Source code for sympy.printing.latex

"""
A Printer which converts an expression into its LaTeX equivalent.
"""

from __future__ import print_function, division

import itertools

from sympy.core import S, Add, Symbol, Mod
from sympy.core.function import _coeff_isneg
from sympy.core.sympify import SympifyError
from sympy.core.alphabets import greeks
from sympy.core.operations import AssocOp
from sympy.core.containers import Tuple
from sympy.logic.boolalg import true

## sympy.printing imports
from sympy.printing.precedence import precedence_traditional
from .printer import Printer
from .conventions import split_super_sub, requires_partial
from .precedence import precedence, PRECEDENCE

import mpmath.libmp as mlib
from mpmath.libmp import prec_to_dps

from sympy.core.compatibility import default_sort_key, range
from sympy.utilities.iterables import has_variety

import re

# Hand-picked functions which can be used directly in both LaTeX and MathJax
# Complete list at http://www.mathjax.org/docs/1.1/tex.html#supported-latex-commands
# This variable only contains those functions which sympy uses.
accepted_latex_functions = ['arcsin', 'arccos', 'arctan', 'sin', 'cos', 'tan',
                    'sinh', 'cosh', 'tanh', 'sqrt', 'ln', 'log', 'sec', 'csc',
                    'cot', 'coth', 're', 'im', 'frac', 'root', 'arg',
                    ]

tex_greek_dictionary = {
    'Alpha': 'A',
    'Beta': 'B',
    'Gamma': r'\Gamma',
    'Delta': r'\Delta',
    'Epsilon': 'E',
    'Zeta': 'Z',
    'Eta': 'H',
    'Theta': r'\Theta',
    'Iota': 'I',
    'Kappa': 'K',
    'Lambda': r'\Lambda',
    'Mu': 'M',
    'Nu': 'N',
    'Xi': r'\Xi',
    'omicron': 'o',
    'Omicron': 'O',
    'Pi': r'\Pi',
    'Rho': 'P',
    'Sigma': r'\Sigma',
    'Tau': 'T',
    'Upsilon': r'\Upsilon',
    'Phi': r'\Phi',
    'Chi': 'X',
    'Psi': r'\Psi',
    'Omega': r'\Omega',
    'lamda': r'\lambda',
    'Lamda': r'\Lambda',
    'khi': r'\chi',
    'Khi': r'X',
    'varepsilon': r'\varepsilon',
    'varkappa': r'\varkappa',
    'varphi': r'\varphi',
    'varpi': r'\varpi',
    'varrho': r'\varrho',
    'varsigma': r'\varsigma',
    'vartheta': r'\vartheta',
}

other_symbols = set(['aleph', 'beth', 'daleth', 'gimel', 'ell', 'eth', 'hbar',
                     'hslash', 'mho', 'wp', ])

# Variable name modifiers
modifier_dict = {
    # Accents
    'mathring': lambda s: r'\mathring{'+s+r'}',
    'ddddot': lambda s: r'\ddddot{'+s+r'}',
    'dddot': lambda s: r'\dddot{'+s+r'}',
    'ddot': lambda s: r'\ddot{'+s+r'}',
    'dot': lambda s: r'\dot{'+s+r'}',
    'check': lambda s: r'\check{'+s+r'}',
    'breve': lambda s: r'\breve{'+s+r'}',
    'acute': lambda s: r'\acute{'+s+r'}',
    'grave': lambda s: r'\grave{'+s+r'}',
    'tilde': lambda s: r'\tilde{'+s+r'}',
    'hat': lambda s: r'\hat{'+s+r'}',
    'bar': lambda s: r'\bar{'+s+r'}',
    'vec': lambda s: r'\vec{'+s+r'}',
    'prime': lambda s: "{"+s+"}'",
    'prm': lambda s: "{"+s+"}'",
    # Faces
    'bold': lambda s: r'\boldsymbol{'+s+r'}',
    'bm': lambda s: r'\boldsymbol{'+s+r'}',
    'cal': lambda s: r'\mathcal{'+s+r'}',
    'scr': lambda s: r'\mathscr{'+s+r'}',
    'frak': lambda s: r'\mathfrak{'+s+r'}',
    # Brackets
    'norm': lambda s: r'\left\|{'+s+r'}\right\|',
    'avg': lambda s: r'\left\langle{'+s+r'}\right\rangle',
    'abs': lambda s: r'\left|{'+s+r'}\right|',
    'mag': lambda s: r'\left|{'+s+r'}\right|',
}

greek_letters_set = frozenset(greeks)

