mode'] != 'inline' \
|
||
|
|
and not self._settings['itex']:
|
||
|
|
tex += r"\limits"
|
||
|
|
|
||
|
|
if len(lim) == 3:
|
||
|
|
tex += "_{%s}^{%s}" % (self._print(lim[1]),
|
||
|
|
self._print(lim[2]))
|
||
|
|
if len(lim) == 2:
|
||
|
|
tex += "^{%s}" % (self._print(lim[1]))
|
||
|
|
|
||
|
|
symbols.insert(0, r"\, %s%s" % (diff_symbol, self._print(symbol)))
|
||
|
|
|
||
|
|
return r"%s %s%s" % (tex, self.parenthesize(expr.function,
|
||
|
|
PRECEDENCE["Mul"],
|
||
|
|
is_neg=any(i.could_extract_minus_sign() for i in expr.args),
|
||
|
|
strict=True),
|
||
|
|
"".join(symbols))
|
||
|
|
|
||
|
|
def _print_Limit(self, expr):
|
||
|
|
e, z, z0, dir = expr.args
|
||
|
|
|
||
|
|
tex = r"\lim_{%s \to " % self._print(z)
|
||
|
|
if str(dir) == '+-' or z0 in (S.Infinity, S.NegativeInfinity):
|
||
|
|
tex += r"%s}" % self._print(z0)
|
||
|
|
else:
|
||
|
|
tex += r"%s^%s}" % (self._print(z0), self._print(dir))
|
||
|
|
|
||
|
|
if isinstance(e, AssocOp):
|
||
|
|
return r"%s\left(%s\right)" % (tex, self._print(e))
|
||
|
|
else:
|
||
|
|
return r"%s %s" % (tex, self._print(e))
|
||
|
|
|
||
|
|
def _hprint_Function(self, func: str) -> str:
|
||
|
|
r'''
|
||
|
|
Logic to decide how to render a function to latex
|
||
|
|
- if it is a recognized latex name, use the appropriate latex command
|
||
|
|
- if it is a single letter, excluding sub- and superscripts, just use that letter
|
||
|
|
- if it is a longer name, then put \operatorname{} around it and be
|
||
|
|
mindful of undercores in the name
|
||
|
|
'''
|
||
|
|
func = self._deal_with_super_sub(func)
|
||
|
|
superscriptidx = func.find("^")
|
||
|
|
subscriptidx = func.find("_")
|
||
|
|
if func in accepted_latex_functions:
|
||
|
|
name = r"\%s" % func
|
||
|
|
elif len(func) == 1 or func.startswith('\\') or subscriptidx == 1 or superscriptidx == 1:
|
||
|
|
name = func
|
||
|
|
else:
|
||
|
|
if superscriptidx > 0 and subscriptidx > 0:
|
||
|
|
name = r"\operatorname{%s}%s" %(
|
||
|
|
func[:min(subscriptidx,superscriptidx)],
|
||
|
|
func[min(subscriptidx,superscriptidx):])
|
||
|
|
elif superscriptidx > 0:
|
||
|
|
name = r"\operatorname{%s}%s" %(
|
||
|
|
func[:superscriptidx],
|
||
|
|
func[superscriptidx:])
|
||
|
|
elif subscriptidx > 0:
|
||
|
|
name = r"\operatorname{%s}%s" %(
|
||
|
|
func[:subscriptidx],
|
||
|
|
func[subscriptidx:])
|
||
|
|
else:
|
||
|
|
name = r"\operatorname{%s}" % func
|
||
|
|
return name
|
||
|
|
|
||
|
|
def _print_Function(self, expr: Function, exp=None) -> str:
|
||
|
|
r'''
|
||
|
|
Render functions to LaTeX, handling functions that LaTeX knows about
|
||
|
|
e.g., sin, cos, ... by using the proper LaTeX command (\sin, \cos, ...).
|
||
|
|
For single-letter function names, render them as regular LaTeX math
|
||
|
|
symbols. For multi-letter function names that LaTeX does not know
|
||
|
|
about, (e.g., Li, sech) use \operatorname{} so that the function name
|
||
|
|
is rendered in Roman font and LaTeX handles spacing properly.
|
||
|
|
|
||
|
|
expr is the expression involving the function
|
||
|
|
exp is an exponent
|
||
|
|
'''
|
||
|
|
func = expr.func.__name__
|
||
|
|
if hasattr(self, '_print_' + func) and \
|
||
|
|
not isinstance(expr, AppliedUndef):
|
||
|
|
return getattr(self, '_print_' + func)(expr, exp)
|
||
|
|
else:
|
||
|
|
args = [str(self._print(arg)) for arg in expr.args]
|
||
|
|
# How inverse trig functions should be displayed, formats are:
|
||
|
|
# abbreviated: asin, full: arcsin, power: sin^-1
|
||
|
|
inv_trig_style = self._settings['inv_trig_style']
|
||
|
|
# If we are dealing with a power-style inverse trig function
|
||
|
|
inv_trig_power_case = False
|
||
|
|
# If it is applicable to fold the argument brackets
|
||
|
|
can_fold_brackets = self._settings['fold_func_brackets'] and \
|
||
|
|
len(args) == 1 and \
|
||
|
|
not self._needs_function_brackets(expr.args[0])
|
||
|
|
|
||
|
|
inv_trig_table = [
|
||
|
|
"asin", "acos", "atan",
|
||
|
|
"acsc", "asec", "acot",
|
||
|
|
"asinh", "acosh", "atanh",
|
||
|
|
"acsch", "asech", "acoth",
|
||
|
|
]
|
||
|
|
|
||
|
|
# If the function is an inverse trig function, handle the style
|
||
|
|
if func in inv_trig_table:
|
||
|
|
if inv_trig_style == "abbreviated":
|
||
|
|
pass
|
||
|
|
elif inv_trig_style == "full":
|
||
|
|
func = ("ar" if func[-1] == "h" else "arc") + func[1:]
|
||
|
|
elif inv_trig_style == "power":
|
||
|
|
func = func[1:]
|
||
|
|
inv_trig_power_case = True
|
||
|
|
|
||
|
|
# Can never fold brackets if we're raised to a power
|
||
|
|
if exp is not None:
|
||
|
|
can_fold_brackets = False
|
||
|
|
|
||
|
|
if inv_trig_power_case:
|
||
|
|
if func in accepted_latex_functions:
|
||
|
|
name = r"\%s^{-1}" % func
|
||
|
|
else:
|
||
|
|
name = r"\operatorname{%s}^{-1}" % func
|
||
|
|
elif exp is not None:
|
||
|
|
func_tex = self._hprint_Function(func)
|
||
|
|
func_tex = self.parenthesize_super(func_tex)
|
||
|
|
name = r'%s^{%s}' % (func_tex, exp)
|
||
|
|
else:
|
||
|
|
name = self._hprint_Function(func)
|
||
|
|
|
||
|
|
if can_fold_brackets:
|
||
|
|
if func in accepted_latex_functions:
|
||
|
|
# Wrap argument safely to avoid parse-time conflicts
|
||
|
|
# with the function name itself
|
||
|
|
name += r" {%s}"
|
||
|
|
else:
|
||
|
|
name += r"%s"
|
||
|
|
else:
|
||
|
|
name += r"{\left(%s \right)}"
|
||
|
|
|
||
|
|
if inv_trig_power_case and exp is not None:
|
||
|
|
name += r"^{%s}" % exp
|
||
|
|
|
||
|
|
return name % ",".join(args)
|
||
|
|
|
||
|
|
def _print_UndefinedFunction(self, expr):
|
||
|
|
return self._hprint_Function(str(expr))
|
||
|
|
|
||
|
|
def _print_ElementwiseApplyFunction(self, expr):
|
||
|
|
return r"{%s}_{\circ}\left({%s}\right)" % (
|
||
|
|
self._print(expr.function),
|
||
|
|
self._print(expr.expr),
|
||
|
|
)
|
||
|
|
|
||
|
|
@property
|
||
|
|
def _special_function_classes(self):
|
||
|
|
from sympy.functions.special.tensor_functions import KroneckerDelta
|
||
|
|
from sympy.functions.special.gamma_functions import gamma, lowergamma
|
||
|
|
from sympy.functions.special.beta_functions import beta
|
||
|
|
from sympy.functions.special.delta_functions import DiracDelta
|
||
|
|
from sympy.functions.special.error_functions import Chi
|
||
|
|
return {KroneckerDelta: r'\delta',
|
||
|
|
gamma: r'\Gamma',
|
||
|
|
lowergamma: r'\gamma',
|
||
|
|
beta: r'\operatorname{B}',
|
||
|
|
DiracDelta: r'\delta',
|
||
|
|
Chi: r'\operatorname{Chi}'}
|
||
|
|
|
||
|
|
def _print_FunctionClass(self, expr):
|
||
|
|
for cls in self._special_function_classes:
|
||
|
|
if issubclass(expr, cls) and expr.__name__ == cls.__name__:
|
||
|
|
return self._special_function_classes[cls]
|
||
|
|
return self._hprint_Function(str(expr))
|
||
|
|
|
||
|
|
def _print_Lambda(self, expr):
|
||
|
|
symbols, expr = expr.args
|
||
|
|
|
||
|
|
if len(symbols) == 1:
|
||
|
|
symbols = self._print(symbols[0])
|
||
|
|
else:
|
||
|
|
symbols = self._print(tuple(symbols))
|
||
|
|
|
||
|
|
tex = r"\left( %s \mapsto %s \right)" % (symbols, self._print(expr))
|
||
|
|
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_IdentityFunction(self, expr):
|
||
|
|
return r"\left( x \mapsto x \right)"
|
||
|
|
|
||
|
|
def _hprint_variadic_function(self, expr, exp=None) -> str:
|
||
|
|
args = sorted(expr.args, key=default_sort_key)
|
||
|
|
texargs = [r"%s" % self._print(symbol) for symbol in args]
|
||
|
|
tex = r"\%s\left(%s\right)" % (str(expr.func).lower(),
|
||
|
|
", ".join(texargs))
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
_print_Min = _print_Max = _hprint_variadic_function
|
||
|
|
|
||
|
|
def _print_floor(self, expr, exp=None):
|
||
|
|
tex = r"\left\lfloor{%s}\right\rfloor" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_ceiling(self, expr, exp=None):
|
||
|
|
tex = r"\left\lceil{%s}\right\rceil" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_log(self, expr, exp=None):
|
||
|
|
if not self._settings["ln_notation"]:
|
||
|
|
tex = r"\log{\left(%s \right)}" % self._print(expr.args[0])
|
||
|
|
else:
|
||
|
|
tex = r"\ln{\left(%s \right)}" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_Abs(self, expr, exp=None):
|
||
|
|
tex = r"\left|{%s}\right|" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_re(self, expr, exp=None):
|
||
|
|
if self._settings['gothic_re_im']:
|
||
|
|
tex = r"\Re{%s}" % self.parenthesize(expr.args[0], PRECEDENCE['Atom'])
|
||
|
|
else:
|
||
|
|
tex = r"\operatorname{{re}}{{{}}}".format(self.parenthesize(expr.args[0], PRECEDENCE['Atom']))
|
||
|
|
|
||
|
|
return self._do_exponent(tex, exp)
|
||
|
|
|
||
|
|
def _print_im(self, expr, exp=None):
|
||
|
|
if self._settings['gothic_re_im']:
|
||
|
|
tex = r"\Im{%s}" % self.parenthesize(expr.args[0], PRECEDENCE['Atom'])
|
||
|
|
else:
|
||
|
|
tex = r"\operatorname{{im}}{{{}}}".format(self.parenthesize(expr.args[0], PRECEDENCE['Atom']))
|
||
|
|
|
||
|
|
return self._do_exponent(tex, exp)
|
||
|
|
|
||
|
|
def _print_Not(self, e):
|
||
|
|
from sympy.logic.boolalg import (Equivalent, Implies)
|
||
|
|
if isinstance(e.args[0], Equivalent):
|
||
|
|
return self._print_Equivalent(e.args[0], r"\not\Leftrightarrow")
|
||
|
|
if isinstance(e.args[0], Implies):
|
||
|
|
return self._print_Implies(e.args[0], r"\not\Rightarrow")
|
||
|
|
if (e.args[0].is_Boolean):
|
||
|
|
return r"\neg \left(%s\right)" % self._print(e.args[0])
|
||
|
|
else:
|
||
|
|
return r"\neg %s" % self._print(e.args[0])
|
||
|
|
|
||
|
|
def _print_LogOp(self, args, char):
|
||
|
|
arg = args[0]
|
||
|
|
if arg.is_Boolean and not arg.is_Not:
|
||
|
|
tex = r"\left(%s\right)" % self._print(arg)
|
||
|
|
else:
|
||
|
|
tex = r"%s" % self._print(arg)
|
||
|
|
|
||
|
|
for arg in args[1:]:
|
||
|
|
if arg.is_Boolean and not arg.is_Not:
|
||
|
|
tex += r" %s \left(%s\right)" % (char, self._print(arg))
|
||
|
|
else:
|
||
|
|
tex += r" %s %s" % (char, self._print(arg))
|
||
|
|
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_And(self, e):
|
||
|
|
args = sorted(e.args, key=default_sort_key)
|
||
|
|
return self._print_LogOp(args, r"\wedge")
|
||
|
|
|
||
|
|
def _print_Or(self, e):
|
||
|
|
args = sorted(e.args, key=default_sort_key)
|
||
|
|
return self._print_LogOp(args, r"\vee")
|
||
|
|
|
||
|
|
def _print_Xor(self, e):
|
||
|
|
args = sorted(e.args, key=default_sort_key)
|
||
|
|
return self._print_LogOp(args, r"\veebar")
|
||
|
|
|
||
|
|
def _print_Implies(self, e, altchar=None):
|
||
|
|
return self._print_LogOp(e.args, altchar or r"\Rightarrow")
|
||
|
|
|
||
|
|
def _print_Equivalent(self, e, altchar=None):
|
||
|
|
args = sorted(e.args, key=default_sort_key)
|
||
|
|
return self._print_LogOp(args, altchar or r"\Leftrightarrow")
|
||
|
|
|
||
|
|
def _print_conjugate(self, expr, exp=None):
|
||
|
|
tex = r"\overline{%s}" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_polar_lift(self, expr, exp=None):
|
||
|
|
func = r"\operatorname{polar\_lift}"
|
||
|
|
arg = r"{\left(%s \right)}" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}%s" % (func, exp, arg)
|
||
|
|
else:
|
||
|
|
return r"%s%s" % (func, arg)
|
||
|
|
|
||
|
|
def _print_ExpBase(self, expr, exp=None):
