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image-handler/image-handler10.0/venv/lib/site-packages/sympy/printing/mathml.py

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"""
A MathML printer.
"""
from __future__ import annotations
from typing import Any
from sympy.core.mul import Mul
from sympy.core.singleton import S
from sympy.core.sorting import default_sort_key
from sympy.core.sympify import sympify
from sympy.printing.conventions import split_super_sub, requires_partial
from sympy.printing.precedence import \
precedence_traditional, PRECEDENCE, PRECEDENCE_TRADITIONAL
from sympy.printing.pretty.pretty_symbology import greek_unicode
from sympy.printing.printer import Printer, print_function
from mpmath.libmp import prec_to_dps, repr_dps, to_str as mlib_to_str
class MathMLPrinterBase(Printer):
"""Contains common code required for MathMLContentPrinter and
MathMLPresentationPrinter.
"""
_default_settings: dict[str, Any] = {
"order": None,
"encoding": "utf-8",
"fold_frac_powers": False,
"fold_func_brackets": False,
"fold_short_frac": None,
"inv_trig_style": "abbreviated",
"ln_notation": False,
"long_frac_ratio": None,
"mat_delim": "[",
"mat_symbol_style": "plain",
"mul_symbol": None,
"root_notation": True,
"symbol_names": {},
"mul_symbol_mathml_numbers": '·',
}
def __init__(self, settings=None):
Printer.__init__(self, settings)
from xml.dom.minidom import Document, Text
self.dom = Document()
# Workaround to allow strings to remain unescaped
# Based on
# https://stackoverflow.com/questions/38015864/python-xml-dom-minidom-\
# please-dont-escape-my-strings/38041194
class RawText(Text):
def writexml(self, writer, indent='', addindent='', newl=''):
if self.data:
writer.write('{}{}{}'.format(indent, self.data, newl))
def createRawTextNode(data):
r = RawText()
r.data = data
r.ownerDocument = self.dom
return r
self.dom.createTextNode = createRawTextNode
def doprint(self, expr):
"""
Prints the expression as MathML.
"""
mathML = Printer._print(self, expr)
unistr = mathML.toxml()
xmlbstr = unistr.encode('ascii', 'xmlcharrefreplace')
res = xmlbstr.decode()
return res
def apply_patch(self):
# Applying the patch of xml.dom.minidom bug
# Date: 2011-11-18
# Description: http://ronrothman.com/public/leftbraned/xml-dom-minidom\
# -toprettyxml-and-silly-whitespace/#best-solution
# Issue: https://bugs.python.org/issue4147
# Patch: https://hg.python.org/cpython/rev/7262f8f276ff/
from xml.dom.minidom import Element, Text, Node, _write_data
def writexml(self, writer, indent="", addindent="", newl=""):
# indent = current indentation
# addindent = indentation to add to higher levels
# newl = newline string
writer.write(indent + "<" + self.tagName)
attrs = self._get_attributes()
a_names = list(attrs.keys())
a_names.sort()
for a_name in a_names:
writer.write(" %s=\"" % a_name)
_write_data(writer, attrs[a_name].value)
writer.write("\"")
if self.childNodes:
writer.write(">")
if (len(self.childNodes) == 1 and
self.childNodes[0].nodeType == Node.TEXT_NODE):
self.childNodes[0].writexml(writer, '', '', '')
else:
writer.write(newl)
for node in self.childNodes:
node.writexml(
writer, indent + addindent, addindent, newl)
writer.write(indent)
writer.write("</%s>%s" % (self.tagName, newl))
else:
writer.write("/>%s" % (newl))
self._Element_writexml_old = Element.writexml
Element.writexml = writexml
def writexml(self, writer, indent="", addindent="", newl=""):
_write_data(writer, "%s%s%s" % (indent, self.data, newl))
self._Text_writexml_old = Text.writexml
Text.writexml = writexml
def restore_patch(self):
from xml.dom.minidom import Element, Text
Element.writexml = self._Element_writexml_old
Text.writexml = self._Text_writexml_old
class MathMLContentPrinter(MathMLPrinterBase):
"""Prints an expression to the Content MathML markup language.
References: https://www.w3.org/TR/MathML2/chapter4.html
"""
printmethod = "_mathml_content"
def mathml_tag(self, e):
"""Returns the MathML tag for an expression."""
translate = {
'Add': 'plus',
'Mul': 'times',
'Derivative': 'diff',
'Number': 'cn',
'int': 'cn',
'Pow': 'power',
'Max': 'max',
'Min': 'min',
'Abs': 'abs',
'And': 'and',
'Or': 'or',
'Xor': 'xor',
'Not': 'not',
'Implies': 'implies',
'Symbol': 'ci',
'MatrixSymbol': 'ci',
'RandomSymbol': 'ci',
'Integral': 'int',
'Sum': 'sum',
'sin': 'sin',
'cos': 'cos',
'tan': 'tan',
'cot': 'cot',
'csc': 'csc',
'sec': 'sec',
'sinh': 'sinh',
'cosh': 'cosh',
'tanh': 'tanh',
'coth': 'coth',
'csch': 'csch',
'sech': 'sech',
'asin': 'arcsin',
'asinh': 'arcsinh',
'acos': 'arccos',
'acosh': 'arccosh',
'atan': 'arctan',
'atanh': 'arctanh',
'atan2': 'arctan',
'acot': 'arccot',
'acoth': 'arccoth',
'asec': 'arcsec',
'asech': 'arcsech',
'acsc': 'arccsc',
'acsch': 'arccsch',
'log': 'ln',
'Equality': 'eq',
'Unequality': 'neq',
'GreaterThan': 'geq',
'LessThan': 'leq',
'StrictGreaterThan': 'gt',
'StrictLessThan': 'lt',
'Union': 'union',
'Intersection': 'intersect',
}
for cls in e.__class__.__mro__:
n = cls.__name__
if n in translate:
return translate[n]
# Not found in the MRO set
n = e.__class__.__name__
return n.lower()
def _print_Mul(self, expr):
if expr.could_extract_minus_sign():
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('minus'))
x.appendChild(self._print_Mul(-expr))
return x
from sympy.simplify import fraction
numer, denom = fraction(expr)
if denom is not S.One:
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('divide'))
x.appendChild(self._print(numer))
x.appendChild(self._print(denom))
return x
coeff, terms = expr.as_coeff_mul()
if coeff is S.One and len(terms) == 1:
# XXX since the negative coefficient has been handled, I don't
# think a coeff of 1 can remain
return self._print(terms[0])
if self.order != 'old':
terms = Mul._from_args(terms).as_ordered_factors()
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('times'))
if coeff != 1:
x.appendChild(self._print(coeff))
for term in terms:
x.appendChild(self._print(term))
return x
def _print_Add(self, expr, order=None):
args = self._as_ordered_terms(expr, order=order)
lastProcessed = self._print(args[0])
plusNodes = []
for arg in args[1:]:
if arg.could_extract_minus_sign():
# use minus
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('minus'))
x.appendChild(lastProcessed)
x.appendChild(self._print(-arg))
# invert expression since this is now minused
lastProcessed = x
if arg == args[-1]:
plusNodes.append(lastProcessed)
else:
plusNodes.append(lastProcessed)
lastProcessed = self._print(arg)
if arg == args[-1]:
plusNodes.append(self._print(arg))
if len(plusNodes) == 1:
return lastProcessed
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('plus'))
while plusNodes:
x.appendChild(plusNodes.pop(0))
return x
def _print_Piecewise(self, expr):
if expr.args[-1].cond != True:
# We need the last conditional to be a True, otherwise the resulting
# function may not return a result.
raise ValueError("All Piecewise expressions must contain an "
"(expr, True) statement to be used as a default "
"condition. Without one, the generated "
"expression may not evaluate to anything under "
"some condition.")
