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569 lines
17 KiB
569 lines
17 KiB
4 years ago
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#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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# :Id: $Id: latex2mathml.py 8366 2019-08-27 12:09:19Z milde $
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# :Copyright: © 2010 Günter Milde.
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# Based on rst2mathml.py from the latex_math sandbox project
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# © 2005 Jens Jørgen Mortensen
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# :License: Released under the terms of the `2-Clause BSD license`_, in short:
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#
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# Copying and distribution of this file, with or without modification,
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# are permitted in any medium without royalty provided the copyright
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# notice and this notice are preserved.
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# This file is offered as-is, without any warranty.
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#
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# .. _2-Clause BSD license: http://www.spdx.org/licenses/BSD-2-Clause
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"""Convert LaTex math code into presentational MathML"""
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# Based on the `latex_math` sandbox project by Jens Jørgen Mortensen
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import docutils.utils.math.tex2unichar as tex2unichar
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# TeX spacing combining
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over = {'acute': u'\u00B4', # u'\u0301',
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'bar': u'\u00AF', # u'\u0304',
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'breve': u'\u02D8', # u'\u0306',
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'check': u'\u02C7', # u'\u030C',
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'dot': u'\u02D9', # u'\u0307',
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'ddot': u'\u00A8', # u'\u0308',
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'dddot': u'\u20DB',
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'grave': u'`', # u'\u0300',
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'hat': u'^', # u'\u0302',
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'mathring': u'\u02DA', # u'\u030A',
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'overleftrightarrow': u'\u20e1',
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# 'overline': # u'\u0305',
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'tilde': u'\u02DC', # u'\u0303',
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'vec': u'\u20D7'}
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Greek = { # Capital Greek letters: (upright in TeX style)
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'Phi':u'\u03a6', 'Xi':u'\u039e', 'Sigma':u'\u03a3',
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'Psi':u'\u03a8', 'Delta':u'\u0394', 'Theta':u'\u0398',
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'Upsilon':u'\u03d2', 'Pi':u'\u03a0', 'Omega':u'\u03a9',
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'Gamma':u'\u0393', 'Lambda':u'\u039b'}
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letters = tex2unichar.mathalpha
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special = tex2unichar.mathbin # Binary symbols
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special.update(tex2unichar.mathrel) # Relation symbols, arrow symbols
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special.update(tex2unichar.mathord) # Miscellaneous symbols
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special.update(tex2unichar.mathop) # Variable-sized symbols
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special.update(tex2unichar.mathopen) # Braces
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special.update(tex2unichar.mathclose) # Braces
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special.update(tex2unichar.mathfence)
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sumintprod = ''.join([special[symbol] for symbol in
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['sum', 'int', 'oint', 'prod']])
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functions = ['arccos', 'arcsin', 'arctan', 'arg', 'cos', 'cosh',
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'cot', 'coth', 'csc', 'deg', 'det', 'dim',
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'exp', 'gcd', 'hom', 'inf', 'ker', 'lg',
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'lim', 'liminf', 'limsup', 'ln', 'log', 'max',
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'min', 'Pr', 'sec', 'sin', 'sinh', 'sup',
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'tan', 'tanh',
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'injlim', 'varinjlim', 'varlimsup',
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'projlim', 'varliminf', 'varprojlim']
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mathbb = {
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'A': u'\U0001D538',
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'B': u'\U0001D539',
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'C': u'\u2102',
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'D': u'\U0001D53B',
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'E': u'\U0001D53C',
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'F': u'\U0001D53D',
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'G': u'\U0001D53E',
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'H': u'\u210D',
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'I': u'\U0001D540',
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'J': u'\U0001D541',
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'K': u'\U0001D542',
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'L': u'\U0001D543',
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'M': u'\U0001D544',
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'N': u'\u2115',
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'O': u'\U0001D546',
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'P': u'\u2119',
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'Q': u'\u211A',
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'R': u'\u211D',
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'S': u'\U0001D54A',
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'T': u'\U0001D54B',
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'U': u'\U0001D54C',
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'V': u'\U0001D54D',
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'W': u'\U0001D54E',
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'X': u'\U0001D54F',
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'Y': u'\U0001D550',
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'Z': u'\u2124',
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}
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mathscr = {
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'A': u'\U0001D49C',
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'B': u'\u212C', # bernoulli function
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'C': u'\U0001D49E',