|
||
|
|
# TODO should exp_polar be printed differently?
|
||
|
|
# what about exp_polar(0), exp_polar(1)?
|
||
|
|
tex = r"e^{%s}" % self._print(expr.args[0])
|
||
|
|
return self._do_exponent(tex, exp)
|
||
|
|
|
||
|
|
def _print_Exp1(self, expr, exp=None):
|
||
|
|
return "e"
|
||
|
|
|
||
|
|
def _print_elliptic_k(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
return r"K^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"K%s" % tex
|
||
|
|
|
||
|
|
def _print_elliptic_f(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s\middle| %s\right)" % \
|
||
|
|
(self._print(expr.args[0]), self._print(expr.args[1]))
|
||
|
|
if exp is not None:
|
||
|
|
return r"F^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"F%s" % tex
|
||
|
|
|
||
|
|
def _print_elliptic_e(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 2:
|
||
|
|
tex = r"\left(%s\middle| %s\right)" % \
|
||
|
|
(self._print(expr.args[0]), self._print(expr.args[1]))
|
||
|
|
else:
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
return r"E^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"E%s" % tex
|
||
|
|
|
||
|
|
def _print_elliptic_pi(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 3:
|
||
|
|
tex = r"\left(%s; %s\middle| %s\right)" % \
|
||
|
|
(self._print(expr.args[0]), self._print(expr.args[1]),
|
||
|
|
self._print(expr.args[2]))
|
||
|
|
else:
|
||
|
|
tex = r"\left(%s\middle| %s\right)" % \
|
||
|
|
(self._print(expr.args[0]), self._print(expr.args[1]))
|
||
|
|
if exp is not None:
|
||
|
|
return r"\Pi^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"\Pi%s" % tex
|
||
|
|
|
||
|
|
def _print_beta(self, expr, exp=None):
|
||
|
|
x = expr.args[0]
|
||
|
|
# Deal with unevaluated single argument beta
|
||
|
|
y = expr.args[0] if len(expr.args) == 1 else expr.args[1]
|
||
|
|
tex = rf"\left({x}, {y}\right)"
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"\operatorname{B}^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"\operatorname{B}%s" % tex
|
||
|
|
|
||
|
|
def _print_betainc(self, expr, exp=None, operator='B'):
|
||
|
|
largs = [self._print(arg) for arg in expr.args]
|
||
|
|
tex = r"\left(%s, %s\right)" % (largs[0], largs[1])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"\operatorname{%s}_{(%s, %s)}^{%s}%s" % (operator, largs[2], largs[3], exp, tex)
|
||
|
|
else:
|
||
|
|
return r"\operatorname{%s}_{(%s, %s)}%s" % (operator, largs[2], largs[3], tex)
|
||
|
|
|
||
|
|
def _print_betainc_regularized(self, expr, exp=None):
|
||
|
|
return self._print_betainc(expr, exp, operator='I')
|
||
|
|
|
||
|
|
def _print_uppergamma(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s, %s\right)" % (self._print(expr.args[0]),
|
||
|
|
self._print(expr.args[1]))
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"\Gamma^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"\Gamma%s" % tex
|
||
|
|
|
||
|
|
def _print_lowergamma(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s, %s\right)" % (self._print(expr.args[0]),
|
||
|
|
self._print(expr.args[1]))
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"\gamma^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"\gamma%s" % tex
|
||
|
|
|
||
|
|
def _hprint_one_arg_func(self, expr, exp=None) -> str:
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}%s" % (self._print(expr.func), exp, tex)
|
||
|
|
else:
|
||
|
|
return r"%s%s" % (self._print(expr.func), tex)
|
||
|
|
|
||
|
|
_print_gamma = _hprint_one_arg_func
|
||
|
|
|
||
|
|
def _print_Chi(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"\operatorname{Chi}^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"\operatorname{Chi}%s" % tex
|
||
|
|
|
||
|
|
def _print_expint(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[1])
|
||
|
|
nu = self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"\operatorname{E}_{%s}^{%s}%s" % (nu, exp, tex)
|
||
|
|
else:
|
||
|
|
return r"\operatorname{E}_{%s}%s" % (nu, tex)
|
||
|
|
|
||
|
|
def _print_fresnels(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"S^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"S%s" % tex
|
||
|
|
|
||
|
|
def _print_fresnelc(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"C^{%s}%s" % (exp, tex)
|
||
|
|
else:
|
||
|
|
return r"C%s" % tex
|
||
|
|
|
||
|
|
def _print_subfactorial(self, expr, exp=None):
|
||
|
|
tex = r"!%s" % self.parenthesize(expr.args[0], PRECEDENCE["Func"])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"\left(%s\right)^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_factorial(self, expr, exp=None):
|
||
|
|
tex = r"%s!" % self.parenthesize(expr.args[0], PRECEDENCE["Func"])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_factorial2(self, expr, exp=None):
|
||
|
|
tex = r"%s!!" % self.parenthesize(expr.args[0], PRECEDENCE["Func"])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_binomial(self, expr, exp=None):
|
||
|
|
tex = r"{\binom{%s}{%s}}" % (self._print(expr.args[0]),
|
||
|
|
self._print(expr.args[1]))
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_RisingFactorial(self, expr, exp=None):
|
||
|
|
n, k = expr.args
|
||
|
|
base = r"%s" % self.parenthesize(n, PRECEDENCE['Func'])
|
||
|
|
|
||
|
|
tex = r"{%s}^{\left(%s\right)}" % (base, self._print(k))
|
||
|
|
|
||
|
|
return self._do_exponent(tex, exp)
|
||
|
|
|
||
|
|
def _print_FallingFactorial(self, expr, exp=None):
|
||
|
|
n, k = expr.args
|
||
|
|
sub = r"%s" % self.parenthesize(k, PRECEDENCE['Func'])
|
||
|
|
|
||
|
|
tex = r"{\left(%s\right)}_{%s}" % (self._print(n), sub)
|
||
|
|
|
||
|
|
return self._do_exponent(tex, exp)
|
||
|
|
|
||
|
|
def _hprint_BesselBase(self, expr, exp, sym: str) -> str:
|
||
|
|
tex = r"%s" % (sym)
|
||
|
|
|
||
|
|
need_exp = False
|
||
|
|
if exp is not None:
|
||
|
|
if tex.find('^') == -1:
|
||
|
|
tex = r"%s^{%s}" % (tex, exp)
|
||
|
|
else:
|
||
|
|
need_exp = True
|
||
|
|
|
||
|
|
tex = r"%s_{%s}\left(%s\right)" % (tex, self._print(expr.order),
|
||
|
|
self._print(expr.argument))
|
||
|
|
|
||
|
|
if need_exp:
|
||
|
|
tex = self._do_exponent(tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _hprint_vec(self, vec) -> str:
|
||
|
|
if not vec:
|
||
|
|
return ""
|
||
|
|
s = ""
|
||
|
|
for i in vec[:-1]:
|
||
|
|
s += "%s, " % self._print(i)
|
||
|
|
s += self._print(vec[-1])
|
||
|
|
return s
|
||
|
|
|
||
|
|
def _print_besselj(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'J')
|
||
|
|
|
||
|
|
def _print_besseli(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'I')
|
||
|
|
|
||
|
|
def _print_besselk(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'K')
|
||
|
|
|
||
|
|
def _print_bessely(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'Y')
|
||
|
|
|
||
|
|
def _print_yn(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'y')
|
||
|
|
|
||
|
|
def _print_jn(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'j')
|
||
|
|
|
||
|
|
def _print_hankel1(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'H^{(1)}')
|
||
|
|
|
||
|
|
def _print_hankel2(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'H^{(2)}')
|
||
|
|
|
||
|
|
def _print_hn1(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'h^{(1)}')
|
||
|
|
|
||
|
|
def _print_hn2(self, expr, exp=None):
|
||
|
|
return self._hprint_BesselBase(expr, exp, 'h^{(2)}')
|
||
|
|
|
||
|
|
def _hprint_airy(self, expr, exp=None, notation="") -> str:
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s^{%s}%s" % (notation, exp, tex)
|
||
|
|
else:
|
||
|
|
return r"%s%s" % (notation, tex)
|
||
|
|
|
||
|
|
def _hprint_airy_prime(self, expr, exp=None, notation="") -> str:
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
return r"{%s^\prime}^{%s}%s" % (notation, exp, tex)
|
||
|
|
else:
|
||
|
|
return r"%s^\prime%s" % (notation, tex)
|
||
|
|
|
||
|
|
def _print_airyai(self, expr, exp=None):
|
||
|
|
return self._hprint_airy(expr, exp, 'Ai')
|
||
|
|
|
||
|
|
def _print_airybi(self, expr, exp=None):
|
||
|
|
return self._hprint_airy(expr, exp, 'Bi')
|
||
|
|
|
||
|
|
def _print_airyaiprime(self, expr, exp=None):
|
||
|
|
return self._hprint_airy_prime(expr, exp, 'Ai')
|
||
|
|
|
||
|
|
def _print_airybiprime(self, expr, exp=None):
|
||
|
|
return self._hprint_airy_prime(expr, exp, 'Bi')
|
||
|
|
|
||
|
|
def _print_hyper(self, expr, exp=None):
|
||
|
|
tex = r"{{}_{%s}F_{%s}\left(\begin{matrix} %s \\ %s \end{matrix}" \
|
||
|
|
r"\middle| {%s} \right)}" % \
|
||
|
|
(self._print(len(expr.ap)), self._print(len(expr.bq)),
|
||
|
|
self._hprint_vec(expr.ap), self._hprint_vec(expr.bq),
|
||
|
|
self._print(expr.argument))
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"{%s}^{%s}" % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_meijerg(self, expr, exp=None):
|
||
|
|
tex = r"{G_{%s, %s}^{%s, %s}\left(\begin{matrix} %s & %s \\" \
|
||
|
|
r"%s & %s \end{matrix} \middle| {%s} \right)}" % \
|
||
|
|
(self._print(len(expr.ap)), self._print(len(expr.bq)),
|
||
|
|
self._print(len(expr.bm)), self._print(len(expr.an)),
|
||
|
|
self._hprint_vec(expr.an), self._hprint_vec(expr.aother),
|
||
|
|
self._hprint_vec(expr.bm), self._hprint_vec(expr.bother),
|
||
|
|
self._print(expr.argument))
|
||
|
|
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"{%s}^{%s}" % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_dirichlet_eta(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
return r"\eta^{%s}%s" % (exp, tex)
|
||
|
|
return r"\eta%s" % tex
|
||
|
|
|
||
|
|
def _print_zeta(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 2:
|
||
|
|
tex = r"\left(%s, %s\right)" % tuple(map(self._print, expr.args))
|
||
|
|
else:
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
return r"\zeta^{%s}%s" % (exp, tex)
|
||
|
|
return r"\zeta%s" % tex
|
||
|
|
|
||
|
|
def _print_stieltjes(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 2:
|
||
|
|
tex = r"_{%s}\left(%s\right)" % tuple(map(self._print, expr.args))
|
||
|
|
else:
|
||
|
|
tex = r"_{%s}" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
return r"\gamma%s^{%s}" % (tex, exp)
|
||
|
|
return r"\gamma%s" % tex
|
||
|
|
|
||
|
|
def _print_lerchphi(self, expr, exp=None):
|
||
|
|
tex = r"\left(%s, %s, %s\right)" % tuple(map(self._print, expr.args))
|
||
|
|
if exp is None:
|
||
|
|
return r"\Phi%s" % tex
|
||
|
|
return r"\Phi^{%s}%s" % (exp, tex)
|
||
|
|
|
||
|
|
def _print_polylog(self, expr, exp=None):
|
||
|
|
s, z = map(self._print, expr.args)
|
||
|
|
tex = r"\left(%s\right)" % z
|
||
|
|
if exp is None:
|
||
|
|
return r"\operatorname{Li}_{%s}%s" % (s, tex)
|
||
|
|
return r"\operatorname{Li}_{%s}^{%s}%s" % (s, exp, tex)
|
||
|
|
|
||
|
|
def _print_jacobi(self, expr, exp=None):
|
||
|
|
n, a, b, x = map(self._print, expr.args)
|
||
|
|
tex = r"P_{%s}^{\left(%s,%s\right)}\left(%s\right)" % (n, a, b, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_gegenbauer(self, expr, exp=None):
|
||
|
|
n, a, x = map(self._print, expr.args)
|
||
|
|
tex = r"C_{%s}^{\left(%s\right)}\left(%s\right)" % (n, a, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_chebyshevt(self, expr, exp=None):