root = self.dom.createElement('piecewise')
for i, (e, c) in enumerate(expr.args):
if i == len(expr.args) - 1 and c == True:
piece = self.dom.createElement('otherwise')
piece.appendChild(self._print(e))
else:
piece = self.dom.createElement('piece')
piece.appendChild(self._print(e))
piece.appendChild(self._print(c))
root.appendChild(piece)
return root
def _print_MatrixBase(self, m):
x = self.dom.createElement('matrix')
for i in range(m.rows):
x_r = self.dom.createElement('matrixrow')
for j in range(m.cols):
x_r.appendChild(self._print(m[i, j]))
x.appendChild(x_r)
return x
def _print_Rational(self, e):
if e.q == 1:
# don't divide
x = self.dom.createElement('cn')
x.appendChild(self.dom.createTextNode(str(e.p)))
return x
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('divide'))
# numerator
xnum = self.dom.createElement('cn')
xnum.appendChild(self.dom.createTextNode(str(e.p)))
# denominator
xdenom = self.dom.createElement('cn')
xdenom.appendChild(self.dom.createTextNode(str(e.q)))
x.appendChild(xnum)
x.appendChild(xdenom)
return x
def _print_Limit(self, e):
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement(self.mathml_tag(e)))
x_1 = self.dom.createElement('bvar')
x_2 = self.dom.createElement('lowlimit')
x_1.appendChild(self._print(e.args[1]))
x_2.appendChild(self._print(e.args[2]))
x.appendChild(x_1)
x.appendChild(x_2)
x.appendChild(self._print(e.args[0]))
return x
def _print_ImaginaryUnit(self, e):
return self.dom.createElement('imaginaryi')
def _print_EulerGamma(self, e):
return self.dom.createElement('eulergamma')
def _print_GoldenRatio(self, e):
"""We use unicode #x3c6 for Greek letter phi as defined here
https://www.w3.org/2003/entities/2007doc/isogrk1.html"""
x = self.dom.createElement('cn')
x.appendChild(self.dom.createTextNode("\N{GREEK SMALL LETTER PHI}"))
return x
def _print_Exp1(self, e):
return self.dom.createElement('exponentiale')
def _print_Pi(self, e):
return self.dom.createElement('pi')
def _print_Infinity(self, e):
return self.dom.createElement('infinity')
def _print_NaN(self, e):
return self.dom.createElement('notanumber')
def _print_EmptySet(self, e):
return self.dom.createElement('emptyset')
def _print_BooleanTrue(self, e):
return self.dom.createElement('true')
def _print_BooleanFalse(self, e):
return self.dom.createElement('false')
def _print_NegativeInfinity(self, e):
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('minus'))
x.appendChild(self.dom.createElement('infinity'))
return x
def _print_Integral(self, e):
def lime_recur(limits):
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement(self.mathml_tag(e)))
bvar_elem = self.dom.createElement('bvar')
bvar_elem.appendChild(self._print(limits[0][0]))
x.appendChild(bvar_elem)
if len(limits[0]) == 3:
low_elem = self.dom.createElement('lowlimit')
low_elem.appendChild(self._print(limits[0][1]))
x.appendChild(low_elem)
up_elem = self.dom.createElement('uplimit')
up_elem.appendChild(self._print(limits[0][2]))
x.appendChild(up_elem)
if len(limits[0]) == 2:
up_elem = self.dom.createElement('uplimit')
up_elem.appendChild(self._print(limits[0][1]))
x.appendChild(up_elem)
if len(limits) == 1:
x.appendChild(self._print(e.function))
else:
x.appendChild(lime_recur(limits[1:]))
return x
limits = list(e.limits)
limits.reverse()
return lime_recur(limits)
def _print_Sum(self, e):
# Printer can be shared because Sum and Integral have the
# same internal representation.
return self._print_Integral(e)
def _print_Symbol(self, sym):
ci = self.dom.createElement(self.mathml_tag(sym))
def join(items):
if len(items) > 1:
mrow = self.dom.createElement('mml:mrow')
for i, item in enumerate(items):
if i > 0:
mo = self.dom.createElement('mml:mo')
mo.appendChild(self.dom.createTextNode(" "))
mrow.appendChild(mo)
mi = self.dom.createElement('mml:mi')
mi.appendChild(self.dom.createTextNode(item))
mrow.appendChild(mi)
return mrow
else:
mi = self.dom.createElement('mml:mi')
mi.appendChild(self.dom.createTextNode(items[0]))
return mi
# translate name, supers and subs to unicode characters
def translate(s):
if s in greek_unicode:
return greek_unicode.get(s)
else:
return s
name, supers, subs = split_super_sub(sym.name)
name = translate(name)
supers = [translate(sup) for sup in supers]
subs = [translate(sub) for sub in subs]
mname = self.dom.createElement('mml:mi')
mname.appendChild(self.dom.createTextNode(name))
if not supers:
if not subs:
ci.appendChild(self.dom.createTextNode(name))
else:
msub = self.dom.createElement('mml:msub')
msub.appendChild(mname)
msub.appendChild(join(subs))
ci.appendChild(msub)
else:
if not subs:
msup = self.dom.createElement('mml:msup')
msup.appendChild(mname)
msup.appendChild(join(supers))
ci.appendChild(msup)
else:
msubsup = self.dom.createElement('mml:msubsup')
msubsup.appendChild(mname)
msubsup.appendChild(join(subs))
msubsup.appendChild(join(supers))
ci.appendChild(msubsup)
return ci
_print_MatrixSymbol = _print_Symbol
_print_RandomSymbol = _print_Symbol
def _print_Pow(self, e):
# Here we use root instead of power if the exponent is the reciprocal
# of an integer
if (self._settings['root_notation'] and e.exp.is_Rational
and e.exp.p == 1):
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('root'))
if e.exp.q != 2:
xmldeg = self.dom.createElement('degree')
xmlcn = self.dom.createElement('cn')
xmlcn.appendChild(self.dom.createTextNode(str(e.exp.q)))
xmldeg.appendChild(xmlcn)
x.appendChild(xmldeg)
x.appendChild(self._print(e.base))
return x
x = self.dom.createElement('apply')
x_1 = self.dom.createElement(self.mathml_tag(e))
x.appendChild(x_1)
x.appendChild(self._print(e.base))
x.appendChild(self._print(e.exp))
return x
def _print_Number(self, e):
x = self.dom.createElement(self.mathml_tag(e))
x.appendChild(self.dom.createTextNode(str(e)))
return x
def _print_Float(self, e):
x = self.dom.createElement(self.mathml_tag(e))
repr_e = mlib_to_str(e._mpf_, repr_dps(e._prec))
x.appendChild(self.dom.createTextNode(repr_e))
return x
def _print_Derivative(self, e):
x = self.dom.createElement('apply')
diff_symbol = self.mathml_tag(e)
if requires_partial(e.expr):
diff_symbol = 'partialdiff'
x.appendChild(self.dom.createElement(diff_symbol))
x_1 = self.dom.createElement('bvar')
for sym, times in reversed(e.variable_count):
x_1.appendChild(self._print(sym))
if times > 1:
degree = self.dom.createElement('degree')
degree.appendChild(self._print(sympify(times)))
x_1.appendChild(degree)
x.appendChild(x_1)
x.appendChild(self._print(e.expr))
return x
def _print_Function(self, e):
x = self.dom.createElement("apply")
x.appendChild(self.dom.createElement(self.mathml_tag(e)))
for arg in e.args:
x.appendChild(self._print(arg))
return x
def _print_Basic(self, e):
x = self.dom.createElement(self.mathml_tag(e))
for arg in e.args:
x.appendChild(self._print(arg))
return x
def _print_AssocOp(self, e):
x = self.dom.createElement('apply')
x_1 = self.dom.createElement(self.mathml_tag(e))
x.appendChild(x_1)
for arg in e.args:
x.appendChild(self._print(arg))
return x
def _print_Relational(self, e):
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement(self.mathml_tag(e)))
x.appendChild(self._print(e.lhs))
x.appendChild(self._print(e.rhs))
return x
def _print_list(self, seq):
"""MathML reference for the <list> element:
https://www.w3.org/TR/MathML2/chapter4.html#contm.list"""
dom_element = self.dom.createElement('list')
for item in seq:
dom_element.appendChild(self._print(item))
return dom_element
def _print_int(self, p):
dom_element = self.dom.createElement(self.mathml_tag(p))
dom_element.appendChild(self.dom.createTextNode(str(p)))
return dom_element
_print_Implies = _print_AssocOp
_print_Not = _print_AssocOp
_print_Xor = _print_AssocOp
def _print_FiniteSet(self, e):
x = self.dom.createElement('set')
for arg in e.args:
x.appendChild(self._print(arg))
return x
def _print_Complement(self, e):
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('setdiff'))
for arg in e.args:
x.appendChild(self._print(arg))
return x
def _print_ProductSet(self, e):
x = self.dom.createElement('apply')
x.appendChild(self.dom.createElement('cartesianproduct'))
for arg in e.args:
x.appendChild(self._print(arg))
return x
# XXX Symmetric difference is not supported for MathML content printers.
class MathMLPresentationPrinter(MathMLPrinterBase):
"""Prints an expression to the Presentation MathML markup language.
References: https://www.w3.org/TR/MathML2/chapter3.html
"""
printmethod = "_mathml_presentation"
def mathml_tag(self, e):
"""Returns the MathML tag for an expression."""
translate = {
'Number': 'mn',
'Limit': '&#x2192;',
'Derivative': '&dd;',
'int': 'mn',
'Symbol': 'mi',
'Integral': '&int;',
'Sum': '&#x2211;',
'sin': 'sin',
'cos': 'cos',
'tan': 'tan',
'cot': 'cot',
'asin': 'arcsin',
'asinh': 'arcsinh',
'acos': 'arccos',
'acosh': 'arccosh',
'atan': 'arctan',
'atanh': 'arctanh',
'acot': 'arccot',
'atan2': 'arctan',
'Equality': '=',
'Unequality': '&#x2260;',
'GreaterThan': '&#x2265;',
'LessThan': '&#x2264;',
'StrictGreaterThan': '>',
'StrictLessThan': '<',
'lerchphi': '&#x3A6;',
'zeta': '&#x3B6;',
'dirichlet_eta': '&#x3B7;',
'elliptic_k': '&#x39A;',
'lowergamma': '&#x3B3;',
'uppergamma': '&#x393;',
'gamma': '&#x393;',
'totient': '&#x3D5;',
'reduced_totient': '&#x3BB;',
'primenu': '&#x3BD;',
'primeomega': '&#x3A9;',
'fresnels': 'S',
'fresnelc': 'C',
'LambertW': 'W',
'Heaviside': '&#x398;',
'BooleanTrue': 'True',
'BooleanFalse': 'False',
'NoneType': 'None',
'mathieus': 'S',
'mathieuc': 'C',
'mathieusprime': 'S&#x2032;',
'mathieucprime': 'C&#x2032;',
}
def mul_symbol_selection():
if (self._settings["mul_symbol"] is None or
self._settings["mul_symbol"] == 'None'):
return '&InvisibleTimes;'
elif self._settings["mul_symbol"] == 'times':
return '&#xD7;'
elif self._settings["mul_symbol"] == 'dot':
return '&#xB7;'
elif self._settings["mul_symbol"] == 'ldot':
return '&#x2024;'
elif not isinstance(self._settings["mul_symbol"], str):
raise TypeError
else:
return self._settings["mul_symbol"]
for cls in e.__class__.__mro__:
n = cls.__name__
if n in translate:
return translate[n]
# Not found in the MRO set
if e.__class__.__name__ == "Mul":
return mul_symbol_selection()
n = e.__class__.__name__
return n.lower()
def parenthesize(self, item, level, strict=False):
prec_val = precedence_traditional(item)
if (prec_val < level) or ((not strict) and prec_val <= level):
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(item))
return brac
else:
return self._print(item)
def _print_Mul(self, expr):
def multiply(expr, mrow):
from sympy.simplify import fraction
numer, denom = fraction(expr)
if denom is not S.One:
frac = self.dom.createElement('mfrac')
if self._settings["fold_short_frac"] and len(str(expr)) < 7:
frac.setAttribute('bevelled', 'true')
xnum = self._print(numer)
xden = self._print(denom)
frac.appendChild(xnum)
frac.appendChild(xden)
mrow.appendChild(frac)
return mrow
coeff, terms = expr.as_coeff_mul()
if coeff is S.One and len(terms) == 1:
mrow.appendChild(self._print(terms[0]))
return mrow
if self.order != 'old':
terms = Mul._from_args(terms).as_ordered_factors()
if coeff != 1:
x = self._print(coeff)
y = self.dom.createElement('mo')
y.appendChild(self.dom.createTextNode(self.mathml_tag(expr)))
mrow.appendChild(x)
mrow.appendChild(y)
for term in terms:
mrow.appendChild(self.parenthesize(term, PRECEDENCE['Mul']))
if not term == terms[-1]:
y = self.dom.createElement('mo')
y.appendChild(self.dom.createTextNode(self.mathml_tag(expr)))
mrow.appendChild(y)
return mrow
mrow = self.dom.createElement('mrow')
if expr.could_extract_minus_sign():
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode('-'))
mrow.appendChild(x)
mrow = multiply(-expr, mrow)
else:
mrow = multiply(expr, mrow)
return mrow
def _print_Add(self, expr, order=None):
mrow = self.dom.createElement('mrow')
args = self._as_ordered_terms(expr, order=order)
mrow.appendChild(self._print(args[0]))
for arg in args[1:]:
if arg.could_extract_minus_sign():
# use minus
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode('-'))
y = self._print(-arg)
# invert expression since this is now minused
else:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode('+'))
y = self._print(arg)
mrow.appendChild(x)
mrow.appendChild(y)
return mrow
def _print_MatrixBase(self, m):
table = self.dom.createElement('mtable')
for i in range(m.rows):
x = self.dom.createElement('mtr')
for j in range(m.cols):
y = self.dom.createElement('mtd')
y.appendChild(self._print(m[i, j]))
x.appendChild(y)
table.appendChild(x)
if self._settings["mat_delim"] == '':
return table
brac = self.dom.createElement('mfenced')
