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latex.py
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latex.py
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"""
A Printer which converts an expression into its LaTeX equivalent.
"""
from sympy.core import S, C, Basic, Symbol
from printer import Printer
from sympy.simplify import fraction
import re
class LatexPrinter(Printer):
printmethod = "_latex_"
def __init__(self, profile=None):
Printer.__init__(self)
self._settings = {
"inline" : True,
"fold_frac_powers" : False,
"fold_func_brackets" : False,
"mul_symbol" : None,
"inv_trig_style" : "abbreviated"
}
if profile is not None:
self._settings.update(profile)
def doprint(self, expr):
tex = Printer.doprint(self, expr)
if self._settings['inline']:
return r"$%s$" % tex
else:
return r"\begin{equation*}%s\end{equation*}" % tex
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)
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/substracted/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 _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_Add(self, expr):
args = list(expr.args)
args.sort(Basic._compare_pretty)
tex = str(self._print(args[0]))
for term in args[1:]:
coeff = term.as_coeff_terms()[0]
if coeff.is_negative:
tex += r" %s" % self._print(term)
else:
tex += r" + %s" % self._print(term)
return tex
def _print_Mul(self, expr):
coeff, terms = expr.as_coeff_terms()
if not coeff.is_negative:
tex = ""
else:
coeff = -coeff
tex = "- "
numer, denom = fraction(C.Mul(*terms))
mul_symbol_table = {
None : r" ",
"ldot" : r" \,.\, ",
"dot" : r" \cdot ",
"times" : r" \times "
}
seperator = mul_symbol_table[self._settings['mul_symbol']]
def convert(terms):
product = []
if not terms.is_Mul:
return str(self._print(terms))
else:
for term in terms.args:
pretty = self._print(term)
if term.is_Add:
product.append(r"\left(%s\right)" % pretty)
else:
product.append(str(pretty))
return seperator.join(product)
if denom is S.One:
if coeff is not S.One:
tex += str(self._print(coeff)) + seperator
if numer.is_Add:
tex += r"\left(%s\right)" % convert(numer)
else:
tex += r"%s" % convert(numer)
else:
if numer is S.One:
if coeff.is_Integer:
numer *= coeff.p
elif coeff.is_Rational:
if coeff.p != 1:
numer *= coeff.p
denom *= coeff.q
elif coeff is not S.One:
tex += str(self._print(coeff)) + " "
else:
if coeff.is_Rational and coeff.p == 1:
denom *= coeff.q
elif coeff is not S.One:
tex += str(self._print(coeff)) + " "
tex += r"\frac{%s}{%s}" % \
(convert(numer), convert(denom))
return tex
def _print_Pow(self, expr):
if expr.exp.is_Rational and expr.exp.q == 2:
base, exp = self._print(expr.base), abs(expr.exp.p)
if exp == 1:
tex = r"\sqrt{%s}" % base
else:
tex = r"\sqrt[%s]{%s}" % (exp, 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._print(expr.base), expr.exp.p, expr.exp.q
return r"%s^{%s/%s}" % (base, p, q)
else:
if expr.base.is_Function:
return self._print(expr.base, self._print(expr.exp))
else:
if expr.exp == S.NegativeOne:
#solves issue 1030
#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()
if self._needs_brackets(expr.base):
tex = r"\left(%s\right)^{%s}"
else:
tex = r"%s^{%s}"
return tex % (self._print(expr.base),
self._print(expr.exp))
def _print_Derivative(self, expr):
dim = len(expr.symbols)
if dim == 1:
tex = r"\frac{\partial}{\partial %s}" % \
self._print(expr.symbols[0])
else:
multiplicity, i, tex = [], 1, ""
current = expr.symbols[0]
for symbol in expr.symbols[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"\partial %s" % self._print(x)