|
||
|
|
n, x = map(self._print, expr.args)
|
||
|
|
tex = r"T_{%s}\left(%s\right)" % (n, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_chebyshevu(self, expr, exp=None):
|
||
|
|
n, x = map(self._print, expr.args)
|
||
|
|
tex = r"U_{%s}\left(%s\right)" % (n, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_legendre(self, expr, exp=None):
|
||
|
|
n, x = map(self._print, expr.args)
|
||
|
|
tex = r"P_{%s}\left(%s\right)" % (n, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_assoc_legendre(self, expr, exp=None):
|
||
|
|
n, a, x = map(self._print, expr.args)
|
||
|
|
tex = r"P_{%s}^{\left(%s\right)}\left(%s\right)" % (n, a, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_hermite(self, expr, exp=None):
|
||
|
|
n, x = map(self._print, expr.args)
|
||
|
|
tex = r"H_{%s}\left(%s\right)" % (n, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_laguerre(self, expr, exp=None):
|
||
|
|
n, x = map(self._print, expr.args)
|
||
|
|
tex = r"L_{%s}\left(%s\right)" % (n, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_assoc_laguerre(self, expr, exp=None):
|
||
|
|
n, a, x = map(self._print, expr.args)
|
||
|
|
tex = r"L_{%s}^{\left(%s\right)}\left(%s\right)" % (n, a, x)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_Ynm(self, expr, exp=None):
|
||
|
|
n, m, theta, phi = map(self._print, expr.args)
|
||
|
|
tex = r"Y_{%s}^{%s}\left(%s,%s\right)" % (n, m, theta, phi)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_Znm(self, expr, exp=None):
|
||
|
|
n, m, theta, phi = map(self._print, expr.args)
|
||
|
|
tex = r"Z_{%s}^{%s}\left(%s,%s\right)" % (n, m, theta, phi)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"\left(" + tex + r"\right)^{%s}" % (exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def __print_mathieu_functions(self, character, args, prime=False, exp=None):
|
||
|
|
a, q, z = map(self._print, args)
|
||
|
|
sup = r"^{\prime}" if prime else ""
|
||
|
|
exp = "" if not exp else "^{%s}" % exp
|
||
|
|
return r"%s%s\left(%s, %s, %s\right)%s" % (character, sup, a, q, z, exp)
|
||
|
|
|
||
|
|
def _print_mathieuc(self, expr, exp=None):
|
||
|
|
return self.__print_mathieu_functions("C", expr.args, exp=exp)
|
||
|
|
|
||
|
|
def _print_mathieus(self, expr, exp=None):
|
||
|
|
return self.__print_mathieu_functions("S", expr.args, exp=exp)
|
||
|
|
|
||
|
|
def _print_mathieucprime(self, expr, exp=None):
|
||
|
|
return self.__print_mathieu_functions("C", expr.args, prime=True, exp=exp)
|
||
|
|
|
||
|
|
def _print_mathieusprime(self, expr, exp=None):
|
||
|
|
return self.__print_mathieu_functions("S", expr.args, prime=True, exp=exp)
|
||
|
|
|
||
|
|
def _print_Rational(self, expr):
|
||
|
|
if expr.q != 1:
|
||
|
|
sign = ""
|
||
|
|
p = expr.p
|
||
|
|
if expr.p < 0:
|
||
|
|
sign = "- "
|
||
|
|
p = -p
|
||
|
|
if self._settings['fold_short_frac']:
|
||
|
|
return r"%s%d / %d" % (sign, p, expr.q)
|
||
|
|
return r"%s\frac{%d}{%d}" % (sign, p, expr.q)
|
||
|
|
else:
|
||
|
|
return self._print(expr.p)
|
||
|
|
|
||
|
|
def _print_Order(self, expr):
|
||
|
|
s = self._print(expr.expr)
|
||
|
|
if expr.point and any(p != S.Zero for p in expr.point) or \
|
||
|
|
len(expr.variables) > 1:
|
||
|
|
s += '; '
|
||
|
|
if len(expr.variables) > 1:
|
||
|
|
s += self._print(expr.variables)
|
||
|
|
elif expr.variables:
|
||
|
|
s += self._print(expr.variables[0])
|
||
|
|
s += r'\rightarrow '
|
||
|
|
if len(expr.point) > 1:
|
||
|
|
s += self._print(expr.point)
|
||
|
|
else:
|
||
|
|
s += self._print(expr.point[0])
|
||
|
|
return r"O\left(%s\right)" % s
|
||
|
|
|
||
|
|
def _print_Symbol(self, expr: Symbol, style='plain'):
|
||
|
|
name: str = self._settings['symbol_names'].get(expr)
|
||
|
|
if name is not None:
|
||
|
|
return name
|
||
|
|
|
||
|
|
return self._deal_with_super_sub(expr.name, style=style)
|
||
|
|
|
||
|
|
_print_RandomSymbol = _print_Symbol
|
||
|
|
|
||
|
|
def _deal_with_super_sub(self, string: str, style='plain') -> str:
|
||
|
|
if '{' in string:
|
||
|
|
name, supers, subs = string, [], []
|
||
|
|
else:
|
||
|
|
name, supers, subs = split_super_sub(string)
|
||
|
|
|
||
|
|
name = translate(name)
|
||
|
|
supers = [translate(sup) for sup in supers]
|
||
|
|
subs = [translate(sub) for sub in subs]
|
||
|
|
|
||
|
|
# apply the style only to the name
|
||
|
|
if style == 'bold':
|
||
|
|
name = "\\mathbf{{{}}}".format(name)
|
||
|
|
|
||
|
|
# glue all items together:
|
||
|
|
if supers:
|
||
|
|
name += "^{%s}" % " ".join(supers)
|
||
|
|
if subs:
|
||
|
|
name += "_{%s}" % " ".join(subs)
|
||
|
|
|
||
|
|
return name
|
||
|
|
|
||
|
|
def _print_Relational(self, expr):
|
||
|
|
if self._settings['itex']:
|
||
|
|
gt = r"\gt"
|
||
|
|
lt = r"\lt"
|
||
|
|
else:
|
||
|
|
gt = ">"
|
||
|
|
lt = "<"
|
||
|
|
|
||
|
|
charmap = {
|
||
|
|
"==": "=",
|
||
|
|
">": gt,
|
||
|
|
"<": lt,
|
||
|
|
">=": r"\geq",
|
||
|
|
"<=": r"\leq",
|
||
|
|
"!=": r"\neq",
|
||
|
|
}
|
||
|
|
|
||
|
|
return "%s %s %s" % (self._print(expr.lhs),
|
||
|
|
charmap[expr.rel_op], self._print(expr.rhs))
|
||
|
|
|
||
|
|
def _print_Piecewise(self, expr):
|
||
|
|
ecpairs = [r"%s & \text{for}\: %s" % (self._print(e), self._print(c))
|
||
|
|
for e, c in expr.args[:-1]]
|
||
|
|
if expr.args[-1].cond == true:
|
||
|
|
ecpairs.append(r"%s & \text{otherwise}" %
|
||
|
|
self._print(expr.args[-1].expr))
|
||
|
|
else:
|
||
|
|
ecpairs.append(r"%s & \text{for}\: %s" %
|
||
|
|
(self._print(expr.args[-1].expr),
|
||
|
|
self._print(expr.args[-1].cond)))
|
||
|
|
tex = r"\begin{cases} %s \end{cases}"
|
||
|
|
return tex % r" \\".join(ecpairs)
|
||
|
|
|
||
|
|
def _print_matrix_contents(self, expr):
|
||
|
|
lines = []
|
||
|
|
|
||
|
|
for line in range(expr.rows): # horrible, should be 'rows'
|
||
|
|
lines.append(" & ".join([self._print(i) for i in expr[line, :]]))
|
||
|
|
|
||
|
|
mat_str = self._settings['mat_str']
|
||
|
|
if mat_str is None:
|
||
|
|
if self._settings['mode'] == 'inline':
|
||
|
|
mat_str = 'smallmatrix'
|
||
|
|
else:
|
||
|
|
if (expr.cols <= 10) is True:
|
||
|
|
mat_str = 'matrix'
|
||
|
|
else:
|
||
|
|
mat_str = 'array'
|
||
|
|
|
||
|
|
out_str = r'\begin{%MATSTR%}%s\end{%MATSTR%}'
|
||
|
|
out_str = out_str.replace('%MATSTR%', mat_str)
|
||
|
|
if mat_str == 'array':
|
||
|
|
out_str = out_str.replace('%s', '{' + 'c'*expr.cols + '}%s')
|
||
|
|
return out_str % r"\\".join(lines)
|
||
|
|
|
||
|
|
def _print_MatrixBase(self, expr):
|
||
|
|
out_str = self._print_matrix_contents(expr)
|
||
|
|
if self._settings['mat_delim']:
|
||
|
|
left_delim = self._settings['mat_delim']
|
||
|
|
right_delim = self._delim_dict[left_delim]
|
||
|
|
out_str = r'\left' + left_delim + out_str + \
|
||
|
|
r'\right' + right_delim
|
||
|
|
return out_str
|
||
|
|
|
||
|
|
def _print_MatrixElement(self, expr):
|
||
|
|
return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True)\
|
||
|
|
+ '_{%s, %s}' % (self._print(expr.i), self._print(expr.j))
|
||
|
|
|
||
|
|
def _print_MatrixSlice(self, expr):
|
||
|
|
def latexslice(x, dim):
|
||
|
|
x = list(x)
|
||
|
|
if x[2] == 1:
|
||
|
|
del x[2]
|
||
|
|
if x[0] == 0:
|
||
|
|
x[0] = None
|
||
|
|
if x[1] == dim:
|
||
|
|
x[1] = None
|
||
|
|
return ':'.join(self._print(xi) if xi is not None else '' for xi in x)
|
||
|
|
return (self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) + r'\left[' +
|
||
|
|
latexslice(expr.rowslice, expr.parent.rows) + ', ' +
|
||
|
|
latexslice(expr.colslice, expr.parent.cols) + r'\right]')
|
||
|
|
|
||
|
|
def _print_BlockMatrix(self, expr):
|
||
|
|
return self._print(expr.blocks)
|
||
|
|
|
||
|
|
def _print_Transpose(self, expr):
|
||
|
|
mat = expr.arg
|
||
|
|
from sympy.matrices import MatrixSymbol, BlockMatrix
|
||
|
|
if (not isinstance(mat, MatrixSymbol) and
|
||
|
|
not isinstance(mat, BlockMatrix) and mat.is_MatrixExpr):
|
||
|
|
return r"\left(%s\right)^{T}" % self._print(mat)
|
||
|
|
else:
|
||
|
|
s = self.parenthesize(mat, precedence_traditional(expr), True)
|
||
|
|
if '^' in s:
|
||
|
|
return r"\left(%s\right)^{T}" % s
|
||
|
|
else:
|
||
|
|
return "%s^{T}" % s
|
||
|
|
|
||
|
|
def _print_Trace(self, expr):
|
||
|
|
mat = expr.arg
|
||
|
|
return r"\operatorname{tr}\left(%s \right)" % self._print(mat)
|
||
|
|
|
||
|
|
def _print_Adjoint(self, expr):
|
||
|
|
mat = expr.arg
|
||
|
|
from sympy.matrices import MatrixSymbol, BlockMatrix
|
||
|
|
if (not isinstance(mat, MatrixSymbol) and
|
||
|
|
not isinstance(mat, BlockMatrix) and mat.is_MatrixExpr):
|
||
|
|
return r"\left(%s\right)^{\dagger}" % self._print(mat)
|
||
|
|
else:
|
||
|
|
s = self.parenthesize(mat, precedence_traditional(expr), True)
|
||
|
|
if '^' in s:
|
||
|
|
return r"\left(%s\right)^{\dagger}" % s
|
||
|
|
else:
|
||
|
|
return r"%s^{\dagger}" % s
|
||
|
|
|
||
|
|
def _print_MatMul(self, expr):
|
||
|
|
from sympy import MatMul
|
||
|
|
|
||
|
|
# Parenthesize nested MatMul but not other types of Mul objects:
|
||
|
|
parens = lambda x: self._print(x) if isinstance(x, Mul) and not isinstance(x, MatMul) else \
|
||
|
|
self.parenthesize(x, precedence_traditional(expr), False)
|
||
|
|
|
||
|
|
args = list(expr.args)
|
||
|
|
if expr.could_extract_minus_sign():
|
||
|
|
if args[0] == -1:
|
||
|
|
args = args[1:]
|
||
|
|
else:
|
||
|
|
args[0] = -args[0]
|
||
|
|
return '- ' + ' '.join(map(parens, args))
|
||
|
|
else:
|
||
|
|
return ' '.join(map(parens, args))
|
||
|
|
|
||
|
|
def _print_Determinant(self, expr):
|
||
|
|
mat = expr.arg
|
||
|
|
if mat.is_MatrixExpr:
|
||
|
|
from sympy.matrices.expressions.blockmatrix import BlockMatrix
|
||
|
|
if isinstance(mat, BlockMatrix):
|
||
|
|
return r"\left|{%s}\right|" % self._print_matrix_contents(mat.blocks)
|
||
|
|
return r"\left|{%s}\right|" % self._print(mat)
|
||
|
|
return r"\left|{%s}\right|" % self._print_matrix_contents(mat)
|
||
|
|
|
||
|
|
|
||
|
|
def _print_Mod(self, expr, exp=None):
|
||
|
|
if exp is not None:
|
||
|
|
return r'\left(%s \bmod %s\right)^{%s}' % \
|
||
|
|
(self.parenthesize(expr.args[0], PRECEDENCE['Mul'],
|
||
|
|
strict=True),
|
||
|
|
self.parenthesize(expr.args[1], PRECEDENCE['Mul'],
|
||
|
|
strict=True),
|
||
|
|
exp)
|
||
|
|
return r'%s \bmod %s' % (self.parenthesize(expr.args[0],
|
||
|
|
PRECEDENCE['Mul'],
|
||
|
|
strict=True),
|
||
|
|
self.parenthesize(expr.args[1],
|
||
|
|
PRECEDENCE['Mul'],
|
||
|
|
strict=True))
|
||
|
|
|
||
|
|
def _print_HadamardProduct(self, expr):
|
||
|
|
args = expr.args
|
||
|
|
prec = PRECEDENCE['Pow']
|
||
|
|
parens = self.parenthesize
|
||
|
|
|
||
|
|
return r' \circ '.join(
|
||
|
|
(parens(arg, prec, strict=True) for arg in args))
|
||
|
|
|
||
|
|
def _print_HadamardPower(self, expr):
|
||
|
|
if precedence_traditional(expr.exp) < PRECEDENCE["Mul"]:
|
||
|
|
template = r"%s^{\circ \left({%s}\right)}"
|
||
|
|
else:
|
||
|
|
template = r"%s^{\circ {%s}}"
|
||
|
|
return self._helper_print_standard_power(expr, template)
|
||
|
|
|
||
|
|
def _print_KroneckerProduct(self, expr):
|
||
|
|
args = expr.args
|