if self._settings["mat_delim"] == "[":
brac.setAttribute('close', ']')
brac.setAttribute('open', '[')
brac.appendChild(table)
return brac
def _get_printed_Rational(self, e, folded=None):
if e.p < 0:
p = -e.p
else:
p = e.p
x = self.dom.createElement('mfrac')
if folded or self._settings["fold_short_frac"]:
x.setAttribute('bevelled', 'true')
x.appendChild(self._print(p))
x.appendChild(self._print(e.q))
if e.p < 0:
mrow = self.dom.createElement('mrow')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('-'))
mrow.appendChild(mo)
mrow.appendChild(x)
return mrow
else:
return x
def _print_Rational(self, e):
if e.q == 1:
# don't divide
return self._print(e.p)
return self._get_printed_Rational(e, self._settings["fold_short_frac"])
def _print_Limit(self, e):
mrow = self.dom.createElement('mrow')
munder = self.dom.createElement('munder')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode('lim'))
x = self.dom.createElement('mrow')
x_1 = self._print(e.args[1])
arrow = self.dom.createElement('mo')
arrow.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
x_2 = self._print(e.args[2])
x.appendChild(x_1)
x.appendChild(arrow)
x.appendChild(x_2)
munder.appendChild(mi)
munder.appendChild(x)
mrow.appendChild(munder)
mrow.appendChild(self._print(e.args[0]))
return mrow
def _print_ImaginaryUnit(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&ImaginaryI;'))
return x
def _print_GoldenRatio(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&#x3A6;'))
return x
def _print_Exp1(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&ExponentialE;'))
return x
def _print_Pi(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&pi;'))
return x
def _print_Infinity(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&#x221E;'))
return x
def _print_NegativeInfinity(self, e):
mrow = self.dom.createElement('mrow')
y = self.dom.createElement('mo')
y.appendChild(self.dom.createTextNode('-'))
x = self._print_Infinity(e)
mrow.appendChild(y)
mrow.appendChild(x)
return mrow
def _print_HBar(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&#x210F;'))
return x
def _print_EulerGamma(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&#x3B3;'))
return x
def _print_TribonacciConstant(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('TribonacciConstant'))
return x
def _print_Dagger(self, e):
msup = self.dom.createElement('msup')
msup.appendChild(self._print(e.args[0]))
msup.appendChild(self.dom.createTextNode('&#x2020;'))
return msup
def _print_Contains(self, e):
mrow = self.dom.createElement('mrow')
mrow.appendChild(self._print(e.args[0]))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x2208;'))
mrow.appendChild(mo)
mrow.appendChild(self._print(e.args[1]))
return mrow
def _print_HilbertSpace(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&#x210B;'))
return x
def _print_ComplexSpace(self, e):
msup = self.dom.createElement('msup')
msup.appendChild(self.dom.createTextNode('&#x1D49E;'))
msup.appendChild(self._print(e.args[0]))
return msup
def _print_FockSpace(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&#x2131;'))
return x
def _print_Integral(self, expr):
intsymbols = {1: "&#x222B;", 2: "&#x222C;", 3: "&#x222D;"}
mrow = self.dom.createElement('mrow')
if len(expr.limits) <= 3 and all(len(lim) == 1 for lim in expr.limits):
# Only up to three-integral signs exists
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode(intsymbols[len(expr.limits)]))
mrow.appendChild(mo)
else:
# Either more than three or limits provided
for lim in reversed(expr.limits):
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode(intsymbols[1]))
if len(lim) == 1:
mrow.appendChild(mo)
if len(lim) == 2:
msup = self.dom.createElement('msup')
msup.appendChild(mo)
msup.appendChild(self._print(lim[1]))
mrow.appendChild(msup)
if len(lim) == 3:
msubsup = self.dom.createElement('msubsup')
msubsup.appendChild(mo)
msubsup.appendChild(self._print(lim[1]))
msubsup.appendChild(self._print(lim[2]))
mrow.appendChild(msubsup)
# print function
mrow.appendChild(self.parenthesize(expr.function, PRECEDENCE["Mul"],
strict=True))
# print integration variables
for lim in reversed(expr.limits):
d = self.dom.createElement('mo')
d.appendChild(self.dom.createTextNode('&dd;'))
mrow.appendChild(d)
mrow.appendChild(self._print(lim[0]))
return mrow
def _print_Sum(self, e):
limits = list(e.limits)
subsup = self.dom.createElement('munderover')
low_elem = self._print(limits[0][1])
up_elem = self._print(limits[0][2])
summand = self.dom.createElement('mo')
summand.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
low = self.dom.createElement('mrow')
var = self._print(limits[0][0])
equal = self.dom.createElement('mo')
equal.appendChild(self.dom.createTextNode('='))
low.appendChild(var)
low.appendChild(equal)
low.appendChild(low_elem)
subsup.appendChild(summand)
subsup.appendChild(low)
subsup.appendChild(up_elem)
mrow = self.dom.createElement('mrow')
mrow.appendChild(subsup)
if len(str(e.function)) == 1:
mrow.appendChild(self._print(e.function))
else:
fence = self.dom.createElement('mfenced')
fence.appendChild(self._print(e.function))
mrow.appendChild(fence)
return mrow
def _print_Symbol(self, sym, style='plain'):
def join(items):
if len(items) > 1:
mrow = self.dom.createElement('mrow')
for i, item in enumerate(items):
if i > 0:
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode(" "))
mrow.appendChild(mo)
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(item))
mrow.appendChild(mi)
return mrow
else:
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(items[0]))
return mi
# translate name, supers and subs to unicode characters
def translate(s):
if s in greek_unicode:
return greek_unicode.get(s)
else:
return s
name, supers, subs = split_super_sub(sym.name)
name = translate(name)
supers = [translate(sup) for sup in supers]
subs = [translate(sub) for sub in subs]
mname = self.dom.createElement('mi')
mname.appendChild(self.dom.createTextNode(name))
if len(supers) == 0:
if len(subs) == 0:
x = mname
else:
x = self.dom.createElement('msub')
x.appendChild(mname)
x.appendChild(join(subs))
else:
if len(subs) == 0:
x = self.dom.createElement('msup')
x.appendChild(mname)
x.appendChild(join(supers))
else:
x = self.dom.createElement('msubsup')
x.appendChild(mname)
x.appendChild(join(subs))
x.appendChild(join(supers))
