571 lines
17 KiB
Python
571 lines
17 KiB
Python
#!/usr/bin/env python
|
|
# -*- coding: utf-8 -*-
|
|
|
|
# :Id: $Id: latex2mathml.py 7995 2016-12-10 17:50:59Z milde $
|
|
# :Copyright: © 2010 Günter Milde.
|
|
# Based on rst2mathml.py from the latex_math sandbox project
|
|
# © 2005 Jens Jørgen Mortensen
|
|
# :License: Released under the terms of the `2-Clause BSD license`_, in short:
|
|
#
|
|
# Copying and distribution of this file, with or without modification,
|
|
# are permitted in any medium without royalty provided the copyright
|
|
# notice and this notice are preserved.
|
|
# This file is offered as-is, without any warranty.
|
|
#
|
|
# .. _2-Clause BSD license: http://www.spdx.org/licenses/BSD-2-Clause
|
|
|
|
|
|
"""Convert LaTex math code into presentational MathML"""
|
|
|
|
# Based on the `latex_math` sandbox project by Jens Jørgen Mortensen
|
|
|
|
import docutils.utils.math.tex2unichar as tex2unichar
|
|
|
|
# TeX spacing combining
|
|
over = {'acute': '\u00B4', # u'\u0301',
|
|
'bar': '\u00AF', # u'\u0304',
|
|
'breve': '\u02D8', # u'\u0306',
|
|
'check': '\u02C7', # u'\u030C',
|
|
'dot': '\u02D9', # u'\u0307',
|
|
'ddot': '\u00A8', # u'\u0308',
|
|
'dddot': '\u20DB',
|
|
'grave': '`', # u'\u0300',
|
|
'hat': '^', # u'\u0302',
|
|
'mathring': '\u02DA', # u'\u030A',
|
|
'overleftrightarrow': '\u20e1',
|
|
# 'overline': # u'\u0305',
|
|
'tilde': '\u02DC', # u'\u0303',
|
|
'vec': '\u20D7'}
|
|
|
|
Greek = { # Capital Greek letters: (upright in TeX style)
|
|
'Phi':'\u03a6', 'Xi':'\u039e', 'Sigma':'\u03a3',
|
|
'Psi':'\u03a8', 'Delta':'\u0394', 'Theta':'\u0398',
|
|
'Upsilon':'\u03d2', 'Pi':'\u03a0', 'Omega':'\u03a9',
|
|
'Gamma':'\u0393', 'Lambda':'\u039b'}
|
|
|
|
letters = tex2unichar.mathalpha
|
|
|
|
special = tex2unichar.mathbin # Binary symbols
|
|
special.update(tex2unichar.mathrel) # Relation symbols, arrow symbols
|
|
special.update(tex2unichar.mathord) # Miscellaneous symbols
|
|
special.update(tex2unichar.mathop) # Variable-sized symbols
|
|
special.update(tex2unichar.mathopen) # Braces
|
|
special.update(tex2unichar.mathclose) # Braces
|
|
special.update(tex2unichar.mathfence)
|
|
|
|
sumintprod = ''.join([special[symbol] for symbol in
|
|
['sum', 'int', 'oint', 'prod']])
|
|
|
|
functions = ['arccos', 'arcsin', 'arctan', 'arg', 'cos', 'cosh',
|
|
'cot', 'coth', 'csc', 'deg', 'det', 'dim',
|
|
'exp', 'gcd', 'hom', 'inf', 'ker', 'lg',
|
|
'lim', 'liminf', 'limsup', 'ln', 'log', 'max',
|
|
'min', 'Pr', 'sec', 'sin', 'sinh', 'sup',
|
|
'tan', 'tanh',
|
|
'injlim', 'varinjlim', 'varlimsup',
|
|
'projlim', 'varliminf', 'varprojlim']
|
|
|
|
|
|
mathbb = {
|
|
'A': '\U0001D538',
|
|
'B': '\U0001D539',
|
|
'C': '\u2102',
|
|
'D': '\U0001D53B',
|
|
'E': '\U0001D53C',
|
|
'F': '\U0001D53D',
|
|
'G': '\U0001D53E',
|
|
'H': '\u210D',