_between_two_numbers_p = (
    re.compile(r'[0-9][} ]*$'),  # search
    re.compile(r'[{ ]*[-+0-9]'),  # match
)


[docs]class LatexPrinter(Printer): printmethod = "_latex" _default_settings = { "order": None, "mode": "plain", "itex": False, "fold_frac_powers": False, "fold_func_brackets": False, "fold_short_frac": None, "long_frac_ratio": 2, "mul_symbol": None, "inv_trig_style": "abbreviated", "mat_str": None, "mat_delim": "[", "symbol_names": {}, } def __init__(self, settings=None): Printer.__init__(self, settings) if 'mode' in self._settings: valid_modes = ['inline', 'plain', 'equation', 'equation*'] if self._settings['mode'] not in valid_modes: raise ValueError("'mode' must be one of 'inline', 'plain', " "'equation' or 'equation*'") if self._settings['fold_short_frac'] is None and \ self._settings['mode'] == 'inline': self._settings['fold_short_frac'] = True mul_symbol_table = { None: r" ", "ldot": r" \,.\, ", "dot": r" \cdot ", "times": r" \times " } self._settings['mul_symbol_latex'] = \ mul_symbol_table[self._settings['mul_symbol']] self._settings['mul_symbol_latex_numbers'] = \ mul_symbol_table[self._settings['mul_symbol'] or 'dot'] self._delim_dict = {'(': ')', '[': ']'} def parenthesize(self, item, level, strict=False): prec_val = precedence_traditional(item) if (prec_val < level) or ((not strict) and prec_val <= level): return r"\left(%s\right)" % self._print(item) else: return self._print(item) def doprint(self, expr): tex = Printer.doprint(self, expr) if self._settings['mode'] == 'plain': return tex elif self._settings['mode'] == 'inline': return r"$%s$" % tex elif self._settings['itex']: return r"$$%s$$" % tex else: env_str = self._settings['mode'] return r"\begin{%s}%s\end{%s}" % (env_str, tex, env_str) def _needs_brackets(self, expr): """ Returns True if the expression needs to be wrapped in brackets when printed, False otherwise. For example: a + b => True; a => False; 10 => False; -10 => True. """ return not ((expr.is_Integer and expr.is_nonnegative) or (expr.is_Atom and (expr is not S.NegativeOne and expr.is_Rational is False))) def _needs_function_brackets(self, expr): """ Returns True if the expression needs to be wrapped in brackets when passed as an argument to a function, False otherwise. This is a more liberal version of _needs_brackets, in that many expressions which need to be wrapped in brackets when added/subtracted/raised to a power do not need them when passed to a function. Such an example is a*b. """ if not self._needs_brackets(expr): return False else: # Muls of the form a*b*c... can be folded if expr.is_Mul and not self._mul_is_clean(expr): return True # Pows which don't need brackets can be folded elif expr.is_Pow and not self._pow_is_clean(expr): return True # Add and Function always need brackets elif expr.is_Add or expr.is_Function: return True else: return False def _needs_mul_brackets(self, expr, first=False, last=False): """ Returns True if the expression needs to be wrapped in brackets when printed as part of a Mul, False otherwise. This is True for Add, but also for some container objects that would not need brackets when appearing last in a Mul, e.g. an Integral. ``last=True`` specifies that this expr is the last to appear in a Mul. ``first=True`` specifies that this expr is the first to appear in a Mul. """ from sympy import Integral, Piecewise, Product, Sum if expr.is_Mul: if not first and _coeff_isneg(expr): return True elif precedence_traditional(expr) < PRECEDENCE["Mul"]: return True elif expr.is_Relational: return True if expr.is_Piecewise: return True if any([expr.has(x) for x in (Mod,)]): return True if (not last and any([expr.has(x) for x in (Integral, Product, Sum)])): return True return False def _needs_add_brackets(self, expr): """ Returns True if the expression needs to be wrapped in brackets when printed as part of an Add, False otherwise. This is False for most things. """ if expr.is_Relational: return True if any([expr.has(x) for x in (Mod,)]): return True if expr.is_Add: return True return False def _mul_is_clean(self, expr): for arg in expr.args: if arg.is_Function: return False return True def _pow_is_clean(self, expr): return not self._needs_brackets(expr.base) def _do_exponent(self, expr, exp): if exp is not None: return r"\left(%s\right)^{%s}" % (expr, exp) else: return expr def _print_bool(self, e): return r"\mathrm{%s}" % e _print_BooleanTrue = _print_bool _print_BooleanFalse = _print_bool def _print_NoneType(self, e): return