# Set bold font?
if style == 'bold':
x.setAttribute('mathvariant', 'bold')
return x
def _print_MatrixSymbol(self, sym):
return self._print_Symbol(sym,
style=self._settings['mat_symbol_style'])
_print_RandomSymbol = _print_Symbol
def _print_conjugate(self, expr):
enc = self.dom.createElement('menclose')
enc.setAttribute('notation', 'top')
enc.appendChild(self._print(expr.args[0]))
return enc
def _print_operator_after(self, op, expr):
row = self.dom.createElement('mrow')
row.appendChild(self.parenthesize(expr, PRECEDENCE["Func"]))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode(op))
row.appendChild(mo)
return row
def _print_factorial(self, expr):
return self._print_operator_after('!', expr.args[0])
def _print_factorial2(self, expr):
return self._print_operator_after('!!', expr.args[0])
def _print_binomial(self, expr):
brac = self.dom.createElement('mfenced')
frac = self.dom.createElement('mfrac')
frac.setAttribute('linethickness', '0')
frac.appendChild(self._print(expr.args[0]))
frac.appendChild(self._print(expr.args[1]))
brac.appendChild(frac)
return brac
def _print_Pow(self, e):
# Here we use root instead of power if the exponent is the
# reciprocal of an integer
if (e.exp.is_Rational and abs(e.exp.p) == 1 and e.exp.q != 1 and
self._settings['root_notation']):
if e.exp.q == 2:
x = self.dom.createElement('msqrt')
x.appendChild(self._print(e.base))
if e.exp.q != 2:
x = self.dom.createElement('mroot')
x.appendChild(self._print(e.base))
x.appendChild(self._print(e.exp.q))
if e.exp.p == -1:
frac = self.dom.createElement('mfrac')
frac.appendChild(self._print(1))
frac.appendChild(x)
return frac
else:
return x
if e.exp.is_Rational and e.exp.q != 1:
if e.exp.is_negative:
top = self.dom.createElement('mfrac')
top.appendChild(self._print(1))
x = self.dom.createElement('msup')
x.appendChild(self.parenthesize(e.base, PRECEDENCE['Pow']))
x.appendChild(self._get_printed_Rational(-e.exp,
self._settings['fold_frac_powers']))
top.appendChild(x)
return top
else:
x = self.dom.createElement('msup')
x.appendChild(self.parenthesize(e.base, PRECEDENCE['Pow']))
x.appendChild(self._get_printed_Rational(e.exp,
self._settings['fold_frac_powers']))
return x
if e.exp.is_negative:
top = self.dom.createElement('mfrac')
top.appendChild(self._print(1))
if e.exp == -1:
top.appendChild(self._print(e.base))
else:
x = self.dom.createElement('msup')
x.appendChild(self.parenthesize(e.base, PRECEDENCE['Pow']))
x.appendChild(self._print(-e.exp))
top.appendChild(x)
return top
x = self.dom.createElement('msup')
x.appendChild(self.parenthesize(e.base, PRECEDENCE['Pow']))
x.appendChild(self._print(e.exp))
return x
def _print_Number(self, e):
x = self.dom.createElement(self.mathml_tag(e))
x.appendChild(self.dom.createTextNode(str(e)))
return x
def _print_AccumulationBounds(self, i):
brac = self.dom.createElement('mfenced')
brac.setAttribute('close', '\u27e9')
brac.setAttribute('open', '\u27e8')
brac.appendChild(self._print(i.min))
brac.appendChild(self._print(i.max))
return brac
def _print_Derivative(self, e):
if requires_partial(e.expr):
d = '&#x2202;'
else:
d = self.mathml_tag(e)
# Determine denominator
m = self.dom.createElement('mrow')
dim = 0 # Total diff dimension, for numerator
for sym, num in reversed(e.variable_count):
dim += num
if num >= 2:
x = self.dom.createElement('msup')
xx = self.dom.createElement('mo')
xx.appendChild(self.dom.createTextNode(d))
x.appendChild(xx)
x.appendChild(self._print(num))
else:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(d))
m.appendChild(x)
y = self._print(sym)
m.appendChild(y)
mnum = self.dom.createElement('mrow')
if dim >= 2:
x = self.dom.createElement('msup')
xx = self.dom.createElement('mo')
xx.appendChild(self.dom.createTextNode(d))
x.appendChild(xx)
x.appendChild(self._print(dim))
else:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(d))
mnum.appendChild(x)
mrow = self.dom.createElement('mrow')
frac = self.dom.createElement('mfrac')
frac.appendChild(mnum)
frac.appendChild(m)
mrow.appendChild(frac)
# Print function
mrow.appendChild(self._print(e.expr))
return mrow
def _print_Function(self, e):
mrow = self.dom.createElement('mrow')
x = self.dom.createElement('mi')
if self.mathml_tag(e) == 'log' and self._settings["ln_notation"]:
x.appendChild(self.dom.createTextNode('ln'))
else:
x.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
y = self.dom.createElement('mfenced')
for arg in e.args:
y.appendChild(self._print(arg))
mrow.appendChild(x)
mrow.appendChild(y)
return mrow
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_mathml_numbers']
mrow = self.dom.createElement('mrow')
if 'e' in str_real:
(mant, exp) = str_real.split('e')
if exp[0] == '+':
exp = exp[1:]
mn = self.dom.createElement('mn')
mn.appendChild(self.dom.createTextNode(mant))
mrow.appendChild(mn)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode(separator))
mrow.appendChild(mo)
msup = self.dom.createElement('msup')
mn = self.dom.createElement('mn')
mn.appendChild(self.dom.createTextNode("10"))
msup.appendChild(mn)
mn = self.dom.createElement('mn')
mn.appendChild(self.dom.createTextNode(exp))
msup.appendChild(mn)
mrow.appendChild(msup)
return mrow
elif str_real == "+inf":
return self._print_Infinity(None)
elif str_real == "-inf":
return self._print_NegativeInfinity(None)
else:
mn = self.dom.createElement('mn')
mn.appendChild(self.dom.createTextNode(str_real))
return mn
def _print_polylog(self, expr):
mrow = self.dom.createElement('mrow')
m = self.dom.createElement('msub')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode('Li'))
m.appendChild(mi)
m.appendChild(self._print(expr.args[0]))
mrow.appendChild(m)
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(expr.args[1]))
mrow.appendChild(brac)
return mrow
def _print_Basic(self, e):
mrow = self.dom.createElement('mrow')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
mrow.appendChild(mi)
brac = self.dom.createElement('mfenced')
for arg in e.args:
brac.appendChild(self._print(arg))
mrow.appendChild(brac)
return mrow
def _print_Tuple(self, e):
mrow = self.dom.createElement('mrow')
x = self.dom.createElement('mfenced')
for arg in e.args:
x.appendChild(self._print(arg))
mrow.appendChild(x)
return mrow
def _print_Interval(self, i):
mrow = self.dom.createElement('mrow')
brac = self.dom.createElement('mfenced')
if i.start == i.end:
# Most often, this type of Interval is converted to a FiniteSet
brac.setAttribute('close', '}')
brac.setAttribute('open', '{')
brac.appendChild(self._print(i.start))
else:
if i.right_open:
brac.setAttribute('close', ')')
else:
brac.setAttribute('close', ']')
if i.left_open:
brac.setAttribute('open', '(')
else:
brac.setAttribute('open', '[')
brac.appendChild(self._print(i.start))
brac.appendChild(self._print(i.end))
mrow.appendChild(brac)
return mrow
def _print_Abs(self, expr, exp=None):
mrow = self.dom.createElement('mrow')
x = self.dom.createElement('mfenced')
x.setAttribute('close', '|')
x.setAttribute('open', '|')
x.appendChild(self._print(expr.args[0]))
mrow.appendChild(x)
return mrow
_print_Determinant = _print_Abs
def _print_re_im(self, c, expr):
mrow = self.dom.createElement('mrow')
mi = self.dom.createElement('mi')
mi.setAttribute('mathvariant', 'fraktur')