else:
tex += r"\partial^{%s} %s" % (i, self._print(x))
tex = r"\frac{\partial^{%s}}{%s} " % (dim, tex)
if isinstance(expr.expr, C.AssocOp):
return r"%s\left(%s\right)" % (tex, self._print(expr.expr))
else:
return r"%s %s" % (tex, self._print(expr.expr))
def _print_Integral(self, expr):
tex, symbols = "", []
for symbol, limits in reversed(expr.limits):
tex += r"\int"
if limits is not None:
if not self._settings['inline']:
tex += r"\limits"
tex += "_{%s}^{%s}" % (self._print(limits[0]),
self._print(limits[1]))
symbols.insert(0, "d%s" % self._print(symbol))
return r"%s %s\,%s" % (tex,
str(self._print(expr.function)), " ".join(symbols))
def _print_Limit(self, expr):
tex = r"\lim_{%s \to %s}" % (self._print(expr.var),
self._print(expr.varlim))
if isinstance(expr.expr, C.AssocOp):
return r"%s\left(%s\right)" % (tex, self._print(expr.expr))
else:
return r"%s %s" % (tex, self._print(expr.expr))
def _print_Function(self, expr, exp=None):
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:
name = r"\operatorname{%s}^{-1}" % func
elif exp is not None:
name = r"\operatorname{%s}^{%s}" % (func, exp)
else:
name = r"\operatorname{%s}" % func
if can_fold_brackets:
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_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"\lvert{%s}\rvert" % 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._needs_brackets(expr.args[0]):
tex = r"\Re\left(%s\right)" % self._print(expr.args[0])
else:
tex = r"\Re{%s}" % self._print(expr.args[0])
return self._do_exponent(tex, exp)
def _print_im(self, expr, exp=None):
if self._needs_brackets(expr.args[0]):
tex = r"\Im\left(%s\right)" % self._print(expr.args[0])
else:
tex = r"\Im{%s}" % self._print(expr.args[0])
return self._do_exponent(tex, exp)
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_exp(self, expr, exp=None):
tex = r"e^{%s}" % self._print(expr.args[0])
return self._do_exponent(tex, exp)
def _print_gamma(self, expr, exp=None):
tex = r"\left(%s\right)" % self._print(expr.args[0])
if exp is not None:
return r"\operatorname{\Gamma}^{%s}%s" % (exp, tex)
else:
return r"\operatorname{\Gamma}%s" % tex
def _print_Factorial(self, expr, exp=None):
x = expr.args[0]
if self._needs_brackets(x):
tex = r"\left(%s\right)!" % self._print(x)
else:
tex = self._print(x) + "!"
if exp is not None:
return r"%s^{%s}" % (tex, exp)
else:
return tex
def _print_Binomial(self, expr, exp=None):
tex = r"{{%s}\choose{%s}}" % (self._print(expr[0]),
self._print(expr[1]))
if exp is not None:
return r"%s^{%s}" % (tex, exp)
else:
return tex
def _print_RisingFactorial(self, expr, exp=None):
tex = r"{\left(%s\right)}^{\left(%s\right)}" % \
(self._print(expr[0]), self._print(expr[1]))
return self._do_exponent(tex, exp)
def _print_FallingFactorial(self, expr, exp=None):
tex = r"{\left(%s\right)}_{\left(%s\right)}" % \
(self._print(expr[0]), self._print(expr[1]))
return self._do_exponent(tex, exp)
def _print_Rational(self, expr):
if expr.q != 1:
sign = ""
p = expr.p
if expr.p < 0:
sign = "- "
p = -p
return r"%s\frac{%d}{%d}" % (sign, p, expr.q)
else:
return self._print(expr.p)
def _print_Infinity(self, expr):
return r"\infty"
def _print_NegativeInfinity(self, expr):
return r"-\infty"
def _print_ComplexInfinity(self, expr):
return r"\tilde{\infty}"
def _print_ImaginaryUnit(self, expr):
return r"\mathbf{\imath}"
def _print_NaN(self, expr):
return r"\bot"
def _print_Pi(self, expr):
return r"\pi"
def _print_Exp1(self, expr):
return r"e"
def _print_EulerGamma(self, expr):
return r"\gamma"