|
|
'I': '\U0001D540',
|
|
'J': '\U0001D541',
|
|
'K': '\U0001D542',
|
|
'L': '\U0001D543',
|
|
'M': '\U0001D544',
|
|
'N': '\u2115',
|
|
'O': '\U0001D546',
|
|
'P': '\u2119',
|
|
'Q': '\u211A',
|
|
'R': '\u211D',
|
|
'S': '\U0001D54A',
|
|
'T': '\U0001D54B',
|
|
'U': '\U0001D54C',
|
|
'V': '\U0001D54D',
|
|
'W': '\U0001D54E',
|
|
'X': '\U0001D54F',
|
|
'Y': '\U0001D550',
|
|
'Z': '\u2124',
|
|
}
|
|
|
|
mathscr = {
|
|
'A': '\U0001D49C',
|
|
'B': '\u212C', # bernoulli function
|
|
'C': '\U0001D49E',
|
|
'D': '\U0001D49F',
|
|
'E': '\u2130',
|
|
'F': '\u2131',
|
|
'G': '\U0001D4A2',
|
|
'H': '\u210B', # hamiltonian
|
|
'I': '\u2110',
|
|
'J': '\U0001D4A5',
|
|
'K': '\U0001D4A6',
|
|
'L': '\u2112', # lagrangian
|
|
'M': '\u2133', # physics m-matrix
|
|
'N': '\U0001D4A9',
|
|
'O': '\U0001D4AA',
|
|
'P': '\U0001D4AB',
|
|
'Q': '\U0001D4AC',
|
|
'R': '\u211B',
|
|
'S': '\U0001D4AE',
|
|
'T': '\U0001D4AF',
|
|
'U': '\U0001D4B0',
|
|
'V': '\U0001D4B1',
|
|
'W': '\U0001D4B2',
|
|
'X': '\U0001D4B3',
|
|
'Y': '\U0001D4B4',
|
|
'Z': '\U0001D4B5',
|
|
'a': '\U0001D4B6',
|
|
'b': '\U0001D4B7',
|
|
'c': '\U0001D4B8',
|
|
'd': '\U0001D4B9',
|
|
'e': '\u212F',
|
|
'f': '\U0001D4BB',
|
|
'g': '\u210A',
|
|
'h': '\U0001D4BD',
|
|
'i': '\U0001D4BE',
|
|
'j': '\U0001D4BF',
|
|
'k': '\U0001D4C0',
|
|
'l': '\U0001D4C1',
|
|
'm': '\U0001D4C2',
|
|
'n': '\U0001D4C3',
|
|
'o': '\u2134', # order of
|
|
'p': '\U0001D4C5',
|
|
'q': '\U0001D4C6',
|
|
'r': '\U0001D4C7',
|
|
's': '\U0001D4C8',
|
|
't': '\U0001D4C9',
|
|
'u': '\U0001D4CA',
|
|
'v': '\U0001D4CB',
|
|
'w': '\U0001D4CC',
|
|
'x': '\U0001D4CD',
|
|
'y': '\U0001D4CE',
|
|
'z': '\U0001D4CF',
|
|
}
|
|
|
|
negatables = {'=': '\u2260',
|
|
r'\in': '\u2209',
|
|
r'\equiv': '\u2262'}
|
|
|
|
# LaTeX to MathML translation stuff:
|
|
class math:
|
|
"""Base class for MathML elements."""
|
|
|
|
nchildren = 1000000
|
|
"""Required number of children"""
|
|
|
|
def __init__(self, children=None, inline=None):
|
|
"""math([children]) -> MathML element
|
|
|
|
children can be one child or a list of children."""
|
|
|
|
self.children = []
|
|
if children is not None:
|
|
if type(children) is list:
|
|
for child in children:
|
|
self.append(child)
|
|
else:
|
|
# Only one child:
|
|
self.append(children)
|
|
|
|
if inline is not None:
|
|
self.inline = inline
|
|
|
|
def __repr__(self):
|
|
if hasattr(self, 'children'):
|
|
return self.__class__.__name__ + '(%s)' % \
|
|
','.join([repr(child) for child in self.children])
|
|
else:
|
|
return self.__class__.__name__
|
|
|
|
def full(self):
|
|
"""Room for more children?"""
|
|
|
|
return len(self.children) >= self.nchildren
|
|
|
|
def append(self, child):
|
|
"""append(child) -> element
|
|
|
|
Appends child and returns self if self is not full or first
|
|
non-full parent."""