mi.appendChild(self.dom.createTextNode(c))
mrow.appendChild(mi)
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(expr))
mrow.appendChild(brac)
return mrow
def _print_re(self, expr, exp=None):
return self._print_re_im('R', expr.args[0])
def _print_im(self, expr, exp=None):
return self._print_re_im('I', expr.args[0])
def _print_AssocOp(self, e):
mrow = self.dom.createElement('mrow')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
mrow.appendChild(mi)
for arg in e.args:
mrow.appendChild(self._print(arg))
return mrow
def _print_SetOp(self, expr, symbol, prec):
mrow = self.dom.createElement('mrow')
mrow.appendChild(self.parenthesize(expr.args[0], prec))
for arg in expr.args[1:]:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(symbol))
y = self.parenthesize(arg, prec)
mrow.appendChild(x)
mrow.appendChild(y)
return mrow
def _print_Union(self, expr):
prec = PRECEDENCE_TRADITIONAL['Union']
return self._print_SetOp(expr, '&#x222A;', prec)
def _print_Intersection(self, expr):
prec = PRECEDENCE_TRADITIONAL['Intersection']
return self._print_SetOp(expr, '&#x2229;', prec)
def _print_Complement(self, expr):
prec = PRECEDENCE_TRADITIONAL['Complement']
return self._print_SetOp(expr, '&#x2216;', prec)
def _print_SymmetricDifference(self, expr):
prec = PRECEDENCE_TRADITIONAL['SymmetricDifference']
return self._print_SetOp(expr, '&#x2206;', prec)
def _print_ProductSet(self, expr):
prec = PRECEDENCE_TRADITIONAL['ProductSet']
return self._print_SetOp(expr, '&#x00d7;', prec)
def _print_FiniteSet(self, s):
return self._print_set(s.args)
def _print_set(self, s):
items = sorted(s, key=default_sort_key)
brac = self.dom.createElement('mfenced')
brac.setAttribute('close', '}')
brac.setAttribute('open', '{')
for item in items:
brac.appendChild(self._print(item))
return brac
_print_frozenset = _print_set
def _print_LogOp(self, args, symbol):
mrow = self.dom.createElement('mrow')
if args[0].is_Boolean and not args[0].is_Not:
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(args[0]))
mrow.appendChild(brac)
else:
mrow.appendChild(self._print(args[0]))
for arg in args[1:]:
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(symbol))
if arg.is_Boolean and not arg.is_Not:
y = self.dom.createElement('mfenced')
y.appendChild(self._print(arg))
else:
y = self._print(arg)
mrow.appendChild(x)
mrow.appendChild(y)
return mrow
def _print_BasisDependent(self, expr):
from sympy.vector import Vector
if expr == expr.zero:
# Not clear if this is ever called
return self._print(expr.zero)
if isinstance(expr, Vector):
items = expr.separate().items()
else:
items = [(0, expr)]
mrow = self.dom.createElement('mrow')
for system, vect in items:
inneritems = list(vect.components.items())
inneritems.sort(key = lambda x:x[0].__str__())
for i, (k, v) in enumerate(inneritems):
if v == 1:
if i: # No + for first item
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('+'))
mrow.appendChild(mo)
mrow.appendChild(self._print(k))
elif v == -1:
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('-'))
mrow.appendChild(mo)
mrow.appendChild(self._print(k))
else:
if i: # No + for first item
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('+'))
mrow.appendChild(mo)
mbrac = self.dom.createElement('mfenced')
mbrac.appendChild(self._print(v))
mrow.appendChild(mbrac)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&InvisibleTimes;'))
mrow.appendChild(mo)
mrow.appendChild(self._print(k))
return mrow
def _print_And(self, expr):
args = sorted(expr.args, key=default_sort_key)
return self._print_LogOp(args, '&#x2227;')
def _print_Or(self, expr):
args = sorted(expr.args, key=default_sort_key)
return self._print_LogOp(args, '&#x2228;')
def _print_Xor(self, expr):
args = sorted(expr.args, key=default_sort_key)
return self._print_LogOp(args, '&#x22BB;')
def _print_Implies(self, expr):
return self._print_LogOp(expr.args, '&#x21D2;')
def _print_Equivalent(self, expr):
args = sorted(expr.args, key=default_sort_key)
return self._print_LogOp(args, '&#x21D4;')
def _print_Not(self, e):
mrow = self.dom.createElement('mrow')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#xAC;'))
mrow.appendChild(mo)
if (e.args[0].is_Boolean):
x = self.dom.createElement('mfenced')
x.appendChild(self._print(e.args[0]))
else:
x = self._print(e.args[0])
mrow.appendChild(x)
return mrow
def _print_bool(self, e):
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
return mi
_print_BooleanTrue = _print_bool
_print_BooleanFalse = _print_bool
def _print_NoneType(self, e):
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
return mi
def _print_Range(self, s):
dots = "\u2026"
brac = self.dom.createElement('mfenced')
brac.setAttribute('close', '}')
brac.setAttribute('open', '{')
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 len(s) > 4:
it = iter(s)
printset = next(it), next(it), dots, s[-1]
else:
printset = tuple(s)
for el in printset:
if el == dots:
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(dots))
brac.appendChild(mi)
else:
brac.appendChild(self._print(el))
return brac
def _hprint_variadic_function(self, expr):
args = sorted(expr.args, key=default_sort_key)
mrow = self.dom.createElement('mrow')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode((str(expr.func)).lower()))
mrow.appendChild(mo)
brac = self.dom.createElement('mfenced')
for symbol in args:
brac.appendChild(self._print(symbol))
mrow.appendChild(brac)
return mrow
_print_Min = _print_Max = _hprint_variadic_function
def _print_exp(self, expr):
msup = self.dom.createElement('msup')
msup.appendChild(self._print_Exp1(None))
msup.appendChild(self._print(expr.args[0]))
return msup
def _print_Relational(self, e):
mrow = self.dom.createElement('mrow')
mrow.appendChild(self._print(e.lhs))
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode(self.mathml_tag(e)))
mrow.appendChild(x)
mrow.appendChild(self._print(e.rhs))
return mrow
def _print_int(self, p):
dom_element = self.dom.createElement(self.mathml_tag(p))
dom_element.appendChild(self.dom.createTextNode(str(p)))
return dom_element
def _print_BaseScalar(self, e):
msub = self.dom.createElement('msub')
index, system = e._id
mi = self.dom.createElement('mi')
mi.setAttribute('mathvariant', 'bold')
mi.appendChild(self.dom.createTextNode(system._variable_names[index]))
msub.appendChild(mi)
mi = self.dom.createElement('mi')
mi.setAttribute('mathvariant', 'bold')
mi.appendChild(self.dom.createTextNode(system._name))
msub.appendChild(mi)
return msub
def _print_BaseVector(self, e):
msub = self.dom.createElement('msub')
index, system = e._id
mover = self.dom.createElement('mover')
mi = self.dom.createElement('mi')
mi.setAttribute('mathvariant', 'bold')
mi.appendChild(self.dom.createTextNode(system._vector_names[index]))
mover.appendChild(mi)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('^'))
mover.appendChild(mo)
msub.appendChild(mover)
mi = self.dom.createElement('mi')
mi.setAttribute('mathvariant', 'bold')
mi.appendChild(self.dom.createTextNode(system._name))
msub.appendChild(mi)
return msub
def _print_VectorZero(self, e):
mover = self.dom.createElement('mover')
mi = self.dom.createElement('mi')
mi.setAttribute('mathvariant', 'bold')
mi.appendChild(self.dom.createTextNode("0"))
mover.appendChild(mi)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('^'))