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'D': u'\U0001D49F',
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'E': u'\u2130',
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'F': u'\u2131',
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'G': u'\U0001D4A2',
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'H': u'\u210B', # hamiltonian
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'I': u'\u2110',
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'J': u'\U0001D4A5',
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'K': u'\U0001D4A6',
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'L': u'\u2112', # lagrangian
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'M': u'\u2133', # physics m-matrix
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'N': u'\U0001D4A9',
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'O': u'\U0001D4AA',
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'P': u'\U0001D4AB',
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'Q': u'\U0001D4AC',
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'R': u'\u211B',
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'S': u'\U0001D4AE',
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'T': u'\U0001D4AF',
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'U': u'\U0001D4B0',
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'V': u'\U0001D4B1',
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'W': u'\U0001D4B2',
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'X': u'\U0001D4B3',
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'Y': u'\U0001D4B4',
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'Z': u'\U0001D4B5',
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'a': u'\U0001D4B6',
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'b': u'\U0001D4B7',
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'c': u'\U0001D4B8',
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'd': u'\U0001D4B9',
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'e': u'\u212F',
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'f': u'\U0001D4BB',
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'g': u'\u210A',
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'h': u'\U0001D4BD',
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'i': u'\U0001D4BE',
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'j': u'\U0001D4BF',
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'k': u'\U0001D4C0',
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'l': u'\U0001D4C1',
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'm': u'\U0001D4C2',
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'n': u'\U0001D4C3',
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'o': u'\u2134', # order of
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'p': u'\U0001D4C5',
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'q': u'\U0001D4C6',
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'r': u'\U0001D4C7',
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's': u'\U0001D4C8',
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't': u'\U0001D4C9',
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'u': u'\U0001D4CA',
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'v': u'\U0001D4CB',
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'w': u'\U0001D4CC',
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'x': u'\U0001D4CD',
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'y': u'\U0001D4CE',
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'z': u'\U0001D4CF',
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}
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negatables = {'=': u'\u2260',
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r'\in': u'\u2209',
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r'\equiv': u'\u2262'}
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# LaTeX to MathML translation stuff:
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class math(object):
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"""Base class for MathML elements."""
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nchildren = 1000000
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"""Required number of children"""
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def __init__(self, children=None, inline=None):
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"""math([children]) -> MathML element
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children can be one child or a list of children."""
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self.children = []
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if children is not None:
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if isinstance(children, list):
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for child in children:
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self.append(child)
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else:
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# Only one child:
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self.append(children)
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if inline is not None:
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self.inline = inline
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def __repr__(self):
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if hasattr(self, 'children'):
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return self.__class__.__name__ + '(%s)' % \
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','.join([repr(child) for child in self.children])
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else:
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return self.__class__.__name__
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def full(self):
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"""Room for more children?"""
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return len(self.children) >= self.nchildren
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def append(self, child):
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"""append(child) -> element
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Appends child and returns self if self is not full or first
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non-full parent."""
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assert not self.full()
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self.children.append(child)
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child.parent = self
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node = self
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while node.full():
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node = node.parent
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return node
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def delete_child(self):
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"""delete_child() -> child
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Delete last child and return it."""
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child = self.children[-1]
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del self.children[-1]
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return child
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def close(self):
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"""close() -> parent
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Close element and return first non-full element."""