|
|
|
|
assert not self.full()
|
|
self.children.append(child)
|
|
child.parent = self
|
|
node = self
|
|
while node.full():
|
|
node = node.parent
|
|
return node
|
|
|
|
def delete_child(self):
|
|
"""delete_child() -> child
|
|
|
|
Delete last child and return it."""
|
|
|
|
child = self.children[-1]
|
|
del self.children[-1]
|
|
return child
|
|
|
|
def close(self):
|
|
"""close() -> parent
|
|
|
|
Close element and return first non-full element."""
|
|
|
|
parent = self.parent
|
|
while parent.full():
|
|
parent = parent.parent
|
|
return parent
|
|
|
|
def xml(self):
|
|
"""xml() -> xml-string"""
|
|
|
|
return self.xml_start() + self.xml_body() + self.xml_end()
|
|
|
|
def xml_start(self):
|
|
if not hasattr(self, 'inline'):
|
|
return ['<%s>' % self.__class__.__name__]
|
|
xmlns = 'http://www.w3.org/1998/Math/MathML'
|
|
if self.inline:
|
|
return ['<math xmlns="%s">' % xmlns]
|
|
else:
|
|
return ['<math xmlns="%s" mode="display">' % xmlns]
|
|
|
|
def xml_end(self):
|
|
return ['</%s>' % self.__class__.__name__]
|
|
|
|
def xml_body(self):
|
|
xml = []
|
|
for child in self.children:
|
|
xml.extend(child.xml())
|
|
return xml
|
|
|
|
class mrow(math):
|
|
def xml_start(self):
|
|
return ['\n<%s>' % self.__class__.__name__]
|
|
|
|
class mtable(math):
|
|
def xml_start(self):
|
|
return ['\n<%s>' % self.__class__.__name__]
|
|
|
|
class mtr(mrow): pass
|
|
class mtd(mrow): pass
|
|
|
|
class mx(math):
|
|
"""Base class for mo, mi, and mn"""
|
|
|
|
nchildren = 0
|
|
def __init__(self, data):
|
|
self.data = data
|
|
|
|
def xml_body(self):
|
|
return [self.data]
|
|
|
|
class mo(mx):
|
|
translation = {'<': '<', '>': '>'}
|
|
def xml_body(self):
|
|
return [self.translation.get(self.data, self.data)]
|
|
|
|
class mi(mx): pass
|
|
class mn(mx): pass
|
|
|
|
class msub(math):
|
|
nchildren = 2
|
|
|
|
class msup(math):
|
|
nchildren = 2
|
|
|
|
class msqrt(math):
|
|
nchildren = 1
|
|
|
|
class mroot(math):
|
|
nchildren = 2
|
|
|
|
class mfrac(math):
|
|
nchildren = 2
|
|
|
|
class msubsup(math):
|
|
nchildren = 3
|
|
def __init__(self, children=None, reversed=False):
|
|
self.reversed = reversed
|
|
math.__init__(self, children)
|
|
|
|
def xml(self):
|
|
if self.reversed:
|
|
## self.children[1:3] = self.children[2:0:-1]
|
|
self.children[1:3] = [self.children[2], self.children[1]]
|
|
self.reversed = False
|
|
return math.xml(self)
|
|
|
|
class mfenced(math):
|
|
translation = {'\\{': '{', '\\langle': '\u2329',
|
|
'\\}': '}', '\\rangle': '\u232A',
|
|
'.': ''}
|
|
def __init__(self, par):
|
|
self.openpar = par
|
|
math.__init__(self)
|
|
|
|
def xml_start(self):
|
|
open = self.translation.get(self.openpar, self.openpar)
|
|
close = self.translation.get(self.closepar, self.closepar)
|
|
return ['<mfenced open="%s" close="%s">' % (open, close)]
|
|
|
|
class mspace(math):
|
|
nchildren = 0
|
|
|
|
class mstyle(math):
|
|
def __init__(self, children=None, nchildren=None, **kwargs):
|
|
if nchildren is not None:
|
|
self.nchildren = nchildren
|
|
math.__init__(self, children)
|
|
self.attrs = kwargs
|
|
|
|
def xml_start(self):
|
|
return ['<mstyle '] + ['%s="%s"' % item
|
|
for item in list(self.attrs.items())] + ['>']
|
|
|
|
class mover(math):
|
|
nchildren = 2
|
|
def __init__(self, children=None, reversed=False):
|
|
self.reversed = reversed
|
|
math.__init__(self, children)
|
|
|
|
def xml(self):
|
|
if self.reversed:
|
|
self.children.reverse()
|
|
self.reversed = False
|
|
return math.xml(self)
|
|
|
|
class munder(math):
|
|
nchildren = 2
|
|
|
|
class munderover(math):
|
|
nchildren = 3
|
|
def __init__(self, children=None):
|
|
math.__init__(self, children)
|
|
|
|
class mtext(math):
|
|
nchildren = 0
|
|
def __init__(self, text):
|
|
self.text = text
|
|
|
|
def xml_body(self):
|
|
return [self.text]
|
|
|
|
def parse_latex_math(string, inline=True):
|
|
"""parse_latex_math(string [,inline]) -> MathML-tree
|
|
|
|
Returns a MathML-tree parsed from string. inline=True is for
|
|
inline math and inline=False is for displayed math.