||
|
|
prec = PRECEDENCE['Pow']
|
||
|
|
parens = self.parenthesize
|
||
|
|
|
||
|
|
return r' \otimes '.join(
|
||
|
|
(parens(arg, prec, strict=True) for arg in args))
|
||
|
|
|
||
|
|
def _print_MatPow(self, expr):
|
||
|
|
base, exp = expr.base, expr.exp
|
||
|
|
from sympy.matrices import MatrixSymbol
|
||
|
|
if not isinstance(base, MatrixSymbol) and base.is_MatrixExpr:
|
||
|
|
return "\\left(%s\\right)^{%s}" % (self._print(base),
|
||
|
|
self._print(exp))
|
||
|
|
else:
|
||
|
|
base_str = self._print(base)
|
||
|
|
if '^' in base_str:
|
||
|
|
return r"\left(%s\right)^{%s}" % (base_str, self._print(exp))
|
||
|
|
else:
|
||
|
|
return "%s^{%s}" % (base_str, self._print(exp))
|
||
|
|
|
||
|
|
def _print_MatrixSymbol(self, expr):
|
||
|
|
return self._print_Symbol(expr, style=self._settings[
|
||
|
|
'mat_symbol_style'])
|
||
|
|
|
||
|
|
def _print_ZeroMatrix(self, Z):
|
||
|
|
return "0" if self._settings[
|
||
|
|
'mat_symbol_style'] == 'plain' else r"\mathbf{0}"
|
||
|
|
|
||
|
|
def _print_OneMatrix(self, O):
|
||
|
|
return "1" if self._settings[
|
||
|
|
'mat_symbol_style'] == 'plain' else r"\mathbf{1}"
|
||
|
|
|
||
|
|
def _print_Identity(self, I):
|
||
|
|
return r"\mathbb{I}" if self._settings[
|
||
|
|
'mat_symbol_style'] == 'plain' else r"\mathbf{I}"
|
||
|
|
|
||
|
|
def _print_PermutationMatrix(self, P):
|
||
|
|
perm_str = self._print(P.args[0])
|
||
|
|
return "P_{%s}" % perm_str
|
||
|
|
|
||
|
|
def _print_NDimArray(self, expr: NDimArray):
|
||
|
|
|
||
|
|
if expr.rank() == 0:
|
||
|
|
return self._print(expr[()])
|
||
|
|
|
||
|
|
mat_str = self._settings['mat_str']
|
||
|
|
if mat_str is None:
|
||
|
|
if self._settings['mode'] == 'inline':
|
||
|
|
mat_str = 'smallmatrix'
|
||
|
|
else:
|
||
|
|
if (expr.rank() == 0) or (expr.shape[-1] <= 10):
|
||
|
|
mat_str = 'matrix'
|
||
|
|
else:
|
||
|
|
mat_str = 'array'
|
||
|
|
block_str = r'\begin{%MATSTR%}%s\end{%MATSTR%}'
|
||
|
|
block_str = block_str.replace('%MATSTR%', mat_str)
|
||
|
|
if mat_str == 'array':
|
||
|
|
block_str= block_str.replace('%s','{}%s')
|
||
|
|
if self._settings['mat_delim']:
|
||
|
|
left_delim: str = self._settings['mat_delim']
|
||
|
|
right_delim = self._delim_dict[left_delim]
|
||
|
|
block_str = r'\left' + left_delim + block_str + \
|
||
|
|
r'\right' + right_delim
|
||
|
|
|
||
|
|
if expr.rank() == 0:
|
||
|
|
return block_str % ""
|
||
|
|
|
||
|
|
level_str: list[list[str]] = [[] for i in range(expr.rank() + 1)]
|
||
|
|
shape_ranges = [list(range(i)) for i in expr.shape]
|
||
|
|
for outer_i in itertools.product(*shape_ranges):
|
||
|
|
level_str[-1].append(self._print(expr[outer_i]))
|
||
|
|
even = True
|
||
|
|
for back_outer_i in range(expr.rank()-1, -1, -1):
|
||
|
|
if len(level_str[back_outer_i+1]) < expr.shape[back_outer_i]:
|
||
|
|
break
|
||
|
|
if even:
|
||
|
|
level_str[back_outer_i].append(
|
||
|
|
r" & ".join(level_str[back_outer_i+1]))
|
||
|
|
else:
|
||
|
|
level_str[back_outer_i].append(
|
||
|
|
block_str % (r"\\".join(level_str[back_outer_i+1])))
|
||
|
|
if len(level_str[back_outer_i+1]) == 1:
|
||
|
|
level_str[back_outer_i][-1] = r"\left[" + \
|
||
|
|
level_str[back_outer_i][-1] + r"\right]"
|
||
|
|
even = not even
|
||
|
|
level_str[back_outer_i+1] = []
|
||
|
|
|
||
|
|
out_str = level_str[0][0]
|
||
|
|
|
||
|
|
if expr.rank() % 2 == 1:
|
||
|
|
out_str = block_str % out_str
|
||
|
|
|
||
|
|
return out_str
|
||
|
|
|
||
|
|
def _printer_tensor_indices(self, name, indices, index_map: dict):
|
||
|
|
out_str = self._print(name)
|
||
|
|
last_valence = None
|
||
|
|
prev_map = None
|
||
|
|
for index in indices:
|
||
|
|
new_valence = index.is_up
|
||
|
|
if ((index in index_map) or prev_map) and \
|
||
|
|
last_valence == new_valence:
|
||
|
|
out_str += ","
|
||
|
|
if last_valence != new_valence:
|
||
|
|
if last_valence is not None:
|
||
|
|
out_str += "}"
|
||
|
|
if index.is_up:
|
||
|
|
out_str += "{}^{"
|
||
|
|
else:
|
||
|
|
out_str += "{}_{"
|
||
|
|
out_str += self._print(index.args[0])
|
||
|
|
if index in index_map:
|
||
|
|
out_str += "="
|
||
|
|
out_str += self._print(index_map[index])
|
||
|
|
prev_map = True
|
||
|
|
else:
|
||
|
|
prev_map = False
|
||
|
|
last_valence = new_valence
|
||
|
|
if last_valence is not None:
|
||
|
|
out_str += "}"
|
||
|
|
return out_str
|
||
|
|
|
||
|
|
def _print_Tensor(self, expr):
|
||
|
|
name = expr.args[0].args[0]
|
||
|
|
indices = expr.get_indices()
|
||
|
|
return self._printer_tensor_indices(name, indices, {})
|
||
|
|
|
||
|
|
def _print_TensorElement(self, expr):
|
||
|
|
name = expr.expr.args[0].args[0]
|
||
|
|
indices = expr.expr.get_indices()
|
||
|
|
index_map = expr.index_map
|
||
|
|
return self._printer_tensor_indices(name, indices, index_map)
|
||
|
|
|
||
|
|
def _print_TensMul(self, expr):
|
||
|
|
# prints expressions like "A(a)", "3*A(a)", "(1+x)*A(a)"
|
||
|
|
sign, args = expr._get_args_for_traditional_printer()
|
||
|
|
return sign + "".join(
|
||
|
|
[self.parenthesize(arg, precedence(expr)) for arg in args]
|
||
|
|
)
|
||
|
|
|
||
|
|
def _print_TensAdd(self, expr):
|
||
|
|
a = []
|
||
|
|
args = expr.args
|
||
|
|
for x in args:
|
||
|
|
a.append(self.parenthesize(x, precedence(expr)))
|
||
|
|
a.sort()
|
||
|
|
s = ' + '.join(a)
|
||
|
|
s = s.replace('+ -', '- ')
|
||
|
|
return s
|
||
|
|
|
||
|
|
def _print_TensorIndex(self, expr):
|
||
|
|
return "{}%s{%s}" % (
|
||
|
|
"^" if expr.is_up else "_",
|
||
|
|
self._print(expr.args[0])
|
||
|
|
)
|
||
|
|
|
||
|
|
def _print_PartialDerivative(self, expr):
|
||
|
|
if len(expr.variables) == 1:
|
||
|
|
return r"\frac{\partial}{\partial {%s}}{%s}" % (
|
||
|
|
self._print(expr.variables[0]),
|
||
|
|
self.parenthesize(expr.expr, PRECEDENCE["Mul"], False)
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
return r"\frac{\partial^{%s}}{%s}{%s}" % (
|
||
|
|
len(expr.variables),
|
||
|
|
" ".join([r"\partial {%s}" % self._print(i) for i in expr.variables]),
|
||
|
|
self.parenthesize(expr.expr, PRECEDENCE["Mul"], False)
|
||
|
|
)
|
||
|
|
|
||
|
|
def _print_ArraySymbol(self, expr):
|
||
|
|
return self._print(expr.name)
|
||
|
|
|
||
|
|
def _print_ArrayElement(self, expr):
|
||
|
|
return "{{%s}_{%s}}" % (
|
||
|
|
self.parenthesize(expr.name, PRECEDENCE["Func"], True),
|
||
|
|
", ".join([f"{self._print(i)}" for i in expr.indices]))
|
||
|
|
|
||
|
|
def _print_UniversalSet(self, expr):
|
||
|
|
return r"\mathbb{U}"
|
||
|
|
|
||
|
|
def _print_frac(self, expr, exp=None):
|
||
|
|
if exp is None:
|
||
|
|
return r"\operatorname{frac}{\left(%s\right)}" % self._print(expr.args[0])
|
||
|
|
else:
|
||
|
|
return r"\operatorname{frac}{\left(%s\right)}^{%s}" % (
|
||
|
|
self._print(expr.args[0]), exp)
|
||
|
|
|
||
|
|
def _print_tuple(self, expr):
|
||
|
|
if self._settings['decimal_separator'] == 'comma':
|
||
|
|
sep = ";"
|
||
|
|
elif self._settings['decimal_separator'] == 'period':
|
||
|
|
sep = ","
|
||
|
|
else:
|
||
|
|
raise ValueError('Unknown Decimal Separator')
|
||
|
|
|
||
|
|
if len(expr) == 1:
|
||
|
|
# 1-tuple needs a trailing separator
|
||
|
|
return self._add_parens_lspace(self._print(expr[0]) + sep)
|
||
|
|
else:
|
||
|
|
return self._add_parens_lspace(
|
||
|
|
(sep + r" \ ").join([self._print(i) for i in expr]))
|
||
|
|
|
||
|
|
def _print_TensorProduct(self, expr):
|
||
|
|
elements = [self._print(a) for a in expr.args]
|
||
|
|
return r' \otimes '.join(elements)
|
||
|
|
|
||
|
|
def _print_WedgeProduct(self, expr):
|
||
|
|
elements = [self._print(a) for a in expr.args]
|
||
|
|
return r' \wedge '.join(elements)
|
||
|
|
|
||
|
|
def _print_Tuple(self, expr):
|
||
|
|
return self._print_tuple(expr)
|
||
|
|
|
||
|
|
def _print_list(self, expr):
|
||
|
|
if self._settings['decimal_separator'] == 'comma':
|
||
|
|
return r"\left[ %s\right]" % \
|
||
|
|
r"; \ ".join([self._print(i) for i in expr])
|
||
|
|
elif self._settings['decimal_separator'] == 'period':
|
||
|
|
return r"\left[ %s\right]" % \
|
||
|
|
r", \ ".join([self._print(i) for i in expr])
|
||
|
|
else:
|
||
|
|
raise ValueError('Unknown Decimal Separator')
|
||
|
|
|
||
|
|
|
||
|
|
def _print_dict(self, d):
|
||
|
|
keys = sorted(d.keys(), key=default_sort_key)
|
||
|
|
items = []
|
||
|
|
|
||
|
|
for key in keys:
|
||
|
|
val = d[key]
|
||
|
|
items.append("%s : %s" % (self._print(key), self._print(val)))
|
||
|
|
|
||
|
|
return r"\left\{ %s\right\}" % r", \ ".join(items)
|
||
|
|
|
||
|
|
def _print_Dict(self, expr):
|
||
|
|
return self._print_dict(expr)
|
||
|
|
|
||
|
|
def _print_DiracDelta(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 1 or expr.args[1] == 0:
|
||
|
|
tex = r"\delta\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
else:
|
||
|
|
tex = r"\delta^{\left( %s \right)}\left( %s \right)" % (
|
||
|
|
self._print(expr.args[1]), self._print(expr.args[0]))
|
||
|
|
if exp:
|
||
|
|
tex = r"\left(%s\right)^{%s}" % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_SingularityFunction(self, expr, exp=None):
|
||
|
|
shift = self._print(expr.args[0] - expr.args[1])
|
||
|
|
power = self._print(expr.args[2])
|
||
|
|
tex = r"{\left\langle %s \right\rangle}^{%s}" % (shift, power)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"{\left({\langle %s \rangle}^{%s}\right)}^{%s}" % (shift, power, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_Heaviside(self, expr, exp=None):
|
||
|
|
pargs = ', '.join(self._print(arg) for arg in expr.pargs)
|
||
|
|
tex = r"\theta\left(%s\right)" % pargs
|
||
|
|
if exp:
|
||
|
|
tex = r"\left(%s\right)^{%s}" % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_KroneckerDelta(self, expr, exp=None):
|
||
|
|
i = self._print(expr.args[0])
|
||
|
|
j = self._print(expr.args[1])
|
||
|
|
if expr.args[0].is_Atom and expr.args[1].is_Atom:
|
||
|
|
tex = r'\delta_{%s %s}' % (i, j)
|
||
|
|
else:
|
||
|
|
tex = r'\delta_{%s, %s}' % (i, j)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r'\left(%s\right)^{%s}' % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_LeviCivita(self, expr, exp=None):
|
||
|
|
indices = map(self._print, expr.args)
|
||
|
|
if all(x.is_Atom for x in expr.args):
|
||
|
|
tex = r'\varepsilon_{%s}' % " ".join(indices)
|
||
|
|
else:
|
||
|
|
tex = r'\varepsilon_{%s}' % ", ".join(indices)
|
||
|
|
if exp:
|
||
|
|
tex = r'\left(%s\right)^{%s}' % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_RandomDomain(self, d):
|
||
|
|
if hasattr(d, 'as_boolean'):
|
||
|
|
return '\\text{Domain: }' + self._print(d.as_boolean())
|
||
|
|
elif hasattr(d, 'set'):
|
||
|
|
return ('\\text{Domain: }' + self._print(d.symbols) + ' \\in ' +
|
||
|
|
self._print(d.set))
|
||
|
|
elif hasattr(d, 'symbols'):
|
||
|
|
return '\\text{Domain on }' + self._print(d.symbols)
|
||
|
|
else:
|
||
|
|
return self._print(None)
|
||
|
|
|
||
|
|
def _print_FiniteSet(self, s):
|
||
|
|
items = sorted(s.args, key=default_sort_key)
|
||
|
|
return self._print_set(items)
|
||
|
|
|
||
|
|
def _print_set(self, s):
|
||
|
|
items = sorted(s, key=default_sort_key)