mover.appendChild(mo)
return mover
def _print_Cross(self, expr):
mrow = self.dom.createElement('mrow')
vec1 = expr._expr1
vec2 = expr._expr2
mrow.appendChild(self.parenthesize(vec1, PRECEDENCE['Mul']))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#xD7;'))
mrow.appendChild(mo)
mrow.appendChild(self.parenthesize(vec2, PRECEDENCE['Mul']))
return mrow
def _print_Curl(self, expr):
mrow = self.dom.createElement('mrow')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x2207;'))
mrow.appendChild(mo)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#xD7;'))
mrow.appendChild(mo)
mrow.appendChild(self.parenthesize(expr._expr, PRECEDENCE['Mul']))
return mrow
def _print_Divergence(self, expr):
mrow = self.dom.createElement('mrow')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x2207;'))
mrow.appendChild(mo)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#xB7;'))
mrow.appendChild(mo)
mrow.appendChild(self.parenthesize(expr._expr, PRECEDENCE['Mul']))
return mrow
def _print_Dot(self, expr):
mrow = self.dom.createElement('mrow')
vec1 = expr._expr1
vec2 = expr._expr2
mrow.appendChild(self.parenthesize(vec1, PRECEDENCE['Mul']))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#xB7;'))
mrow.appendChild(mo)
mrow.appendChild(self.parenthesize(vec2, PRECEDENCE['Mul']))
return mrow
def _print_Gradient(self, expr):
mrow = self.dom.createElement('mrow')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x2207;'))
mrow.appendChild(mo)
mrow.appendChild(self.parenthesize(expr._expr, PRECEDENCE['Mul']))
return mrow
def _print_Laplacian(self, expr):
mrow = self.dom.createElement('mrow')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x2206;'))
mrow.appendChild(mo)
mrow.appendChild(self.parenthesize(expr._expr, PRECEDENCE['Mul']))
return mrow
def _print_Integers(self, e):
x = self.dom.createElement('mi')
x.setAttribute('mathvariant', 'normal')
x.appendChild(self.dom.createTextNode('&#x2124;'))
return x
def _print_Complexes(self, e):
x = self.dom.createElement('mi')
x.setAttribute('mathvariant', 'normal')
x.appendChild(self.dom.createTextNode('&#x2102;'))
return x
def _print_Reals(self, e):
x = self.dom.createElement('mi')
x.setAttribute('mathvariant', 'normal')
x.appendChild(self.dom.createTextNode('&#x211D;'))
return x
def _print_Naturals(self, e):
x = self.dom.createElement('mi')
x.setAttribute('mathvariant', 'normal')
x.appendChild(self.dom.createTextNode('&#x2115;'))
return x
def _print_Naturals0(self, e):
sub = self.dom.createElement('msub')
x = self.dom.createElement('mi')
x.setAttribute('mathvariant', 'normal')
x.appendChild(self.dom.createTextNode('&#x2115;'))
sub.appendChild(x)
sub.appendChild(self._print(S.Zero))
return sub
def _print_SingularityFunction(self, expr):
shift = expr.args[0] - expr.args[1]
power = expr.args[2]
sup = self.dom.createElement('msup')
brac = self.dom.createElement('mfenced')
brac.setAttribute('close', '\u27e9')
brac.setAttribute('open', '\u27e8')
brac.appendChild(self._print(shift))
sup.appendChild(brac)
sup.appendChild(self._print(power))
return sup
def _print_NaN(self, e):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('NaN'))
return x
def _print_number_function(self, e, name):
# Print name_arg[0] for one argument or name_arg[0](arg[1])
# for more than one argument
sub = self.dom.createElement('msub')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode(name))
sub.appendChild(mi)
sub.appendChild(self._print(e.args[0]))
if len(e.args) == 1:
return sub
# TODO: copy-pasted from _print_Function: can we do better?
mrow = self.dom.createElement('mrow')
y = self.dom.createElement('mfenced')
for arg in e.args[1:]:
y.appendChild(self._print(arg))
mrow.appendChild(sub)
mrow.appendChild(y)
return mrow
def _print_bernoulli(self, e):
return self._print_number_function(e, 'B')
_print_bell = _print_bernoulli
def _print_catalan(self, e):
return self._print_number_function(e, 'C')
def _print_euler(self, e):
return self._print_number_function(e, 'E')
def _print_fibonacci(self, e):
return self._print_number_function(e, 'F')
def _print_lucas(self, e):
return self._print_number_function(e, 'L')
def _print_stieltjes(self, e):
return self._print_number_function(e, '&#x03B3;')
def _print_tribonacci(self, e):
return self._print_number_function(e, 'T')
def _print_ComplexInfinity(self, e):
x = self.dom.createElement('mover')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x221E;'))
x.appendChild(mo)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('~'))
x.appendChild(mo)
return x
def _print_EmptySet(self, e):
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode('&#x2205;'))
return x
def _print_UniversalSet(self, e):
x = self.dom.createElement('mo')
x.appendChild(self.dom.createTextNode('&#x1D54C;'))
return x
def _print_Adjoint(self, expr):
from sympy.matrices import MatrixSymbol
mat = expr.arg
sup = self.dom.createElement('msup')
if not isinstance(mat, MatrixSymbol):
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(mat))
sup.appendChild(brac)
else:
sup.appendChild(self._print(mat))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x2020;'))
sup.appendChild(mo)
return sup
def _print_Transpose(self, expr):
from sympy.matrices import MatrixSymbol
mat = expr.arg
sup = self.dom.createElement('msup')
if not isinstance(mat, MatrixSymbol):
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(mat))
sup.appendChild(brac)
else:
sup.appendChild(self._print(mat))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('T'))
sup.appendChild(mo)
return sup
def _print_Inverse(self, expr):
from sympy.matrices import MatrixSymbol
mat = expr.arg
sup = self.dom.createElement('msup')
if not isinstance(mat, MatrixSymbol):
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(mat))
sup.appendChild(brac)
else:
sup.appendChild(self._print(mat))
sup.appendChild(self._print(-1))
return sup
def _print_MatMul(self, expr):
from sympy.matrices.expressions.matmul import MatMul
x = self.dom.createElement('mrow')
args = expr.args
if isinstance(args[0], Mul):
args = args[0].as_ordered_factors() + list(args[1:])
else:
args = list(args)
if isinstance(expr, MatMul) and expr.could_extract_minus_sign():
if args[0] == -1:
args = args[1:]
else:
args[0] = -args[0]
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('-'))
x.appendChild(mo)
for arg in args[:-1]:
x.appendChild(self.parenthesize(arg, precedence_traditional(expr),
False))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&InvisibleTimes;'))
x.appendChild(mo)
x.appendChild(self.parenthesize(args[-1], precedence_traditional(expr),
False))
return x
def _print_MatPow(self, expr):
from sympy.matrices import MatrixSymbol
base, exp = expr.base, expr.exp
sup = self.dom.createElement('msup')
if not isinstance(base, MatrixSymbol):
brac = self.dom.createElement('mfenced')
brac.appendChild(self._print(base))
sup.appendChild(brac)
else:
sup.appendChild(self._print(base))
sup.appendChild(self._print(exp))
return sup
def _print_HadamardProduct(self, expr):
x = self.dom.createElement('mrow')
args = expr.args
for arg in args[:-1]:
x.appendChild(
self.parenthesize(arg, precedence_traditional(expr), False))
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x2218;'))