|
|
|
|
tree is the whole tree and node is the current element."""
|
|
|
|
# Normalize white-space:
|
|
string = ' '.join(string.split())
|
|
|
|
if inline:
|
|
node = mrow()
|
|
tree = math(node, inline=True)
|
|
else:
|
|
node = mtd()
|
|
tree = math(mtable(mtr(node)), inline=False)
|
|
|
|
while len(string) > 0:
|
|
n = len(string)
|
|
c = string[0]
|
|
skip = 1 # number of characters consumed
|
|
if n > 1:
|
|
c2 = string[1]
|
|
else:
|
|
c2 = ''
|
|
## print n, string, c, c2, node.__class__.__name__
|
|
if c == ' ':
|
|
pass
|
|
elif c == '\\':
|
|
if c2 in '{}':
|
|
node = node.append(mo(c2))
|
|
skip = 2
|
|
elif c2 == ' ':
|
|
node = node.append(mspace())
|
|
skip = 2
|
|
elif c2 == ',': # TODO: small space
|
|
node = node.append(mspace())
|
|
skip = 2
|
|
elif c2.isalpha():
|
|
# We have a LaTeX-name:
|
|
i = 2
|
|
while i < n and string[i].isalpha():
|
|
i += 1
|
|
name = string[1:i]
|
|
node, skip = handle_keyword(name, node, string[i:])
|
|
skip += i
|
|
elif c2 == '\\':
|
|
# End of a row:
|
|
entry = mtd()
|
|
row = mtr(entry)
|
|
node.close().close().append(row)
|
|
node = entry
|
|
skip = 2
|
|
else:
|
|
raise SyntaxError(r'Syntax error: "%s%s"' % (c, c2))
|
|
elif c.isalpha():
|
|
node = node.append(mi(c))
|
|
elif c.isdigit():
|
|
node = node.append(mn(c))
|
|
elif c in "+-*/=()[]|<>,.!?':;@":
|
|
node = node.append(mo(c))
|
|
elif c == '_':
|
|
child = node.delete_child()
|
|
if isinstance(child, msup):
|
|
sub = msubsup(child.children, reversed=True)
|
|
elif isinstance(child, mo) and child.data in sumintprod:
|
|
sub = munder(child)
|
|
else:
|
|
sub = msub(child)
|
|
node.append(sub)
|
|
node = sub
|
|
elif c == '^':
|
|
child = node.delete_child()
|
|
if isinstance(child, msub):
|
|
sup = msubsup(child.children)
|
|
elif isinstance(child, mo) and child.data in sumintprod:
|
|
sup = mover(child)
|
|
elif (isinstance(child, munder) and
|
|
child.children[0].data in sumintprod):
|
|
sup = munderover(child.children)
|
|
else:
|
|
sup = msup(child)
|
|
node.append(sup)
|
|
node = sup
|
|
elif c == '{':
|
|
row = mrow()
|
|
node.append(row)
|
|
node = row
|
|
elif c == '}':
|
|
node = node.close()
|
|
elif c == '&':
|
|
entry = mtd()
|
|
node.close().append(entry)
|
|
node = entry
|
|
else:
|
|
raise SyntaxError(r'Illegal character: "%s"' % c)
|
|
string = string[skip:]
|
|
return tree
|
|
|
|
|
|
def handle_keyword(name, node, string):
|
|
skip = 0
|
|
if len(string) > 0 and string[0] == ' ':
|
|
string = string[1:]
|
|
skip = 1
|
|
if name == 'begin':
|
|
if not string.startswith('{matrix}'):
|
|
raise SyntaxError('Environment not supported! '
|
|
'Supported environment: "matrix".')