|
||
|
|
if self._settings['decimal_separator'] == 'comma':
|
||
|
|
items = "; ".join(map(self._print, items))
|
||
|
|
elif self._settings['decimal_separator'] == 'period':
|
||
|
|
items = ", ".join(map(self._print, items))
|
||
|
|
else:
|
||
|
|
raise ValueError('Unknown Decimal Separator')
|
||
|
|
return r"\left\{%s\right\}" % items
|
||
|
|
|
||
|
|
|
||
|
|
_print_frozenset = _print_set
|
||
|
|
|
||
|
|
def _print_Range(self, s):
|
||
|
|
def _print_symbolic_range():
|
||
|
|
# Symbolic Range that cannot be resolved
|
||
|
|
if s.args[0] == 0:
|
||
|
|
if s.args[2] == 1:
|
||
|
|
cont = self._print(s.args[1])
|
||
|
|
else:
|
||
|
|
cont = ", ".join(self._print(arg) for arg in s.args)
|
||
|
|
else:
|
||
|
|
if s.args[2] == 1:
|
||
|
|
cont = ", ".join(self._print(arg) for arg in s.args[:2])
|
||
|
|
else:
|
||
|
|
cont = ", ".join(self._print(arg) for arg in s.args)
|
||
|
|
|
||
|
|
return(f"\\text{{Range}}\\left({cont}\\right)")
|
||
|
|
|
||
|
|
dots = object()
|
||
|
|
|
||
|
|
if s.start.is_infinite and s.stop.is_infinite:
|
||
|
|
if s.step.is_positive:
|
||
|
|
printset = dots, -1, 0, 1, dots
|
||
|
|
else:
|
||
|
|
printset = dots, 1, 0, -1, dots
|
||
|
|
elif s.start.is_infinite:
|
||
|
|
printset = dots, s[-1] - s.step, s[-1]
|
||
|
|
elif s.stop.is_infinite:
|
||
|
|
it = iter(s)
|
||
|
|
printset = next(it), next(it), dots
|
||
|
|
elif s.is_empty is not None:
|
||
|
|
if (s.size < 4) == True:
|
||
|
|
printset = tuple(s)
|
||
|
|
elif s.is_iterable:
|
||
|
|
it = iter(s)
|
||
|
|
printset = next(it), next(it), dots, s[-1]
|
||
|
|
else:
|
||
|
|
return _print_symbolic_range()
|
||
|
|
else:
|
||
|
|
return _print_symbolic_range()
|
||
|
|
return (r"\left\{" +
|
||
|
|
r", ".join(self._print(el) if el is not dots else r'\ldots' for el in printset) +
|
||
|
|
r"\right\}")
|
||
|
|
|
||
|
|
def __print_number_polynomial(self, expr, letter, exp=None):
|
||
|
|
if len(expr.args) == 2:
|
||
|
|
if exp is not None:
|
||
|
|
return r"%s_{%s}^{%s}\left(%s\right)" % (letter,
|
||
|
|
self._print(expr.args[0]), exp,
|
||
|
|
self._print(expr.args[1]))
|
||
|
|
return r"%s_{%s}\left(%s\right)" % (letter,
|
||
|
|
self._print(expr.args[0]), self._print(expr.args[1]))
|
||
|
|
|
||
|
|
tex = r"%s_{%s}" % (letter, self._print(expr.args[0]))
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"%s^{%s}" % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_bernoulli(self, expr, exp=None):
|
||
|
|
return self.__print_number_polynomial(expr, "B", exp)
|
||
|
|
|
||
|
|
def _print_genocchi(self, expr, exp=None):
|
||
|
|
return self.__print_number_polynomial(expr, "G", exp)
|
||
|
|
|
||
|
|
def _print_bell(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 3:
|
||
|
|
tex1 = r"B_{%s, %s}" % (self._print(expr.args[0]),
|
||
|
|
self._print(expr.args[1]))
|
||
|
|
tex2 = r"\left(%s\right)" % r", ".join(self._print(el) for
|
||
|
|
el in expr.args[2])
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"%s^{%s}%s" % (tex1, exp, tex2)
|
||
|
|
else:
|
||
|
|
tex = tex1 + tex2
|
||
|
|
return tex
|
||
|
|
return self.__print_number_polynomial(expr, "B", exp)
|
||
|
|
|
||
|
|
def _print_fibonacci(self, expr, exp=None):
|
||
|
|
return self.__print_number_polynomial(expr, "F", exp)
|
||
|
|
|
||
|
|
def _print_lucas(self, expr, exp=None):
|
||
|
|
tex = r"L_{%s}" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"%s^{%s}" % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_tribonacci(self, expr, exp=None):
|
||
|
|
return self.__print_number_polynomial(expr, "T", exp)
|
||
|
|
|
||
|
|
def _print_SeqFormula(self, s):
|
||
|
|
dots = object()
|
||
|
|
if len(s.start.free_symbols) > 0 or len(s.stop.free_symbols) > 0:
|
||
|
|
return r"\left\{%s\right\}_{%s=%s}^{%s}" % (
|
||
|
|
self._print(s.formula),
|
||
|
|
self._print(s.variables[0]),
|
||
|
|
self._print(s.start),
|
||
|
|
self._print(s.stop)
|
||
|
|
)
|
||
|
|
if s.start is S.NegativeInfinity:
|
||
|
|
stop = s.stop
|
||
|
|
printset = (dots, s.coeff(stop - 3), s.coeff(stop - 2),
|
||
|
|
s.coeff(stop - 1), s.coeff(stop))
|
||
|
|
elif s.stop is S.Infinity or s.length > 4:
|
||
|
|
printset = s[:4]
|
||
|
|
printset.append(dots)
|
||
|
|
else:
|
||
|
|
printset = tuple(s)
|
||
|
|
|
||
|
|
return (r"\left[" +
|
||
|
|
r", ".join(self._print(el) if el is not dots else r'\ldots' for el in printset) +
|
||
|
|
r"\right]")
|
||
|
|
|
||
|
|
_print_SeqPer = _print_SeqFormula
|
||
|
|
_print_SeqAdd = _print_SeqFormula
|
||
|
|
_print_SeqMul = _print_SeqFormula
|
||
|
|
|
||
|
|
def _print_Interval(self, i):
|
||
|
|
if i.start == i.end:
|
||
|
|
return r"\left\{%s\right\}" % self._print(i.start)
|
||
|
|
|
||
|
|
else:
|
||
|
|
if i.left_open:
|
||
|
|
left = '('
|
||
|
|
else:
|
||
|
|
left = '['
|
||
|
|
|
||
|
|
if i.right_open:
|
||
|
|
right = ')'
|
||
|
|
else:
|
||
|
|
right = ']'
|
||
|
|
|
||
|
|
return r"\left%s%s, %s\right%s" % \
|
||
|
|
(left, self._print(i.start), self._print(i.end), right)
|
||
|
|
|
||
|
|
def _print_AccumulationBounds(self, i):
|
||
|
|
return r"\left\langle %s, %s\right\rangle" % \
|
||
|
|
(self._print(i.min), self._print(i.max))
|
||
|
|
|
||
|
|
def _print_Union(self, u):
|
||
|
|
prec = precedence_traditional(u)
|
||
|
|
args_str = [self.parenthesize(i, prec) for i in u.args]
|
||
|
|
return r" \cup ".join(args_str)
|
||
|
|
|
||
|
|
def _print_Complement(self, u):
|
||
|
|
prec = precedence_traditional(u)
|
||
|
|
args_str = [self.parenthesize(i, prec) for i in u.args]
|
||
|
|
return r" \setminus ".join(args_str)
|
||
|
|
|
||
|
|
def _print_Intersection(self, u):
|
||
|
|
prec = precedence_traditional(u)
|
||
|
|
args_str = [self.parenthesize(i, prec) for i in u.args]
|
||
|
|
return r" \cap ".join(args_str)
|
||
|
|
|
||
|
|
def _print_SymmetricDifference(self, u):
|
||
|
|
prec = precedence_traditional(u)
|
||
|
|
args_str = [self.parenthesize(i, prec) for i in u.args]
|
||
|
|
return r" \triangle ".join(args_str)
|
||
|
|
|
||
|
|
def _print_ProductSet(self, p):
|
||
|
|
prec = precedence_traditional(p)
|
||
|
|
if len(p.sets) >= 1 and not has_variety(p.sets):
|
||
|
|
return self.parenthesize(p.sets[0], prec) + "^{%d}" % len(p.sets)
|
||
|
|
return r" \times ".join(
|
||
|
|
self.parenthesize(set, prec) for set in p.sets)
|
||
|
|
|
||
|
|
def _print_EmptySet(self, e):
|
||
|
|
return r"\emptyset"
|
||
|
|
|
||
|
|
def _print_Naturals(self, n):
|
||
|
|
return r"\mathbb{N}"
|
||
|
|
|
||
|
|
def _print_Naturals0(self, n):
|
||
|
|
return r"\mathbb{N}_0"
|
||
|
|
|
||
|
|
def _print_Integers(self, i):
|
||
|
|
return r"\mathbb{Z}"
|
||
|
|
|
||
|
|
def _print_Rationals(self, i):
|
||
|
|
return r"\mathbb{Q}"
|
||
|
|
|
||
|
|
def _print_Reals(self, i):
|
||
|
|
return r"\mathbb{R}"
|
||
|
|
|
||
|
|
def _print_Complexes(self, i):
|
||
|
|
return r"\mathbb{C}"
|
||
|
|
|
||
|
|
def _print_ImageSet(self, s):
|
||
|
|
expr = s.lamda.expr
|
||
|
|
sig = s.lamda.signature
|
||
|
|
xys = ((self._print(x), self._print(y)) for x, y in zip(sig, s.base_sets))
|
||
|
|
xinys = r", ".join(r"%s \in %s" % xy for xy in xys)
|
||
|
|
return r"\left\{%s\; \middle|\; %s\right\}" % (self._print(expr), xinys)
|
||
|
|
|
||
|
|
def _print_ConditionSet(self, s):
|
||
|
|
vars_print = ', '.join([self._print(var) for var in Tuple(s.sym)])
|
||
|
|
if s.base_set is S.UniversalSet:
|
||
|
|
return r"\left\{%s\; \middle|\; %s \right\}" % \
|
||
|
|
(vars_print, self._print(s.condition))
|
||
|
|
|
||
|
|
return r"\left\{%s\; \middle|\; %s \in %s \wedge %s \right\}" % (
|
||
|
|
vars_print,
|
||
|
|
vars_print,
|
||
|
|
self._print(s.base_set),
|
||
|
|
self._print(s.condition))
|
||
|
|
|
||
|
|
def _print_PowerSet(self, expr):
|
||
|
|
arg_print = self._print(expr.args[0])
|
||
|
|
return r"\mathcal{{P}}\left({}\right)".format(arg_print)
|
||
|
|
|
||
|
|
def _print_ComplexRegion(self, s):
|
||
|
|
vars_print = ', '.join([self._print(var) for var in s.variables])
|
||
|
|
return r"\left\{%s\; \middle|\; %s \in %s \right\}" % (
|
||
|
|
self._print(s.expr),
|
||
|
|
vars_print,
|
||
|
|
self._print(s.sets))
|
||
|
|
|
||
|
|
def _print_Contains(self, e):
|
||
|
|
return r"%s \in %s" % tuple(self._print(a) for a in e.args)
|
||
|
|
|
||
|
|
def _print_FourierSeries(self, s):
|
||
|
|
if s.an.formula is S.Zero and s.bn.formula is S.Zero:
|
||
|
|
return self._print(s.a0)
|
||
|
|
return self._print_Add(s.truncate()) + r' + \ldots'
|
||
|
|
|
||
|
|
def _print_FormalPowerSeries(self, s):
|
||
|
|
return self._print_Add(s.infinite)
|
||
|
|
|
||
|
|
def _print_FiniteField(self, expr):
|
||
|
|
return r"\mathbb{F}_{%s}" % expr.mod
|
||
|
|
|
||
|
|
def _print_IntegerRing(self, expr):
|
||
|
|
return r"\mathbb{Z}"
|
||
|
|
|
||
|
|
def _print_RationalField(self, expr):
|
||
|
|
return r"\mathbb{Q}"
|
||
|
|
|
||
|
|
def _print_RealField(self, expr):
|
||
|
|
return r"\mathbb{R}"
|
||
|
|
|
||
|
|
def _print_ComplexField(self, expr):
|
||
|
|
return r"\mathbb{C}"
|
||
|
|
|
||
|
|
def _print_PolynomialRing(self, expr):
|
||
|
|
domain = self._print(expr.domain)
|
||
|
|
symbols = ", ".join(map(self._print, expr.symbols))
|
||
|
|
return r"%s\left[%s\right]" % (domain, symbols)
|
||
|
|
|
||
|
|
def _print_FractionField(self, expr):
|
||
|
|
domain = self._print(expr.domain)
|
||
|
|
symbols = ", ".join(map(self._print, expr.symbols))
|
||
|
|
return r"%s\left(%s\right)" % (domain, symbols)
|
||
|
|
|
||
|
|
def _print_PolynomialRingBase(self, expr):
|
||
|
|
domain = self._print(expr.domain)
|
||
|
|
symbols = ", ".join(map(self._print, expr.symbols))
|
||
|
|
inv = ""
|
||
|
|
if not expr.is_Poly:
|
||
|
|
inv = r"S_<^{-1}"
|
||
|
|
return r"%s%s\left[%s\right]" % (inv, domain, symbols)
|
||
|
|
|
||
|
|
def _print_Poly(self, poly):
|
||
|
|
cls = poly.__class__.__name__
|
||
|
|
terms = []
|
||
|
|
for monom, coeff in poly.terms():
|
||
|
|
s_monom = ''
|
||
|
|
for i, exp in enumerate(monom):
|
||
|
|
if exp > 0:
|
||
|
|
if exp == 1:
|
||
|
|
s_monom += self._print(poly.gens[i])
|
||
|
|
else:
|
||
|
|
s_monom += self._print(pow(poly.gens[i], exp))
|
||
|
|
|
||
|
|
if coeff.is_Add:
|
||
|
|
if s_monom:
|
||
|
|
s_coeff = r"\left(%s\right)" % self._print(coeff)
|
||
|
|
else:
|
||
|
|
s_coeff = self._print(coeff)
|
||
|
|
else:
|
||
|
|
if s_monom:
|
||
|
|
if coeff is S.One:
|
||
|
|
terms.extend(['+', s_monom])
|
||
|
|
continue
|
||
|
|
|
||
|
|
if coeff is S.NegativeOne:
|
||
|
|
terms.extend(['-', s_monom])
|
||
|
|
continue
|
||
|
|
|
||
|
|
s_coeff = self._print(coeff)
|
||
|
|
|
||
|
|
if not s_monom:
|
||
|
|
s_term = s_coeff
|
||
|
|
else:
|
||
|
|
s_term = s_coeff + " " + s_monom
|
||
|
|
|
||
|
|
if s_term.startswith('-'):
|
||
|
|
terms.extend(['-', s_term[1:]])
|
||
|
|
else:
|
||
|
|
terms.extend(['+', s_term])
|
||
|
|
|
||
|
|
if terms[0] in ('-', '+'):
|
||
|
|
modifier = terms.pop(0)
|
||
|
|
|
||
|
|
if modifier == '-':
|
||
|
|
terms[0] = '-' + terms[0]
|
||
|
|
|
||
|
|
expr = ' '.join(terms)
|
||
|
|
gens = list(map(self._print, poly.gens))
|
||
|
|
domain = "domain=%s" % self._print(poly.get_domain())