def _print_Order(self, expr):
return r"\operatorname{\mathcal{O}}\left(%s\right)" % \
self._print(expr.args[0])
def _print_Symbol(self, expr):
if len(expr.name) == 1:
return expr.name
#convert trailing digits to subscript
m = re.match('(^[a-zA-Z]+)([0-9]+)$', expr.name)
if m is not None:
name, sub=m.groups()
tex=self._print_Symbol(Symbol(name))
tex="%s_{%s}" %(tex, sub)
return tex
# insert braces to expresions containing '_' or '^'
m = re.match('(^[a-zA-Z0-9]+)([_\^]{1})([a-zA-Z0-9]+)$', expr.name)
if m is not None:
name, sep, rest=m.groups()
tex=self._print_Symbol(Symbol(name))
tex="%s%s{%s}" %(tex, sep, rest)
return tex
greek = set([ 'alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta',
'eta', 'theta', 'iota', 'kappa', 'lambda', 'mu', 'nu',
'xi', 'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon',
'phi', 'chi', 'psi', 'omega' ])
other = set( ['aleph', 'beth', 'daleth', 'gimel', 'ell', 'eth',
'hbar', 'hslash', 'mho' ])
if expr.name.lower() in greek:
return "\\" + expr.name
elif expr.name in other:
return "\\" + expr.name
else:
return expr.name
def _print_Relational(self, expr):
charmap = {
"==" : "=",
"<" : "<",
"<=" : 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 & for %s" % (self._print(e), self._print(c)) \
for e, c in expr.args[:-1]]
if expr.args[-1].cond is S.One:
ecpairs.append(r"%s & \textrm{otherwise}" % \
self._print(expr.args[-1].expr))
else:
ecpairs.append(r"%s & for %s" % \
(self._print(expr.args[-1].cond),
self._print(expr.args[-1].expr)))
tex = r"\left\{\begin{array}{cl} %s \end{array}\right."
return tex % r" \\".join(ecpairs)
def _print_Matrix(self, expr):
lines = []
for line in range(expr.lines): # horrible, should be 'rows'
lines.append(" & ".join([ self._print(i) for i in expr[line,:] ]))
if self._settings['inline']:
tex = r"\left(\begin{smallmatrix}%s\end{smallmatrix}\right)"
else:
tex = r"\begin{pmatrix}%s\end{pmatrix}"
return tex % r"\\".join(lines)
def _print_tuple(self, expr):
return r"\begin{pmatrix}%s\end{pmatrix}" % \
r", & ".join([ self._print(i) for i in expr ])
def _print_list(self, expr):
return r"\begin{bmatrix}%s\end{bmatrix}" % \
r", & ".join([ self._print(i) for i in expr ])
def _print_dict(self, expr):
items = []
keys = expr.keys()
keys.sort(Basic.compare_pretty)
for key in keys:
val = expr[key]
items.append("%s : %s" % (self._print(key), self._print(val)))
return r"\begin{Bmatrix}%s\end{Bmatrix}" % r", & ".join(items)
def _print_DiracDelta(self, expr):
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]))
return tex
def latex(expr, profile=None, **kargs):
r"""Convert the given expression to LaTeX representation.
You can specify how the generated code will be delimited.
If the 'inline' keyword is set then inline LaTeX $ $ will
be used. Otherwise the resulting code will be enclosed in
'equation*' environment (remember to import 'amsmath').
>>> from sympy import *
>>> from sympy.abc import *
>>> latex((2*tau)**Rational(7,2))
'$8 \\sqrt{2} \\sqrt[7]{\\tau}$'
>>> latex((2*mu)**Rational(7,2), inline=False)
'\\begin{equation*}8 \\sqrt{2} \\sqrt[7]{\\mu}\\end{equation*}'
Besides all Basic based expressions, you can recursively
convert Pyhon containers (lists, tuples and dicts) and
also SymPy matrices:
>>> latex([2/x, y])
'$\\begin{bmatrix}\\frac{2}{x}, & y\\end{bmatrix}$'
"""
if profile is not None:
profile.update(kargs)
else:
profile = kargs
return LatexPrinter(profile).doprint(expr)
def print_latex(expr):
"""Prints LaTeX representation of the given expression."""
print latex(expr)