|
|
skip += 8
|
|
entry = mtd()
|
|
table = mtable(mtr(entry))
|
|
node.append(table)
|
|
node = entry
|
|
elif name == 'end':
|
|
if not string.startswith('{matrix}'):
|
|
raise SyntaxError(r'Expected "\end{matrix}"!')
|
|
skip += 8
|
|
node = node.close().close().close()
|
|
elif name in ('text', 'mathrm'):
|
|
if string[0] != '{':
|
|
raise SyntaxError(r'Expected "\text{...}"!')
|
|
i = string.find('}')
|
|
if i == -1:
|
|
raise SyntaxError(r'Expected "\text{...}"!')
|
|
node = node.append(mtext(string[1:i]))
|
|
skip += i + 1
|
|
elif name == 'sqrt':
|
|
sqrt = msqrt()
|
|
node.append(sqrt)
|
|
node = sqrt
|
|
elif name == 'frac':
|
|
frac = mfrac()
|
|
node.append(frac)
|
|
node = frac
|
|
elif name == 'left':
|
|
for par in ['(', '[', '|', '\\{', '\\langle', '.']:
|
|
if string.startswith(par):
|
|
break
|
|
else:
|
|
raise SyntaxError('Missing left-brace!')
|
|
fenced = mfenced(par)
|
|
node.append(fenced)
|
|
row = mrow()
|
|
fenced.append(row)
|
|
node = row
|
|
skip += len(par)
|
|
elif name == 'right':
|
|
for par in [')', ']', '|', '\\}', '\\rangle', '.']:
|
|
if string.startswith(par):
|
|
break
|
|
else:
|
|
raise SyntaxError('Missing right-brace!')
|
|
node = node.close()
|
|
node.closepar = par
|
|
node = node.close()
|
|
skip += len(par)
|
|
elif name == 'not':
|
|
for operator in negatables:
|
|
if string.startswith(operator):
|
|
break
|
|
else:
|
|
raise SyntaxError(r'Expected something to negate: "\not ..."!')
|
|
node = node.append(mo(negatables[operator]))
|
|
skip += len(operator)
|
|
elif name == 'mathbf':
|
|
style = mstyle(nchildren=1, fontweight='bold')
|
|
node.append(style)
|
|
node = style
|
|
elif name == 'mathbb':
|
|
if string[0] != '{' or not string[1].isupper() or string[2] != '}':
|
|
raise SyntaxError(r'Expected something like "\mathbb{A}"!')
|
|
node = node.append(mi(mathbb[string[1]]))
|
|
skip += 3
|
|
elif name in ('mathscr', 'mathcal'):
|
|
if string[0] != '{' or string[2] != '}':
|
|
raise SyntaxError(r'Expected something like "\mathscr{A}"!')
|
|
node = node.append(mi(mathscr[string[1]]))
|
|
skip += 3
|
|
elif name == 'colon': # "normal" colon, not binary operator
|
|
node = node.append(mo(':')) # TODO: add ``lspace="0pt"``
|
|
elif name in Greek: # Greek capitals (upright in "TeX style")
|
|
node = node.append(mo(Greek[name]))
|
|
# TODO: "ISO style" sets them italic. Could we use a class argument
|
|
# to enable styling via CSS?
|
|
elif name in letters:
|
|
node = node.append(mi(letters[name]))
|
|
elif name in special:
|
|
node = node.append(mo(special[name]))
|
|
elif name in functions:
|
|
node = node.append(mo(name))
|
|
elif name in over:
|
|
ovr = mover(mo(over[name]), reversed=True)
|
|
node.append(ovr)
|
|
node = ovr
|
|
else:
|
|
raise SyntaxError('Unknown LaTeX command: ' + name)
|
|
|
|
return node, skip
|
|
|
|
def tex2mathml(tex_math, inline=True):
|
|
"""Return string with MathML code corresponding to `tex_math`.
|
|
|
|
`inline`=True is for inline math and `inline`=False for displayed math.
|
|
"""
|
|
|
|
mathml_tree = parse_latex_math(tex_math, inline=inline)
|
|
return ''.join(mathml_tree.xml())
|
|
|
|
|