|
||
|
|
|
||
|
|
args = ", ".join([expr] + gens + [domain])
|
||
|
|
if cls in accepted_latex_functions:
|
||
|
|
tex = r"\%s {\left(%s \right)}" % (cls, args)
|
||
|
|
else:
|
||
|
|
tex = r"\operatorname{%s}{\left( %s \right)}" % (cls, args)
|
||
|
|
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_ComplexRootOf(self, root):
|
||
|
|
cls = root.__class__.__name__
|
||
|
|
if cls == "ComplexRootOf":
|
||
|
|
cls = "CRootOf"
|
||
|
|
expr = self._print(root.expr)
|
||
|
|
index = root.index
|
||
|
|
if cls in accepted_latex_functions:
|
||
|
|
return r"\%s {\left(%s, %d\right)}" % (cls, expr, index)
|
||
|
|
else:
|
||
|
|
return r"\operatorname{%s} {\left(%s, %d\right)}" % (cls, expr,
|
||
|
|
index)
|
||
|
|
|
||
|
|
def _print_RootSum(self, expr):
|
||
|
|
cls = expr.__class__.__name__
|
||
|
|
args = [self._print(expr.expr)]
|
||
|
|
|
||
|
|
if expr.fun is not S.IdentityFunction:
|
||
|
|
args.append(self._print(expr.fun))
|
||
|
|
|
||
|
|
if cls in accepted_latex_functions:
|
||
|
|
return r"\%s {\left(%s\right)}" % (cls, ", ".join(args))
|
||
|
|
else:
|
||
|
|
return r"\operatorname{%s} {\left(%s\right)}" % (cls,
|
||
|
|
", ".join(args))
|
||
|
|
|
||
|
|
def _print_OrdinalOmega(self, expr):
|
||
|
|
return r"\omega"
|
||
|
|
|
||
|
|
def _print_OmegaPower(self, expr):
|
||
|
|
exp, mul = expr.args
|
||
|
|
if mul != 1:
|
||
|
|
if exp != 1:
|
||
|
|
return r"{} \omega^{{{}}}".format(mul, exp)
|
||
|
|
else:
|
||
|
|
return r"{} \omega".format(mul)
|
||
|
|
else:
|
||
|
|
if exp != 1:
|
||
|
|
return r"\omega^{{{}}}".format(exp)
|
||
|
|
else:
|
||
|
|
return r"\omega"
|
||
|
|
|
||
|
|
def _print_Ordinal(self, expr):
|
||
|
|
return " + ".join([self._print(arg) for arg in expr.args])
|
||
|
|
|
||
|
|
def _print_PolyElement(self, poly):
|
||
|
|
mul_symbol = self._settings['mul_symbol_latex']
|
||
|
|
return poly.str(self, PRECEDENCE, "{%s}^{%d}", mul_symbol)
|
||
|
|
|
||
|
|
def _print_FracElement(self, frac):
|
||
|
|
if frac.denom == 1:
|
||
|
|
return self._print(frac.numer)
|
||
|
|
else:
|
||
|
|
numer = self._print(frac.numer)
|
||
|
|
denom = self._print(frac.denom)
|
||
|
|
return r"\frac{%s}{%s}" % (numer, denom)
|
||
|
|
|
||
|
|
def _print_euler(self, expr, exp=None):
|
||
|
|
m, x = (expr.args[0], None) if len(expr.args) == 1 else expr.args
|
||
|
|
tex = r"E_{%s}" % self._print(m)
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"%s^{%s}" % (tex, exp)
|
||
|
|
if x is not None:
|
||
|
|
tex = r"%s\left(%s\right)" % (tex, self._print(x))
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_catalan(self, expr, exp=None):
|
||
|
|
tex = r"C_{%s}" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
tex = r"%s^{%s}" % (tex, exp)
|
||
|
|
return tex
|
||
|
|
|
||
|
|
def _print_UnifiedTransform(self, expr, s, inverse=False):
|
||
|
|
return r"\mathcal{{{}}}{}_{{{}}}\left[{}\right]\left({}\right)".format(s, '^{-1}' if inverse else '', self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2]))
|
||
|
|
|
||
|
|
def _print_MellinTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'M')
|
||
|
|
|
||
|
|
def _print_InverseMellinTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'M', True)
|
||
|
|
|
||
|
|
def _print_LaplaceTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'L')
|
||
|
|
|
||
|
|
def _print_InverseLaplaceTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'L', True)
|
||
|
|
|
||
|
|
def _print_FourierTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'F')
|
||
|
|
|
||
|
|
def _print_InverseFourierTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'F', True)
|
||
|
|
|
||
|
|
def _print_SineTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'SIN')
|
||
|
|
|
||
|
|
def _print_InverseSineTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'SIN', True)
|
||
|
|
|
||
|
|
def _print_CosineTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'COS')
|
||
|
|
|
||
|
|
def _print_InverseCosineTransform(self, expr):
|
||
|
|
return self._print_UnifiedTransform(expr, 'COS', True)
|
||
|
|
|
||
|
|
def _print_DMP(self, p):
|
||
|
|
try:
|
||
|
|
if p.ring is not None:
|
||
|
|
# TODO incorporate order
|
||
|
|
return self._print(p.ring.to_sympy(p))
|
||
|
|
except SympifyError:
|
||
|
|
pass
|
||
|
|
return self._print(repr(p))
|
||
|
|
|
||
|
|
def _print_DMF(self, p):
|
||
|
|
return self._print_DMP(p)
|
||
|
|
|
||
|
|
def _print_Object(self, object):
|
||
|
|
return self._print(Symbol(object.name))
|
||
|
|
|
||
|
|
def _print_LambertW(self, expr, exp=None):
|
||
|
|
arg0 = self._print(expr.args[0])
|
||
|
|
exp = r"^{%s}" % (exp,) if exp is not None else ""
|
||
|
|
if len(expr.args) == 1:
|
||
|
|
result = r"W%s\left(%s\right)" % (exp, arg0)
|
||
|
|
else:
|
||
|
|
arg1 = self._print(expr.args[1])
|
||
|
|
result = "W{0}_{{{1}}}\\left({2}\\right)".format(exp, arg1, arg0)
|
||
|
|
return result
|
||
|
|
|
||
|
|
def _print_Expectation(self, expr):
|
||
|
|
return r"\operatorname{{E}}\left[{}\right]".format(self._print(expr.args[0]))
|
||
|
|
|
||
|
|
def _print_Variance(self, expr):
|
||
|
|
return r"\operatorname{{Var}}\left({}\right)".format(self._print(expr.args[0]))
|
||
|
|
|
||
|
|
def _print_Covariance(self, expr):
|
||
|
|
return r"\operatorname{{Cov}}\left({}\right)".format(", ".join(self._print(arg) for arg in expr.args))
|
||
|
|
|
||
|
|
def _print_Probability(self, expr):
|
||
|
|
return r"\operatorname{{P}}\left({}\right)".format(self._print(expr.args[0]))
|
||
|
|
|
||
|
|
def _print_Morphism(self, morphism):
|
||
|
|
domain = self._print(morphism.domain)
|
||
|
|
codomain = self._print(morphism.codomain)
|
||
|
|
return "%s\\rightarrow %s" % (domain, codomain)
|
||
|
|
|
||
|
|
def _print_TransferFunction(self, expr):
|
||
|
|
num, den = self._print(expr.num), self._print(expr.den)
|
||
|
|
return r"\frac{%s}{%s}" % (num, den)
|
||
|
|
|
||
|
|
def _print_Series(self, expr):
|
||
|
|
args = list(expr.args)
|
||
|
|
parens = lambda x: self.parenthesize(x, precedence_traditional(expr),
|
||
|
|
False)
|
||
|
|
return ' '.join(map(parens, args))
|
||
|
|
|
||
|
|
def _print_MIMOSeries(self, expr):
|
||
|
|
from sympy.physics.control.lti import MIMOParallel
|
||
|
|
args = list(expr.args)[::-1]
|
||
|
|
parens = lambda x: self.parenthesize(x, precedence_traditional(expr),
|
||
|
|
False) if isinstance(x, MIMOParallel) else self._print(x)
|
||
|
|
return r"\cdot".join(map(parens, args))
|
||
|
|
|
||
|
|
def _print_Parallel(self, expr):
|
||
|
|
return ' + '.join(map(self._print, expr.args))
|
||
|
|
|
||
|
|
def _print_MIMOParallel(self, expr):
|
||
|
|
return ' + '.join(map(self._print, expr.args))
|
||
|
|
|
||
|
|
def _print_Feedback(self, expr):
|
||
|
|
from sympy.physics.control import TransferFunction, Series
|
||
|
|
|
||
|
|
num, tf = expr.sys1, TransferFunction(1, 1, expr.var)
|
||
|
|
num_arg_list = list(num.args) if isinstance(num, Series) else [num]
|
||
|
|
den_arg_list = list(expr.sys2.args) if \
|
||
|
|
isinstance(expr.sys2, Series) else [expr.sys2]
|
||
|
|
den_term_1 = tf
|
||
|
|
|
||
|
|
if isinstance(num, Series) and isinstance(expr.sys2, Series):
|
||
|
|
den_term_2 = Series(*num_arg_list, *den_arg_list)
|
||
|
|
elif isinstance(num, Series) and isinstance(expr.sys2, TransferFunction):
|
||
|
|
if expr.sys2 == tf:
|
||
|
|
den_term_2 = Series(*num_arg_list)
|
||
|
|
else:
|
||
|
|
den_term_2 = tf, Series(*num_arg_list, expr.sys2)
|
||
|
|
elif isinstance(num, TransferFunction) and isinstance(expr.sys2, Series):
|
||
|
|
if num == tf:
|
||
|
|
den_term_2 = Series(*den_arg_list)
|
||
|
|
else:
|
||
|
|
den_term_2 = Series(num, *den_arg_list)
|
||
|
|
else:
|
||
|
|
if num == tf:
|
||
|
|
den_term_2 = Series(*den_arg_list)
|
||
|
|
elif expr.sys2 == tf:
|
||
|
|
den_term_2 = Series(*num_arg_list)
|
||
|
|
else:
|
||
|
|
den_term_2 = Series(*num_arg_list, *den_arg_list)
|
||
|
|
|
||
|
|
numer = self._print(num)
|
||
|
|
denom_1 = self._print(den_term_1)
|
||
|
|
denom_2 = self._print(den_term_2)
|
||
|
|
_sign = "+" if expr.sign == -1 else "-"
|
||
|
|
|
||
|
|
return r"\frac{%s}{%s %s %s}" % (numer, denom_1, _sign, denom_2)
|
||
|
|
|
||
|
|
def _print_MIMOFeedback(self, expr):
|
||
|
|
from sympy.physics.control import MIMOSeries
|
||
|
|
inv_mat = self._print(MIMOSeries(expr.sys2, expr.sys1))
|
||
|
|
sys1 = self._print(expr.sys1)
|
||
|
|
_sign = "+" if expr.sign == -1 else "-"
|
||
|
|
return r"\left(I_{\tau} %s %s\right)^{-1} \cdot %s" % (_sign, inv_mat, sys1)
|
||
|
|
|
||
|
|
def _print_TransferFunctionMatrix(self, expr):
|
||
|
|
mat = self._print(expr._expr_mat)
|
||
|
|
return r"%s_\tau" % mat
|
||
|
|
|
||
|
|
def _print_DFT(self, expr):
|
||
|
|
return r"\text{{{}}}_{{{}}}".format(expr.__class__.__name__, expr.n)
|
||
|
|
_print_IDFT = _print_DFT
|
||
|
|
|
||
|
|
def _print_NamedMorphism(self, morphism):
|
||
|
|
pretty_name = self._print(Symbol(morphism.name))
|
||
|
|
pretty_morphism = self._print_Morphism(morphism)
|
||
|
|
return "%s:%s" % (pretty_name, pretty_morphism)
|
||
|
|
|
||
|
|
def _print_IdentityMorphism(self, morphism):
|
||
|
|
from sympy.categories import NamedMorphism
|
||
|
|
return self._print_NamedMorphism(NamedMorphism(
|
||
|
|
morphism.domain, morphism.codomain, "id"))
|
||
|
|
|
||
|
|
def _print_CompositeMorphism(self, morphism):
|
||
|
|
# All components of the morphism have names and it is thus
|
||
|
|
# possible to build the name of the composite.
|
||
|
|
component_names_list = [self._print(Symbol(component.name)) for
|
||
|
|
component in morphism.components]
|
||
|
|
component_names_list.reverse()
|
||
|
|
component_names = "\\circ ".join(component_names_list) + ":"
|
||
|
|
|
||
|
|
pretty_morphism = self._print_Morphism(morphism)
|
||
|
|
return component_names + pretty_morphism
|
||
|
|
|
||
|
|
def _print_Category(self, morphism):
|
||
|
|
return r"\mathbf{{{}}}".format(self._print(Symbol(morphism.name)))
|
||
|
|
|
||
|
|
def _print_Diagram(self, diagram):
|
||
|
|
if not diagram.premises:
|
||
|
|
# This is an empty diagram.
|
||
|
|
return self._print(S.EmptySet)
|
||
|
|
|
||
|
|
latex_result = self._print(diagram.premises)
|
||
|
|
if diagram.conclusions:
|
||
|
|
latex_result += "\\Longrightarrow %s" % \
|
||
|
|
self._print(diagram.conclusions)
|
||
|
|
|
||
|
|
return latex_result
|
||
|
|
|
||
|
|
def _print_DiagramGrid(self, grid):
|
||
|
|
latex_result = "\\begin{array}{%s}\n" % ("c" * grid.width)
|
||
|
|
|
||
|
|
for i in range(grid.height):
|
||
|
|
for j in range(grid.width):
|
||
|
|
if grid[i, j]:
|
||
|
|
latex_result += latex(grid[i, j])
|
||
|
|
latex_result += " "
|
||
|
|
if j != grid.width - 1:
|
||
|
|
latex_result += "& "
|
||
|
|
|
||
|
|
if i != grid.height - 1:
|
||
|
|
latex_result += "\\\\"
|
||
|
|
latex_result += "\n"
|
||
|
|
|
||
|
|
latex_result += "\\end{array}\n"
|
||
|
|
return latex_result
|
||
|
|
|
||
|
|
def _print_FreeModule(self, M):
|
||
|
|
return '{{{}}}^{{{}}}'.format(self._print(M.ring), self._print(M.rank))
|
||
|
|
|
||
|
|
def _print_FreeModuleElement(self, m):