r"\mathrm{%s}" % e def _print_Add(self, expr, order=None): if self.order == 'none': terms = list(expr.args) else: terms = self._as_ordered_terms(expr, order=order) tex = "" for i, term in enumerate(terms): if i == 0: pass elif _coeff_isneg(term): 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 _print_Permutation = _print_Cycle def _print_Float(self, expr): # Based off of that in StrPrinter dps = prec_to_dps(expr._prec) str_real = mlib.to_str(expr._mpf_, dps, strip_zeros=True) # 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:] return r"%s%s10^{%s}" % (mant, separator, exp) elif str_real == "+inf": return r"\infty" elif str_real == "-inf": return r"- \infty" else: 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\cdot %s" % self.parenthesize(func, PRECEDENCE['Mul']) def _print_Mul(self, expr): from sympy.core.power import Pow include_parens = False if _coeff_isneg(expr): expr = -expr tex = "- " if expr.is_Add: tex += "(" include_parens = True else: tex = "" from sympy.simplify import fraction numer, denom = fraction(expr, exact=True) separator = self._settings['mul_symbol_latex'] numbersep = self._settings['mul_symbol_latex_numbers'] def convert(expr): if not expr.is_Mul: return str(self._print(expr)) else: _tex = last_term_tex = "" if self.order not in ('old', 'none'): args = expr.as_ordered_factors() else: args = expr.args for i, term in enumerate(args): term_tex = self._print(term) 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(term_tex): # between two numbers _tex += numbersep elif _tex: _tex += separator _tex += term_tex last_term_tex = term_tex return _tex 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 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_Pow(self, expr): # Treat x**Rational(1,n) as special case if expr.exp.is_Rational and abs(expr.exp.p) == 1 and expr.exp.q != 1: base = self._print(expr.base) expq = expr.exp.q if expq == 2: tex = r"\sqrt{%s}" % base elif self._settings['itex']: tex = r"\root{%d}{%s}" % (expq, base) else: tex = r"\sqrt[%d]{%s}" % (expq, base) if expr.exp.is_negative: return r"\frac{1}{%s}" % tex else: return tex elif self._settings['fold_frac_powers'] \ and expr.exp.is_Rational \ and expr.exp.q != 1: base, p, q = self.parenthesize(expr.base, PRECEDENCE['Pow']), expr.exp.p, expr.exp.q #fixes issue #12886, adds parentheses before superscripts raised to powers if '^' in base and expr.base.is_Symbol: base = r"\left(%s\right)" % base if expr.base.is_Function: return self._print(expr.base, "%s/%s" % (p, q)) return r"%s^{%s/%s}" % (base, p, q) elif expr.exp.is_Rational and expr.exp.is_negative and expr.base.is_commutative: # Things like 1/x return self._print_Mul(expr) else: if expr.base.is_Function: return self._print(expr.base, self._print(expr.exp)) else: if expr.is_commutative and expr.exp == -1: #solves issue 4129 #As Mul always simplify 1/x to x**-1 #The objective is achieved with this hack #first we get the latex for -1 * expr, #which is a Mul expression tex = self._print(S.NegativeOne * expr).strip() #the result comes with a minus and a space, so we remove if tex[:1] == "-": return tex[1:].strip() tex = r"%s^{%s}" #fixes issue #12886, adds parentheses before superscripts raised to powers base = self.parenthesize(expr.base, PRECEDENCE['Pow']) if '^' in base and expr.base.is_Symbol: base = r"\left(%s\right)" % base exp = self._print(expr.exp) return tex % (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): from sympy.vector import Vector o1 = [] 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 = '(' + LatexPrinter().doprint(v) + ')' 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 = self._print(expr.base)+'_{%s}' % ','.join( map(self._print, expr.indices)) return tex def _print_IndexedBase(self, expr): return self._print(expr.label) def _print_Derivative(self, expr): dim = len(expr.variables) if requires_partial(expr): diff_symbol = r'\partial' else: diff_symbol = r'd' if dim == 1: tex = r"\frac{%s}{%s %s}" % (diff_symbol, diff_symbol, self._print(expr.variables[0])) else: multiplicity, i, tex = [], 1, "" current = expr.variables[0] for symbol in expr.variables[1:]: if symbol == current: i = i + 1 else: multiplicity.append((current, i)) current, i = symbol, 1 else: multiplicity.append((current, i)) for x, i in multiplicity: if i == 1: tex += r"%s %s" % (diff_symbol, self._print(x)) else: tex += r"%s %s^{%s}" % (diff_symbol, self._print(x), i) tex = r"\frac{%s^{%s}}{%s} " % (diff_symbol, dim, tex) if