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parent = self.parent
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while parent.full():
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parent = parent.parent
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return parent
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def xml(self):
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"""xml() -> xml-string"""
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return self.xml_start() + self.xml_body() + self.xml_end()
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def xml_start(self):
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if not hasattr(self, 'inline'):
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return ['<%s>' % self.__class__.__name__]
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xmlns = 'http://www.w3.org/1998/Math/MathML'
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if self.inline:
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return ['<math xmlns="%s">' % xmlns]
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else:
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return ['<math xmlns="%s" mode="display">' % xmlns]
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def xml_end(self):
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return ['</%s>' % self.__class__.__name__]
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def xml_body(self):
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xml = []
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for child in self.children:
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xml.extend(child.xml())
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return xml
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class mrow(math):
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def xml_start(self):
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return ['\n<%s>' % self.__class__.__name__]
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class mtable(math):
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def xml_start(self):
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return ['\n<%s>' % self.__class__.__name__]
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class mtr(mrow): pass
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class mtd(mrow): pass
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class mx(math):
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"""Base class for mo, mi, and mn"""
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nchildren = 0
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def __init__(self, data):
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self.data = data
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def xml_body(self):
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return [self.data]
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class mo(mx):
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translation = {'<': '<', '>': '>'}
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def xml_body(self):
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return [self.translation.get(self.data, self.data)]
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class mi(mx): pass
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class mn(mx): pass
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class msub(math):
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nchildren = 2
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class msup(math):
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nchildren = 2
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class msqrt(math):
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nchildren = 1
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class mroot(math):
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nchildren = 2
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class mfrac(math):
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nchildren = 2
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class msubsup(math):
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nchildren = 3
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def __init__(self, children=None, reversed=False):
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self.reversed = reversed
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math.__init__(self, children)
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def xml(self):
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if self.reversed:
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## self.children[1:3] = self.children[2:0:-1]
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self.children[1:3] = [self.children[2], self.children[1]]
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self.reversed = False
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return math.xml(self)
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class mfenced(math):
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translation = {'\\{': '{', '\\langle': u'\u2329',
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'\\}': '}', '\\rangle': u'\u232A',
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'.': ''}
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def __init__(self, par):
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self.openpar = par
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math.__init__(self)
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def xml_start(self):
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open = self.translation.get(self.openpar, self.openpar)
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close = self.translation.get(self.closepar, self.closepar)
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return ['<mfenced open="%s" close="%s">' % (open, close)]
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class mspace(math):
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nchildren = 0
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class mstyle(math):
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def __init__(self, children=None, nchildren=None, **kwargs):
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if nchildren is not None:
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self.nchildren = nchildren
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math.__init__(self, children)
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self.attrs = kwargs
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def xml_start(self):
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return ['<mstyle '] + ['%s="%s"' % item
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for item in self.attrs.items()] + ['>']
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class mover(math):
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nchildren = 2
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def __init__(self, children=None, reversed=False):
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self.reversed = reversed
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math.__init__(self, children)
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def xml(self):
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if self.reversed:
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self.children.reverse()
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self.reversed = False
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return math.xml(self)
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class munder(math):
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nchildren = 2
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class munderover(math):
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nchildren = 3
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def __init__(self, children=None):
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math.__init__(self, children)
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class mtext(math):
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nchildren = 0
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def __init__(self, text):
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self.text = text
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def xml_body(self):
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return [self.text]
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def parse_latex_math(string, inline=True):
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"""parse_latex_math(string [,inline]) -> MathML-tree
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Returns a MathML-tree parsed from string. inline=True is for
|
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inline math and inline=False is for displayed math.
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tree is the whole tree and node is the current element."""
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||
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# Normalize white-space:
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||
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string = ' '.join(string.split())
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if inline:
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||
|
|
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 = ''
|
||
|
|
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(u'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(u'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(u'Environment not supported! '
|
||
|
|
u'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(u'Expected "\\end{matrix}"!')
|
||
|
|
skip += 8
|
||
|
|
node = node.close().close().close()
|
||
|
|
elif name in ('text', 'mathrm'):
|
||
|
|
if string[0] != '{':
|
||
|
|
raise SyntaxError(u'Expected "\\text{...}"!')
|
||
|
|
i = string.find('}')
|
||
|
|
if i == -1:
|
||
|
|
raise SyntaxError(u'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(u'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(u'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(u'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(u'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(u'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(u'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())
|