|
||
|
|
# Print as row vector for convenience, for now.
|
||
|
|
return r"\left[ {} \right]".format(",".join(
|
||
|
|
'{' + self._print(x) + '}' for x in m))
|
||
|
|
|
||
|
|
def _print_SubModule(self, m):
|
||
|
|
return r"\left\langle {} \right\rangle".format(",".join(
|
||
|
|
'{' + self._print(x) + '}' for x in m.gens))
|
||
|
|
|
||
|
|
def _print_ModuleImplementedIdeal(self, m):
|
||
|
|
return r"\left\langle {} \right\rangle".format(",".join(
|
||
|
|
'{' + self._print(x) + '}' for [x] in m._module.gens))
|
||
|
|
|
||
|
|
def _print_Quaternion(self, expr):
|
||
|
|
# TODO: This expression is potentially confusing,
|
||
|
|
# shall we print it as `Quaternion( ... )`?
|
||
|
|
s = [self.parenthesize(i, PRECEDENCE["Mul"], strict=True)
|
||
|
|
for i in expr.args]
|
||
|
|
a = [s[0]] + [i+" "+j for i, j in zip(s[1:], "ijk")]
|
||
|
|
return " + ".join(a)
|
||
|
|
|
||
|
|
def _print_QuotientRing(self, R):
|
||
|
|
# TODO nicer fractions for few generators...
|
||
|
|
return r"\frac{{{}}}{{{}}}".format(self._print(R.ring),
|
||
|
|
self._print(R.base_ideal))
|
||
|
|
|
||
|
|
def _print_QuotientRingElement(self, x):
|
||
|
|
return r"{{{}}} + {{{}}}".format(self._print(x.data),
|
||
|
|
self._print(x.ring.base_ideal))
|
||
|
|
|
||
|
|
def _print_QuotientModuleElement(self, m):
|
||
|
|
return r"{{{}}} + {{{}}}".format(self._print(m.data),
|
||
|
|
self._print(m.module.killed_module))
|
||
|
|
|
||
|
|
def _print_QuotientModule(self, M):
|
||
|
|
# TODO nicer fractions for few generators...
|
||
|
|
return r"\frac{{{}}}{{{}}}".format(self._print(M.base),
|
||
|
|
self._print(M.killed_module))
|
||
|
|
|
||
|
|
def _print_MatrixHomomorphism(self, h):
|
||
|
|
return r"{{{}}} : {{{}}} \to {{{}}}".format(self._print(h._sympy_matrix()),
|
||
|
|
self._print(h.domain), self._print(h.codomain))
|
||
|
|
|
||
|
|
def _print_Manifold(self, manifold):
|
||
|
|
string = manifold.name.name
|
||
|
|
if '{' in string:
|
||
|
|
name, supers, subs = string, [], []
|
||
|
|
else:
|
||
|
|
name, supers, subs = split_super_sub(string)
|
||
|
|
|
||
|
|
name = translate(name)
|
||
|
|
supers = [translate(sup) for sup in supers]
|
||
|
|
subs = [translate(sub) for sub in subs]
|
||
|
|
|
||
|
|
name = r'\text{%s}' % name
|
||
|
|
if supers:
|
||
|
|
name += "^{%s}" % " ".join(supers)
|
||
|
|
if subs:
|
||
|
|
name += "_{%s}" % " ".join(subs)
|
||
|
|
|
||
|
|
return name
|
||
|
|
|
||
|
|
def _print_Patch(self, patch):
|
||
|
|
return r'\text{%s}_{%s}' % (self._print(patch.name), self._print(patch.manifold))
|
||
|
|
|
||
|
|
def _print_CoordSystem(self, coordsys):
|
||
|
|
return r'\text{%s}^{\text{%s}}_{%s}' % (
|
||
|
|
self._print(coordsys.name), self._print(coordsys.patch.name), self._print(coordsys.manifold)
|
||
|
|
)
|
||
|
|
|
||
|
|
def _print_CovarDerivativeOp(self, cvd):
|
||
|
|
return r'\mathbb{\nabla}_{%s}' % self._print(cvd._wrt)
|
||
|
|
|
||
|
|
def _print_BaseScalarField(self, field):
|
||
|
|
string = field._coord_sys.symbols[field._index].name
|
||
|
|
return r'\mathbf{{{}}}'.format(self._print(Symbol(string)))
|
||
|
|
|
||
|
|
def _print_BaseVectorField(self, field):
|
||
|
|
string = field._coord_sys.symbols[field._index].name
|
||
|
|
return r'\partial_{{{}}}'.format(self._print(Symbol(string)))
|
||
|
|
|
||
|
|
def _print_Differential(self, diff):
|
||
|
|
field = diff._form_field
|
||
|
|
if hasattr(field, '_coord_sys'):
|
||
|
|
string = field._coord_sys.symbols[field._index].name
|
||
|
|
return r'\operatorname{{d}}{}'.format(self._print(Symbol(string)))
|
||
|
|
else:
|
||
|
|
string = self._print(field)
|
||
|
|
return r'\operatorname{{d}}\left({}\right)'.format(string)
|
||
|
|
|
||
|
|
def _print_Tr(self, p):
|
||
|
|
# TODO: Handle indices
|
||
|
|
contents = self._print(p.args[0])
|
||
|
|
return r'\operatorname{{tr}}\left({}\right)'.format(contents)
|
||
|
|
|
||
|
|
def _print_totient(self, expr, exp=None):
|
||
|
|
if exp is not None:
|
||
|
|
return r'\left(\phi\left(%s\right)\right)^{%s}' % \
|
||
|
|
(self._print(expr.args[0]), exp)
|
||
|
|
return r'\phi\left(%s\right)' % self._print(expr.args[0])
|
||
|
|
|
||
|
|
def _print_reduced_totient(self, expr, exp=None):
|
||
|
|
if exp is not None:
|
||
|
|
return r'\left(\lambda\left(%s\right)\right)^{%s}' % \
|
||
|
|
(self._print(expr.args[0]), exp)
|
||
|
|
return r'\lambda\left(%s\right)' % self._print(expr.args[0])
|
||
|
|
|
||
|
|
def _print_divisor_sigma(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 2:
|
||
|
|
tex = r"_%s\left(%s\right)" % tuple(map(self._print,
|
||
|
|
(expr.args[1], expr.args[0])))
|
||
|
|
else:
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
return r"\sigma^{%s}%s" % (exp, tex)
|
||
|
|
return r"\sigma%s" % tex
|
||
|
|
|
||
|
|
def _print_udivisor_sigma(self, expr, exp=None):
|
||
|
|
if len(expr.args) == 2:
|
||
|
|
tex = r"_%s\left(%s\right)" % tuple(map(self._print,
|
||
|
|
(expr.args[1], expr.args[0])))
|
||
|
|
else:
|
||
|
|
tex = r"\left(%s\right)" % self._print(expr.args[0])
|
||
|
|
if exp is not None:
|
||
|
|
return r"\sigma^*^{%s}%s" % (exp, tex)
|
||
|
|
return r"\sigma^*%s" % tex
|
||
|
|
|
||
|
|
def _print_primenu(self, expr, exp=None):
|
||
|
|
if exp is not None:
|
||
|
|
return r'\left(\nu\left(%s\right)\right)^{%s}' % \
|
||
|
|
(self._print(expr.args[0]), exp)
|
||
|
|
return r'\nu\left(%s\right)' % self._print(expr.args[0])
|
||
|
|
|
||
|
|
def _print_primeomega(self, expr, exp=None):
|
||
|
|
if exp is not None:
|
||
|
|
return r'\left(\Omega\left(%s\right)\right)^{%s}' % \
|
||
|
|
(self._print(expr.args[0]), exp)
|
||
|
|
return r'\Omega\left(%s\right)' % self._print(expr.args[0])
|
||
|
|
|
||
|
|
def _print_Str(self, s):
|
||
|
|
return str(s.name)
|
||
|
|
|
||
|
|
def _print_float(self, expr):
|
||
|
|
return self._print(Float(expr))
|
||
|
|
|
||
|
|
def _print_int(self, expr):
|
||
|
|
return str(expr)
|
||
|
|
|
||
|
|
def _print_mpz(self, expr):
|
||
|
|
return str(expr)
|
||
|
|
|
||
|
|
def _print_mpq(self, expr):
|
||
|
|
return str(expr)
|
||
|
|
|
||
|
|
def _print_Predicate(self, expr):
|
||
|
|
return r"\operatorname{{Q}}_{{\text{{{}}}}}".format(latex_escape(str(expr.name)))
|
||
|
|
|
||
|
|
def _print_AppliedPredicate(self, expr):
|
||
|
|
pred = expr.function
|
||
|
|
args = expr.arguments
|
||
|
|
pred_latex = self._print(pred)
|
||
|
|
args_latex = ', '.join([self._print(a) for a in args])
|
||
|
|
return '%s(%s)' % (pred_latex, args_latex)
|
||
|
|
|
||
|
|
def emptyPrinter(self, expr):
|
||
|
|
# default to just printing as monospace, like would normally be shown
|
||
|
|
s = super().emptyPrinter(expr)
|
||
|
|
|
||
|
|
return r"\mathtt{\text{%s}}" % latex_escape(s)
|
||
|
|
|
||
|
|
|
||
|
|
def translate(s: str) -> str:
|
||
|
|
r'''
|
||
|
|
Check for a modifier ending the string. If present, convert the
|
||
|
|
modifier to latex and translate the rest recursively.
|
||
|
|
|
||
|
|
Given a description of a Greek letter or other special character,
|
||
|
|
return the appropriate latex.
|
||
|
|
|
||
|
|
Let everything else pass as given.
|
||
|
|
|
||
|
|
>>> from sympy.printing.latex import translate
|
||
|
|
>>> translate('alphahatdotprime')
|
||
|
|
"{\\dot{\\hat{\\alpha}}}'"
|
||
|
|
'''
|
||
|
|
# Process the rest
|
||
|
|
tex = tex_greek_dictionary.get(s)
|
||
|
|
if tex:
|
||
|
|
return tex
|
||
|
|
elif s.lower() in greek_letters_set:
|
||
|
|
return "\\" + s.lower()
|
||
|
|
elif s in other_symbols:
|
||
|
|
return "\\" + s
|
||
|
|
else:
|
||
|
|
# Process modifiers, if any, and recurse
|
||
|
|
for key in sorted(modifier_dict.keys(), key=len, reverse=True):
|
||
|
|
if s.lower().endswith(key) and len(s) > len(key):
|
||
|
|
return modifier_dict[key](translate(s[:-len(key)]))
|
||
|
|
return s
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
@print_function(LatexPrinter)
|
||
|
|
def latex(expr, **settings):
|
||
|
|
r"""Convert the given expression to LaTeX string representation.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
==========
|
||
|
|
full_prec: boolean, optional
|
||
|
|
If set to True, a floating point number is printed with full precision.
|
||
|
|
fold_frac_powers : boolean, optional
|
||
|
|
Emit ``^{p/q}`` instead of ``^{\frac{p}{q}}`` for fractional powers.
|
||
|
|
fold_func_brackets : boolean, optional
|
||
|
|
Fold function brackets where applicable.
|
||
|
|
fold_short_frac : boolean, optional
|
||
|
|
Emit ``p / q`` instead of ``\frac{p}{q}`` when the denominator is
|
||
|
|
simple enough (at most two terms and no powers). The default value is
|
||
|
|
``True`` for inline mode, ``False`` otherwise.
|
||
|
|
inv_trig_style : string, optional
|
||
|
|
How inverse trig functions should be displayed. Can be one of
|
||
|
|
``'abbreviated'``, ``'full'``, or ``'power'``. Defaults to
|
||
|
|
``'abbreviated'``.
|
||
|
|
itex : boolean, optional
|
||
|
|
Specifies if itex-specific syntax is used, including emitting
|
||
|
|
``$$...$$``.
|
||
|
|
ln_notation : boolean, optional
|
||
|
|
If set to ``True``, ``\ln`` is used instead of default ``\log``.
|
||
|
|
long_frac_ratio : float or None, optional
|
||
|
|
The allowed ratio of the width of the numerator to the width of the
|
||
|
|
denominator before the printer breaks off long fractions. If ``None``
|
||
|
|
(the default value), long fractions are not broken up.
|
||
|
|
mat_delim : string, optional
|
||
|
|
The delimiter to wrap around matrices. Can be one of ``'['``, ``'('``,
|
||
|
|
or the empty string ``''``. Defaults to ``'['``.
|
||
|
|
mat_str : string, optional
|
||
|
|
Which matrix environment string to emit. ``'smallmatrix'``,
|
||
|
|
``'matrix'``, ``'array'``, etc. Defaults to ``'smallmatrix'`` for
|
||
|
|
inline mode, ``'matrix'`` for matrices of no more than 10 columns, and
|
||
|
|
``'array'`` otherwise.
|
||
|
|
mode: string, optional
|
||
|
|
Specifies how the generated code will be delimited. ``mode`` can be one
|
||
|
|
of ``'plain'``, ``'inline'``, ``'equation'`` or ``'equation*'``. If
|
||
|
|
``mode`` is set to ``'plain'``, then the resulting code will not be
|
||
|
|
delimited at all (this is the default). If ``mode`` is set to
|
||
|
|
``'inline'`` then inline LaTeX ``$...$`` will be used. If ``mode`` is
|
||
|
|
set to ``'equation'`` or ``'equation*'``, the resulting code will be
|
||
|
|
enclosed in the ``equation`` or ``equation*`` environment (remember to
|
||
|
|
import ``amsmath`` for ``equation*``), unless the ``itex`` option is
|
||
|
|
set. In the latter case, the ``$$...$$`` syntax is used.
|
||
|
|
mul_symbol : string or None, optional
|
||
|
|
The symbol to use for multiplication. Can be one of ``None``,
|
||
|
|
``'ldot'``, ``'dot'``, or ``'times'``.
|
||
|
|
order: string, optional
|
||
|
|
Any of the supported monomial orderings (currently ``'lex'``,
|
||
|
|
``'grlex'``, or ``'grevlex'``), ``'old'``, and ``'none'``. This
|
||
|
|
parameter does nothing for `~.Mul` objects. Setting order to ``'old'``
|
||
|
|
uses the compatibility ordering for ``~.Add`` defined in Printer. For
|
||
|
|
very large expressions, set the ``order`` keyword to ``'none'`` if
|
||
|
|
speed is a concern.
|
||
|
|
symbol_names : dictionary of strings mapped to symbols, optional
|
||
|
|
Dictionary of symbols and the custom strings they should be emitted as.
|
||
|
|
root_notation : boolean, optional
|
||
|
|
If set to ``False``, exponents of the form 1/n are printed in fractonal
|
||
|
|
form. Default is ``True``, to print exponent in root form.
|
||
|
|
mat_symbol_style : string, optional
|
||
|
|
Can be either ``'plain'`` (default) or ``'bold'``. If set to
|
||
|
|
``'bold'``, a `~.MatrixSymbol` A will be printed as ``\mathbf{A}``,
|
||
|
|
otherwise as ``A``.