isinstance(expr.expr, AssocOp): return r"%s\left(%s\right)" % (tex, self._print(expr.expr)) else: return r"%s %s" % (tex, self._print(expr.expr)) 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 = "", [] # 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"\, d%s" % 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'] in ['equation', 'equation*'] \ 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"\, d%s" % self._print(symbol)) return r"%s %s%s" % (tex, self.parenthesize(expr.function, PRECEDENCE["Mul"], 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): 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, 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) if func in accepted_latex_functions: name = r"\%s" % func elif len(func) == 1 or func.startswith('\\'): name = func else: name = r"\operatorname{%s}" % func return name def _print_Function(self, expr, exp=None): 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): 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", "acot"] # If the function is an inverse trig function, handle the style if func in inv_trig_table: if inv_trig_style == "abbreviated": func = func elif inv_trig_style == "full": func = "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: name = r'%s^{%s}' % (self._hprint_Function(func), 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_FunctionClass(self, expr): if hasattr(expr, '_latex_no_arg'): return expr._latex_no_arg(self) 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)) args = (symbols, self._print(expr)) tex = r"\left( %s \mapsto %s \right)" % (symbols, self._print(expr)) return tex def _print_Min(self, expr, exp=None): args = sorted(expr.args, key=default_sort_key) texargs = [r"%s" % self._print(symbol) for symbol in args] tex = r"\min\left(%s\right)" % ", ".join(texargs) if exp is not None: return r"%s^{%s}" % (tex, exp) else: return tex def _print_Max(self, expr, exp=None): args = sorted(expr.args, key=default_sort_key) texargs = [r"%s" % self._print(symbol) for symbol in args] tex = r"\max\left(%s\right)" % ", ".join(texargs) if exp is not None: return r"%s^{%s}" % (tex, exp) else: return tex def _print_floor(self, expr, exp=None): tex = r"\lfloor{%s}\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"\lceil{%s}\rceil" % 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 _print_Determinant = _print_Abs def _print_re(self, expr, exp=None): tex = r"\Re{%s}" % self.parenthesize(expr.args[0], PRECEDENCE['Atom']) return self._do_exponent(tex, exp) def _print_im(self, expr, exp=None): tex = r"\Im{%s}" % self.parenthesize(expr.args[0], PRECEDENCE['Func']) return self._do_exponent(tex, exp) def _print_Not(self, e): from sympy import Equivalent, Implies if isinstance(e.args[0], Equivalent): return self._print_Equivalent(e.args[0], r"\not\equiv") 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 (%s)" % 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"\equiv") 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_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_gamma(self, expr, exp=None): tex = r"\left(%s\right)" % self._print(expr.args[0]) if exp is not None: return r"\Gamma^{%s}%s" % (exp, tex) else: return r"\Gamma%s" % tex 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 _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"%s^{%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): tex = r"%s" % (sym) need_exp = False if exp is not None: if tex.find('^') == -1: tex = r"%s^{%s}" % (tex, self._print(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): if len(vec) == 0: 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=""): 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=""): 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, self._print(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, self._print(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" % (self._print(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" % (self._print(exp), tex) return r"\zeta%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" % (self._print(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, self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(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}" % (self._print(exp)) return tex 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 len(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"\mathcal{O}\left(%s\right)" % s def _print_Symbol(self, expr): if expr in self._settings['symbol_names']: return self._settings['symbol_names'][expr] return self._deal_with_super_sub(expr.name) if \ '\\' not in expr.name else expr.name _print_RandomSymbol = _print_Symbol _print_MatrixSymbol = _print_Symbol def _deal_with_super_sub(self, string): if '{' in string: return string name, supers, subs = split_super_sub(string) name = translate(name) supers = [translate(sup) for sup in supers] subs = [translate(sub) for sub in subs] # glue all items together: if len(supers) > 0: name += "^{%s}" % " ".join(supers) if len(subs) > 0: 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_MatrixBase(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') 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 % r"\\".join(lines) _print_ImmutableMatrix = _print_ImmutableDenseMatrix \ = _print_Matrix \ = _print_MatrixBase def _print_MatrixElement(self, expr): return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) \ + '_{%s, %s}' % (expr.i, expr.j) def _print_MatrixSlice(self, expr): def latexslice(x): x = list(x) if x[2] == 1: del x[2] if x[1] == x[0] + 1: del x[1] if x[0] == 0: x[0] = '' return ':'.join(map(self._print, x)) return (self._print(expr.parent) + r'\left[' + latexslice(expr.rowslice) + ', ' + latexslice(expr.colslice) + 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 if not isinstance(mat, MatrixSymbol): return r"\left(%s\right)^T" % self._print(mat) else: return "%s^T" % self._print(mat) def _print_Adjoint(self, expr): mat = expr.arg from sympy.matrices import MatrixSymbol if not isinstance(mat, MatrixSymbol): return r"\left(%s\right)^\dagger" % self._print(mat) else: return r"%s^\dagger" % self._print(mat) def _print_MatAdd(self, expr): terms = list(expr.args) tex = " + ".join(map(self._print, terms)) return tex def _print_MatMul(self, expr): from sympy import Add, MatAdd, HadamardProduct def parens(x): if isinstance(x, (Add, MatAdd, HadamardProduct)): return r"\left(%s\right)" % self._print(x) return self._print(x) return ' '.join(map(parens, expr.args)) 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._print(expr.args[1]), self._print(exp)) return r'%s\bmod{%s}' % (self.parenthesize(expr.args[0], PRECEDENCE['Mul'], strict=True), self._print(expr.args[1])) def _print_HadamardProduct(self, expr): from sympy import Add, MatAdd, MatMul def parens(x): if isinstance(x, (Add, MatAdd, MatMul)): return r"\left(%s\right)" % self._print(x) return self._print(x) return r' \circ '.join(map(parens, expr.args)) def _print_MatPow(self, expr): base, exp = expr.base, expr.exp from sympy.matrices import MatrixSymbol if not isinstance(base, MatrixSymbol): return r"\left(%s\right)^{%s}" % (self._print(base), self._print(exp)) else: return "%s^{%s}" % (self._print(base), self._print(exp)) def _print_ZeroMatrix(self, Z): return r"\mathbb{0}" def _print_Identity(self, I): return r"\mathbb{I}" def _print_NDimArray(self, expr): 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 self._settings['mat_delim']: left_delim = 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 = [[]] + [[] for i in range(expr.rank())] 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 _print_ImmutableDenseNDimArray = _print_NDimArray _print_ImmutableSparseNDimArray = _print_NDimArray _print_MutableDenseNDimArray = _print_NDimArray _print_MutableSparseNDimArray = _print_NDimArray def _print_tuple(self, expr): return r"\left ( %s\right )" % \ r", \quad ".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): return r"\left [ %s\right ]" % \ r", \quad ".join([ self._print(i) for i in expr ]) 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", \quad ".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): shift = self._print(expr.args[0] - expr.args[1]) power = self._print(expr.args[2]) tex = r"{\langle %s \rangle}^{%s}" % (shift, power) return tex def _print_Heaviside(self, expr, exp=None): tex = r"\theta\left(%s\right)" % self._print(expr.args[0]) 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: 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_ProductSet(self, p): if len(p.sets) > 1 and not has_variety(p.sets): return self._print(p.sets[0]) + "^%d" % len(p.sets) else: return r" \times ".join(self._print(set) for set in p.sets) def _print_RandomDomain(self, d): if hasattr(d, 'as_boolean'): return 'Domain: ' + self._print(d.as_boolean()) elif hasattr(d, 'set'): return ('Domain: ' + self._print(d.symbols) + ' in ' + self._print(d.set)) elif hasattr(d, 'symbols'): return '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) items = ", ".join(map(self._print, items)) return r"\left\{%s\right\}" % items _print_frozenset = _print_set def _print_Range(self, s): dots = r'\ldots' if s.start.is_infinite: printset = s.start, dots, s[-1] - s.step, s[-1] elif s.stop.is_infinite or len(s) > 4: it = iter(s) printset = next(it), next(it), dots, s[-1] else: printset = tuple(s) return (r"\left\{" + r", ".join(self._print(el) for el in printset) + r"\right\}") def _print_SeqFormula(self, s): if s.start is S.NegativeInfinity: stop = s.stop printset = (r'\ldots', 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(r'\ldots') else: printset = tuple(s) return (r"\left\[" + r", ".join(self._print(el) for el in printset) + r"\right\]") _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"\langle %s, %s\rangle" % \ (self._print(i.min), self._print(i.max)) def _print_Union(self, u): return r" \cup ".join([self._print(i) for i in u.args]) def _print_Complement(self, u): return r" \setminus ".join([self._print(i) for i in u.args]) def _print_Intersection(self, u): return r" \cap ".join([self._print(i) for i in u.args]) def _print_SymmetricDifference(self, u): return r" \triangle ".join([self._print(i) for i in u.args]) 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_Reals(self, i): return r"\mathbb{R}" def _print_Complexes(self, i): return r"\mathbb{C}" def _print_ImageSet(self, s): return r"\left\{%s\; |\; %s \in %s\right\}" % ( self._print(s.lamda.expr), ', '.join([self._print(var) for var in s.lamda.variables]), self._print(s.base_set)) def _print_ConditionSet(self, s): vars_print = ', '.join([self._print(var) for var in Tuple(s.sym)]) return r"\left\{%s\; |\; %s \in %s \wedge %s \right\}" % ( vars_print, vars_print, self._print(s.base_set), self._print(s.condition.as_expr())) def _print_ComplexRegion(self, s): vars_print = ', '.join([self._print(var) for var in s.variables]) return r"\left\{%s\; |\; %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): return self._print_Add(s.truncate()) + self._print(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__ expr = self._print(poly.as_expr()) 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_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, self._print(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, self._print(exp)) return tex def _print_MellinTransform(self, expr): return r"\mathcal{M}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_InverseMellinTransform(self, expr): return r"\mathcal{M}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_LaplaceTransform(self, expr): return r"\mathcal{L}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_InverseLaplaceTransform(self, expr): return r"\mathcal{L}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_FourierTransform(self, expr): return r"\mathcal{F}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_InverseFourierTransform(self, expr): return r"\mathcal{F}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_SineTransform(self, expr): return r"\mathcal{SIN}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_InverseSineTransform(self, expr): return r"\mathcal{SIN}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_CosineTransform(self, expr): return r"\mathcal{COS}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) def _print_InverseCosineTransform(self, expr): return r"\mathcal{COS}^{-1}_{%s}\left[%s\right]\left(%s\right)" % (self._print(expr.args[1]), self._print(expr.args[0]), self._print(expr.args[2])) 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_Morphism(self, morphism): domain = self._print(morphism.domain) codomain = self._print(morphism.codomain) return "%s\\rightarrow %s" % (domain, codomain) 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 "\\mathbf{%s}" % 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 '{%s}^{%s}' % (self._print(M.ring), self._print(M.rank)) def _print_FreeModuleElement(self, m): # Print as row vector for convenience, for now. return r"\left[ %s \right]" % ",".join( '{' + self._print(x) + '}' for x in m) def _print_SubModule(self, m): return r"\left< %s \right>" % ",".join( '{' + self._print(x) + '}' for x in m.gens) def _print_ModuleImplementedIdeal(self, m): return r"\left< %s \right>" % ",".