mathml.py

"""A MathML printer."""

from ..core import Mul
from ..core.function import _coeff_isneg
from .conventions import requires_partial, split_super_sub
from .pretty_symbology import greek_unicode
from .printer import Printer


class MathMLPrinter(Printer):
    """Prints an expression to the MathML markup language

    Whenever possible tries to use Content markup and not Presentation markup.

    References
    ==========

    * https://www.w3.org/TR/MathML3/

    """

    printmethod = '_mathml'
    _default_settings = {
        'order': None,
        'encoding': 'utf-8'
    }

    def __init__(self, settings=None):
        """Initialize self."""
        Printer.__init__(self, settings)
        from xml.dom.minidom import Document
        self.dom = Document()

    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 mathml_tag(self, e):
        """Returns the MathML tag for an expression."""
        translate = {
            'Add': 'plus',
            'Mul': 'times',
            'Derivative': 'diff',
            'Number': 'cn',
            'int': 'cn',
            'Pow': 'power',
            'Symbol': 'ci',
            'Integral': 'int',
            'Sum': 'sum',
            'sin': 'sin',
            'cos': 'cos',
            'tan': 'tan',
            'cot': 'cot',
            'asin': 'arcsin',
            'asinh': 'arcsinh',
            'acos': 'arccos',
            'acosh': 'arccosh',
            'atan': 'arctan',
            'atanh': 'arctanh',
            'acot': 'arccot',
            'atan2': 'arctan',
            'log': 'ln',
            'Equality': 'eq',
            'Unequality': 'neq',
            'GreaterThan': 'geq',
            'LessThan': 'leq',
            'StrictGreaterThan': 'gt',
            'StrictLessThan': 'lt',
        }

        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 _coeff_isneg(expr):
            x = self.dom.createElement('apply')
            x.appendChild(self.dom.createElement('minus'))
            x.appendChild(self._print_Mul(-expr))
            return x

        from ..simplify import fraction
        numer, denom = fraction(expr)

        if denom != 1:
            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()
        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 = expr.as_ordered_terms(order=order or self.order)
        lastProcessed = self._print(args[0])
        plusNodes = []
        for arg in args[1:]:
            if _coeff_isneg(arg):
                # 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 len(plusNodes) > 0:
            x.appendChild(plusNodes.pop(0))
        return x

    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.denominator == 1:
            # don't divide
            x = self.dom.createElement('cn')
            x.appendChild(self.dom.createTextNode(str(e.numerator)))
            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.numerator)))
        # denominator
        xdenom = self.dom.createElement('cn')
        xdenom.appendChild(self.dom.createTextNode(str(e.denominator)))
        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
        http://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_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)
            elif 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
            mi = self.dom.createElement('mml:mi')
            mi.appendChild(self.dom.createTextNode(items[0]))
            return mi

        def translate(s):
            if s in greek_unicode:
                return greek_unicode.get(s)
            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 len(supers) == 0:
            if len(subs) == 0:
                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 len(subs) == 0:
                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

    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 e.exp.numerator == 1:
            x = self.dom.createElement('apply')
            x.appendChild(self.dom.createElement('root'))
            if e.exp.denominator != 2:
                xmldeg = self.dom.createElement('degree')
                xmlci = self.dom.createElement('ci')
                xmlci.appendChild(self.dom.createTextNode(str(e.exp.denominator)))
                xmldeg.appendChild(xmlci)
                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_Derivative(self, e):
        x = self.dom.createElement('apply')
        diff_symbol = self.mathml_tag(e)
        if requires_partial(e):
            diff_symbol = 'partialdiff'
        x.appendChild(self.dom.createElement(diff_symbol))

        x_1 = self.dom.createElement('bvar')
        for sym in e.variables:
            x_1.appendChild(self._print(sym))

        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_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):
        """See MathML reference for the <list> element:
        http://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


def mathml(expr, **settings):
    """Returns the MathML representation of expr."""
    return MathMLPrinter(settings).doprint(expr)