|
||
|
|
imaginary_unit : string, optional
|
||
|
|
String to use for the imaginary unit. Defined options are ``'i'``
|
||
|
|
(default) and ``'j'``. Adding ``r`` or ``t`` in front gives ``\mathrm``
|
||
|
|
or ``\text``, so ``'ri'`` leads to ``\mathrm{i}`` which gives
|
||
|
|
`\mathrm{i}`.
|
||
|
|
gothic_re_im : boolean, optional
|
||
|
|
If set to ``True``, `\Re` and `\Im` is used for ``re`` and ``im``, respectively.
|
||
|
|
The default is ``False`` leading to `\operatorname{re}` and `\operatorname{im}`.
|
||
|
|
decimal_separator : string, optional
|
||
|
|
Specifies what separator to use to separate the whole and fractional parts of a
|
||
|
|
floating point number as in `2.5` for the default, ``period`` or `2{,}5`
|
||
|
|
when ``comma`` is specified. Lists, sets, and tuple are printed with semicolon
|
||
|
|
separating the elements when ``comma`` is chosen. For example, [1; 2; 3] when
|
||
|
|
``comma`` is chosen and [1,2,3] for when ``period`` is chosen.
|
||
|
|
parenthesize_super : boolean, optional
|
||
|
|
If set to ``False``, superscripted expressions will not be parenthesized when
|
||
|
|
powered. Default is ``True``, which parenthesizes the expression when powered.
|
||
|
|
min: Integer or None, optional
|
||
|
|
Sets the lower bound for the exponent to print floating point numbers in
|
||
|
|
fixed-point format.
|
||
|
|
max: Integer or None, optional
|
||
|
|
Sets the upper bound for the exponent to print floating point numbers in
|
||
|
|
fixed-point format.
|
||
|
|
diff_operator: string, optional
|
||
|
|
String to use for differential operator. Default is ``'d'``, to print in italic
|
||
|
|
form. ``'rd'``, ``'td'`` are shortcuts for ``\mathrm{d}`` and ``\text{d}``.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
=====
|
||
|
|
|
||
|
|
Not using a print statement for printing, results in double backslashes for
|
||
|
|
latex commands since that's the way Python escapes backslashes in strings.
|
||
|
|
|
||
|
|
>>> from sympy import latex, Rational
|
||
|
|
>>> from sympy.abc import tau
|
||
|
|
>>> latex((2*tau)**Rational(7,2))
|
||
|
|
'8 \\sqrt{2} \\tau^{\\frac{7}{2}}'
|
||
|
|
>>> print(latex((2*tau)**Rational(7,2)))
|
||
|
|
8 \sqrt{2} \tau^{\frac{7}{2}}
|
||
|
|
|
||
|
|
Examples
|
||
|
|
========
|
||
|
|
|
||
|
|
>>> from sympy import latex, pi, sin, asin, Integral, Matrix, Rational, log
|
||
|
|
>>> from sympy.abc import x, y, mu, r, tau
|
||
|
|
|
||
|
|
Basic usage:
|
||
|
|
|
||
|
|
>>> print(latex((2*tau)**Rational(7,2)))
|
||
|
|
8 \sqrt{2} \tau^{\frac{7}{2}}
|
||
|
|
|
||
|
|
``mode`` and ``itex`` options:
|
||
|
|
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
|
||
|
|
8 \sqrt{2} \mu^{\frac{7}{2}}
|
||
|
|
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
|
||
|
|
$8 \sqrt{2} \tau^{7 / 2}$
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
|
||
|
|
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
|
||
|
|
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
|
||
|
|
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
|
||
|
|
8 \sqrt{2} \mu^{\frac{7}{2}}
|
||
|
|
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
|
||
|
|
$8 \sqrt{2} \tau^{7 / 2}$
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
|
||
|
|
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
|
||
|
|
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
|
||
|
|
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
|
||
|
|
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$
|
||
|
|
|
||
|
|
Fraction options:
|
||
|
|
|
||
|
|
>>> print(latex((2*tau)**Rational(7,2), fold_frac_powers=True))
|
||
|
|
8 \sqrt{2} \tau^{7/2}
|
||
|
|
>>> print(latex((2*tau)**sin(Rational(7,2))))
|
||
|
|
\left(2 \tau\right)^{\sin{\left(\frac{7}{2} \right)}}
|
||
|
|
>>> print(latex((2*tau)**sin(Rational(7,2)), fold_func_brackets=True))
|
||
|
|
\left(2 \tau\right)^{\sin {\frac{7}{2}}}
|
||
|
|
>>> print(latex(3*x**2/y))
|
||
|
|
\frac{3 x^{2}}{y}
|
||
|
|
>>> print(latex(3*x**2/y, fold_short_frac=True))
|
||
|
|
3 x^{2} / y
|
||
|
|
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=2))
|
||
|
|
\frac{\int r\, dr}{2 \pi}
|
||
|
|
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=0))
|
||
|
|
\frac{1}{2 \pi} \int r\, dr
|
||
|
|
|
||
|
|
Multiplication options:
|
||
|
|
|
||
|
|
>>> print(latex((2*tau)**sin(Rational(7,2)), mul_symbol="times"))
|
||
|
|
\left(2 \times \tau\right)^{\sin{\left(\frac{7}{2} \right)}}
|
||
|
|
|
||
|
|
Trig options:
|
||
|
|
|
||
|
|
>>> print(latex(asin(Rational(7,2))))
|
||
|
|
\operatorname{asin}{\left(\frac{7}{2} \right)}
|
||
|
|
>>> print(latex(asin(Rational(7,2)), inv_trig_style="full"))
|
||
|
|
\arcsin{\left(\frac{7}{2} \right)}
|
||
|
|
>>> print(latex(asin(Rational(7,2)), inv_trig_style="power"))
|
||
|
|
\sin^{-1}{\left(\frac{7}{2} \right)}
|
||
|
|
|
||
|
|
Matrix options:
|
||
|
|
|
||
|
|
>>> print(latex(Matrix(2, 1, [x, y])))
|
||
|
|
\left[\begin{matrix}x\\y\end{matrix}\right]
|
||
|
|
>>> print(latex(Matrix(2, 1, [x, y]), mat_str = "array"))
|
||
|
|
\left[\begin{array}{c}x\\y\end{array}\right]
|
||
|
|
>>> print(latex(Matrix(2, 1, [x, y]), mat_delim="("))
|
||
|
|
\left(\begin{matrix}x\\y\end{matrix}\right)
|
||
|
|
|
||
|
|
Custom printing of symbols:
|
||
|
|
|
||
|
|
>>> print(latex(x**2, symbol_names={x: 'x_i'}))
|
||
|
|
x_i^{2}
|
||
|
|
|
||
|
|
Logarithms:
|
||
|
|
|
||
|
|
>>> print(latex(log(10)))
|
||
|
|
\log{\left(10 \right)}
|
||
|
|
>>> print(latex(log(10), ln_notation=True))
|
||
|
|
\ln{\left(10 \right)}
|
||
|
|
|
||
|
|
``latex()`` also supports the builtin container types :class:`list`,
|
||
|
|
:class:`tuple`, and :class:`dict`:
|
||
|
|
|
||
|
|
>>> print(latex([2/x, y], mode='inline'))
|
||
|
|
$\left[ 2 / x, \ y\right]$
|
||
|
|
|
||
|
|
Unsupported types are rendered as monospaced plaintext:
|
||
|
|
|
||
|
|
>>> print(latex(int))
|
||
|
|
\mathtt{\text{<class 'int'>}}
|
||
|
|
>>> print(latex("plain % text"))
|
||
|
|
\mathtt{\text{plain \% text}}
|
||
|
|
|
||
|
|
See :ref:`printer_method_example` for an example of how to override
|
||
|
|
this behavior for your own types by implementing ``_latex``.
|
||
|
|
|
||
|
|
.. versionchanged:: 1.7.0
|
||
|
|
Unsupported types no longer have their ``str`` representation treated as valid latex.
|
||
|
|
|
||
|
|
"""
|
||
|
|
return LatexPrinter(settings).doprint(expr)
|
||
|
|
|
||
|
|
|
||
|
|
def print_latex(expr, **settings):
|
||
|
|
"""Prints LaTeX representation of the given expression. Takes the same
|
||
|
|
settings as ``latex()``."""
|
||
|
|
|
||
|
|
print(latex(expr, **settings))
|
||
|
|
|
||
|
|
|
||
|
|
def multiline_latex(lhs, rhs, terms_per_line=1, environment="align*", use_dots=False, **settings):
|
||
|
|
r"""
|
||
|
|
This function generates a LaTeX equation with a multiline right-hand side
|
||
|
|
in an ``align*``, ``eqnarray`` or ``IEEEeqnarray`` environment.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
==========
|
||
|
|
|
||
|
|
lhs : Expr
|
||
|
|
Left-hand side of equation
|
||
|
|
|
||
|
|
rhs : Expr
|
||
|
|
Right-hand side of equation
|
||
|
|
|
||
|
|
terms_per_line : integer, optional
|
||
|
|
Number of terms per line to print. Default is 1.
|
||
|
|
|
||
|
|
environment : "string", optional
|
||
|
|
Which LaTeX wnvironment to use for the output. Options are "align*"
|
||
|
|
(default), "eqnarray", and "IEEEeqnarray".
|
||
|
|
|
||
|
|
use_dots : boolean, optional
|
||
|
|
If ``True``, ``\\dots`` is added to the end of each line. Default is ``False``.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
========
|
||
|
|
|
||
|
|
>>> from sympy import multiline_latex, symbols, sin, cos, exp, log, I
|
||
|
|
>>> x, y, alpha = symbols('x y alpha')
|
||
|
|
>>> expr = sin(alpha*y) + exp(I*alpha) - cos(log(y))
|
||
|
|
>>> print(multiline_latex(x, expr))
|
||
|
|
\begin{align*}
|
||
|
|
x = & e^{i \alpha} \\
|
||
|
|
& + \sin{\left(\alpha y \right)} \\
|
||
|
|
& - \cos{\left(\log{\left(y \right)} \right)}
|
||
|
|
\end{align*}
|
||
|
|
|
||
|
|
Using at most two terms per line:
|
||
|
|
>>> print(multiline_latex(x, expr, 2))
|
||
|
|
\begin{align*}
|
||
|
|
x = & e^{i \alpha} + \sin{\left(\alpha y \right)} \\
|
||
|
|
& - \cos{\left(\log{\left(y \right)} \right)}
|
||
|
|
\end{align*}
|
||
|
|
|
||
|
|
Using ``eqnarray`` and dots:
|
||
|
|
>>> print(multiline_latex(x, expr, terms_per_line=2, environment="eqnarray", use_dots=True))
|
||
|
|
\begin{eqnarray}
|
||
|
|
x & = & e^{i \alpha} + \sin{\left(\alpha y \right)} \dots\nonumber\\
|
||
|
|
& & - \cos{\left(\log{\left(y \right)} \right)}
|
||
|
|
\end{eqnarray}
|
||
|
|
|
||
|
|
Using ``IEEEeqnarray``:
|
||
|
|
>>> print(multiline_latex(x, expr, environment="IEEEeqnarray"))
|
||
|
|
\begin{IEEEeqnarray}{rCl}
|
||
|
|
x & = & e^{i \alpha} \nonumber\\
|
||
|
|
& & + \sin{\left(\alpha y \right)} \nonumber\\
|
||
|
|
& & - \cos{\left(\log{\left(y \right)} \right)}
|
||
|
|
\end{IEEEeqnarray}
|
||
|
|
|
||
|
|
Notes
|
||
|
|
=====
|
||
|
|
|
||
|
|
All optional parameters from ``latex`` can also be used.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
# Based on code from https://github.com/sympy/sympy/issues/3001
|
||
|
|
l = LatexPrinter(**settings)
|
||
|
|
if environment == "eqnarray":
|
||
|
|
result = r'\begin{eqnarray}' + '\n'
|
||
|
|
first_term = '& = &'
|
||
|
|
nonumber = r'\nonumber'
|
||
|
|
end_term = '\n\\end{eqnarray}'
|
||
|
|
doubleet = True
|
||
|
|
elif environment == "IEEEeqnarray":
|
||
|
|
result = r'\begin{IEEEeqnarray}{rCl}' + '\n'
|
||
|
|
first_term = '& = &'
|
||
|
|
nonumber = r'\nonumber'
|
||
|
|
end_term = '\n\\end{IEEEeqnarray}'
|
||
|
|
doubleet = True
|
||
|
|
elif environment == "align*":
|
||
|
|
result = r'\begin{align*}' + '\n'
|
||
|
|
first_term = '= &'
|
||
|
|
nonumber = ''
|
||
|
|
end_term = '\n\\end{align*}'
|
||
|
|
doubleet = False
|
||
|
|
else:
|
||
|
|
raise ValueError("Unknown environment: {}".format(environment))
|
||
|
|
dots = ''
|
||
|
|
if use_dots:
|
||
|
|
dots=r'\dots'
|
||
|
|
terms = rhs.as_ordered_terms()
|
||
|
|
n_terms = len(terms)
|
||
|
|
term_count = 1
|
||
|
|
for i in range(n_terms):
|
||
|
|
term = terms[i]
|
||
|
|
term_start = ''
|
||
|
|
term_end = ''
|
||
|
|
sign = '+'
|
||
|
|
if term_count > terms_per_line:
|
||
|
|
if doubleet:
|
||
|
|
term_start = '& & '
|
||
|
|
else:
|
||
|
|
term_start = '& '
|
||
|
|
term_count = 1
|
||
|
|
if term_count == terms_per_line:
|
||
|
|
# End of line
|
||
|
|
if i < n_terms-1:
|
||
|
|
# There are terms remaining
|
||
|
|
term_end = dots + nonumber + r'\\' + '\n'
|
||
|
|
else:
|
||
|
|
term_end = ''
|
||
|
|
|
||
|
|
if term.as_ordered_factors()[0] == -1:
|
||
|
|
term = -1*term
|
||
|
|
sign = r'-'
|
||
|
|
if i == 0: # beginning
|
||
|
|
if sign == '+':
|
||
|
|
sign = ''
|
||
|
|
result += r'{:s} {:s}{:s} {:s} {:s}'.format(l.doprint(lhs),
|
||
|
|
first_term, sign, l.doprint(term), term_end)
|
||
|
|
else:
|
||
|
|
result += r'{:s}{:s} {:s} {:s}'.format(term_start, sign,
|
||
|
|
l.doprint(term), term_end)
|
||
|
|
term_count += 1
|
||
|
|
result += end_term
|
||
|
|
return result
|