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{%s}{%s}" % (self._print(R.ring), self._print(R.base_ideal)) def _print_QuotientRingElement(self, x): return r"{%s} + {%s}" % (self._print(x.data), self._print(x.ring.base_ideal)) def _print_QuotientModuleElement(self, m): return r"{%s} + {%s}" % (self._print(m.data), self._print(m.module.killed_module)) def _print_QuotientModule(self, M): # TODO nicer fractions for few generators... return r"\frac{%s}{%s}" % (self._print(M.base), self._print(M.killed_module)) def _print_MatrixHomomorphism(self, h): return r"{%s} : {%s} \to {%s}" % (self._print(h._sympy_matrix()), self._print(h.domain), self._print(h.codomain)) def _print_BaseScalarField(self, field): string = field._coord_sys._names[field._index] return r'\boldsymbol{\mathrm{%s}}' % self._print(Symbol(string)) def _print_BaseVectorField(self, field): string = field._coord_sys._names[field._index] return r'\partial_{%s}' % self._print(Symbol(string)) def _print_Differential(self, diff): field = diff._form_field if hasattr(field, '_coord_sys'): string = field._coord_sys._names[field._index] return r'\mathrm{d}%s' % self._print(Symbol(string)) else: return 'd(%s)' % self._print(field) string = self._print(field) return r'\mathrm{d}\left(%s\right)' % string def _print_Tr(self, p): #Todo: Handle indices contents = self._print(p.args[0]) return r'\mbox{Tr}\left(%s\right)' % (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]), self._print(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]), self._print(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" % (self._print(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" % (self._print(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]), self._print(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]), self._print(exp)) return r'\Omega\left(%s\right)' % self._print(expr.args[0])
def translate(s): 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=lambda k:len(k), reverse=True): if s.lower().endswith(key) and len(s)>len(key): return modifier_dict[key](translate(s[:-len(key)])) return s
[docs]def latex(expr, **settings): r""" Convert the given expression to LaTeX representation. >>> from sympy import latex, pi, sin, asin, Integral, Matrix, Rational >>> from sympy.abc import x, y, mu, r, tau >>> print(latex((2*tau)**Rational(7,2))) 8 \sqrt{2} \tau^{\frac{7}{2}} Not using a print statement for printing, results in double backslashes for latex commands since that's the way Python escapes backslashes in strings. >>> latex((2*tau)**Rational(7,2)) '8 \\sqrt{2} \\tau^{\\frac{7}{2}}' order: 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. mode: 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. >>> 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} itex: Specifies if itex-specific syntax is used, including emitting ``$$ $$``. >>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True)) $$8 \sqrt{2} \mu^{\frac{7}{2}}$$ fold_frac_powers: Emit "^{p/q}" instead of "^{\frac{p}{q}}" for fractional powers. >>> print(latex((2*tau)**Rational(7,2), fold_frac_powers=True)) 8 \sqrt{2} \tau^{7/2} fold_func_brackets: Fold function brackets where applicable. >>> 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}}} fold_short_frac: 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. >>> 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 long_frac_ratio: The allowed ratio of the width of the numerator to the width of the denominator before we start breaking off long fractions. The default value is 2. >>> 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 mul_symbol: The symbol to use for multiplication. Can be one of None, "ldot", "dot", or "times". >>> print(latex((2*tau)**sin(Rational(7,2)), mul_symbol="times")) \left(2 \times \tau\right)^{\sin{\left (\frac{7}{2} \right )}} inv_trig_style: How inverse trig functions should be displayed. Can be one of "abbreviated", "full", or "power". Defaults to "abbreviated". >>> 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 )} mat_str: 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. >>> 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] mat_delim: The delimiter to wrap around matrices. Can be one of "[", "(", or the empty string. Defaults to "[". >>> print(latex(Matrix(2, 1, [x, y]), mat_delim="(")) \left(\begin{matrix}x\\y\end{matrix}\right) symbol_names: Dictionary of symbols and the custom strings they should be emitted as. >>> print(latex(x**2, symbol_names={x:'x_i'})) x_i^{2} ``latex`` also supports the builtin container types list, tuple, and dictionary. >>> print(latex([2/x, y], mode='inline')) $\left [ 2 / x, \quad y\right ]$ """ return LatexPrinter(settings).doprint(expr)