x.appendChild(mo)
x.appendChild(
self.parenthesize(args[-1], precedence_traditional(expr), False))
return x
def _print_ZeroMatrix(self, Z):
x = self.dom.createElement('mn')
x.appendChild(self.dom.createTextNode('&#x1D7D8'))
return x
def _print_OneMatrix(self, Z):
x = self.dom.createElement('mn')
x.appendChild(self.dom.createTextNode('&#x1D7D9'))
return x
def _print_Identity(self, I):
x = self.dom.createElement('mi')
x.appendChild(self.dom.createTextNode('&#x1D540;'))
return x
def _print_floor(self, e):
mrow = self.dom.createElement('mrow')
x = self.dom.createElement('mfenced')
x.setAttribute('close', '\u230B')
x.setAttribute('open', '\u230A')
x.appendChild(self._print(e.args[0]))
mrow.appendChild(x)
return mrow
def _print_ceiling(self, e):
mrow = self.dom.createElement('mrow')
x = self.dom.createElement('mfenced')
x.setAttribute('close', '\u2309')
x.setAttribute('open', '\u2308')
x.appendChild(self._print(e.args[0]))
mrow.appendChild(x)
return mrow
def _print_Lambda(self, e):
x = self.dom.createElement('mfenced')
mrow = self.dom.createElement('mrow')
symbols = e.args[0]
if len(symbols) == 1:
symbols = self._print(symbols[0])
else:
symbols = self._print(symbols)
mrow.appendChild(symbols)
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('&#x21A6;'))
mrow.appendChild(mo)
mrow.appendChild(self._print(e.args[1]))
x.appendChild(mrow)
return x
def _print_tuple(self, e):
x = self.dom.createElement('mfenced')
for i in e:
x.appendChild(self._print(i))
return x
def _print_IndexedBase(self, e):
return self._print(e.label)
def _print_Indexed(self, e):
x = self.dom.createElement('msub')
x.appendChild(self._print(e.base))
if len(e.indices) == 1:
x.appendChild(self._print(e.indices[0]))
return x
x.appendChild(self._print(e.indices))
return x
def _print_MatrixElement(self, e):
x = self.dom.createElement('msub')
x.appendChild(self.parenthesize(e.parent, PRECEDENCE["Atom"], strict = True))
brac = self.dom.createElement('mfenced')
brac.setAttribute("close", "")
brac.setAttribute("open", "")
for i in e.indices:
brac.appendChild(self._print(i))
x.appendChild(brac)
return x
def _print_elliptic_f(self, e):
x = self.dom.createElement('mrow')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode('&#x1d5a5;'))
x.appendChild(mi)
y = self.dom.createElement('mfenced')
y.setAttribute("separators", "|")
for i in e.args:
y.appendChild(self._print(i))
x.appendChild(y)
return x
def _print_elliptic_e(self, e):
x = self.dom.createElement('mrow')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode('&#x1d5a4;'))
x.appendChild(mi)
y = self.dom.createElement('mfenced')
y.setAttribute("separators", "|")
for i in e.args:
y.appendChild(self._print(i))
x.appendChild(y)
return x
def _print_elliptic_pi(self, e):
x = self.dom.createElement('mrow')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode('&#x1d6f1;'))
x.appendChild(mi)
y = self.dom.createElement('mfenced')
if len(e.args) == 2:
y.setAttribute("separators", "|")
else:
y.setAttribute("separators", ";|")
for i in e.args:
y.appendChild(self._print(i))
x.appendChild(y)
return x
def _print_Ei(self, e):
x = self.dom.createElement('mrow')
mi = self.dom.createElement('mi')
mi.appendChild(self.dom.createTextNode('Ei'))
x.appendChild(mi)
x.appendChild(self._print(e.args))
return x
def _print_expint(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msub')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('E'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
x.appendChild(y)
x.appendChild(self._print(e.args[1:]))
return x
def _print_jacobi(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msubsup')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('P'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
y.appendChild(self._print(e.args[1:3]))
x.appendChild(y)
x.appendChild(self._print(e.args[3:]))
return x
def _print_gegenbauer(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msubsup')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('C'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
y.appendChild(self._print(e.args[1:2]))
x.appendChild(y)
x.appendChild(self._print(e.args[2:]))
return x
def _print_chebyshevt(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msub')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('T'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
x.appendChild(y)
x.appendChild(self._print(e.args[1:]))
return x
def _print_chebyshevu(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msub')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('U'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
x.appendChild(y)
x.appendChild(self._print(e.args[1:]))
return x
def _print_legendre(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msub')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('P'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
x.appendChild(y)
x.appendChild(self._print(e.args[1:]))
return x
def _print_assoc_legendre(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msubsup')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('P'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
y.appendChild(self._print(e.args[1:2]))
x.appendChild(y)
x.appendChild(self._print(e.args[2:]))
return x
def _print_laguerre(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msub')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('L'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
x.appendChild(y)
x.appendChild(self._print(e.args[1:]))
return x
def _print_assoc_laguerre(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msubsup')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('L'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
y.appendChild(self._print(e.args[1:2]))
x.appendChild(y)
x.appendChild(self._print(e.args[2:]))
return x
def _print_hermite(self, e):
x = self.dom.createElement('mrow')
y = self.dom.createElement('msub')
mo = self.dom.createElement('mo')
mo.appendChild(self.dom.createTextNode('H'))
y.appendChild(mo)
y.appendChild(self._print(e.args[0]))
x.appendChild(y)
x.appendChild(self._print(e.args[1:]))
return x
@print_function(MathMLPrinterBase)
def mathml(expr, printer='content', **settings):
"""Returns the MathML representation of expr. If printer is presentation
then prints Presentation MathML else prints content MathML.
"""
if printer == 'presentation':
return MathMLPresentationPrinter(settings).doprint(expr)
else:
return MathMLContentPrinter(settings).doprint(expr)
def print_mathml(expr, printer='content', **settings):
"""
Prints a pretty representation of the MathML code for expr. If printer is
presentation then prints Presentation MathML else prints content MathML.
Examples
========
>>> ##
>>> from sympy import print_mathml
>>> from sympy.abc import x
>>> print_mathml(x+1) #doctest: +NORMALIZE_WHITESPACE
<apply>
<plus/>
<ci>x</ci>
<cn>1</cn>
</apply>
>>> print_mathml(x+1, printer='presentation')
<mrow>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
"""
if printer == 'presentation':
s = MathMLPresentationPrinter(settings)
else:
s = MathMLContentPrinter(settings)
xml = s._print(sympify(expr))
s.apply_patch()
pretty_xml = xml.toprettyxml()
s.restore_patch()
print(pretty_xml)
# For backward compatibility
MathMLPrinter = MathMLContentPrinter