venv/lib/python3.11/site-packages/sympy/printing/mathml.py

"""
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": '·',
        "disable_split_super_sub": False,
    }

    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 _split_super_sub(self, name):
        if self._settings["disable_split_super_sub"]:
            return (name, [], [])
        else:
            return split_super_sub(name)


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 = self._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

    def _print_Lambda(self, e):
        # MathML reference for the lambda element:
        # https://www.w3.org/TR/MathML2/chapter4.html#id.4.2.1.7
        x = self.dom.createElement(self.mathml_tag(e))
        for arg in e.signature:
            x_1 = self.dom.createElement('bvar')
            x_1.appendChild(self._print(arg))
            x.appendChild(x_1)
        x.appendChild(self._print(e.expr))
        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;',
            'Lambda': 'lambda',
        }

        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 _l_paren(self):
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode('('))
        return mo

    def _r_paren(self):
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode(')'))
        return mo

    def _l_brace(self):
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode('{'))
        return mo

    def _r_brace(self):
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode('}'))
        return mo

    def _comma(self):
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode(','))
        return mo

    def _bar(self):
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode('|'))
        return mo

    def _semicolon(self):
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode(';'))
        return mo

    def _paren_comma_separated(self, *args):
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(self._l_paren())
        for i, arg in enumerate(args):
            if i:
                mrow.appendChild(self._comma())
            mrow.appendChild(self._print(arg))
        mrow.appendChild(self._r_paren())
        return mrow

    def _paren_bar_separated(self, *args):
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(self._l_paren())
        for i, arg in enumerate(args):
            if i:
                mrow.appendChild(self._bar())
            mrow.appendChild(self._print(arg))
        mrow.appendChild(self._r_paren())
        return mrow

    def parenthesize(self, item, level, strict=False):
        prec_val = precedence_traditional(item)
        if (prec_val < level) or ((not strict) and prec_val <= level):
            mrow = self.dom.createElement('mrow')
            mrow.appendChild(self._l_paren())
            mrow.appendChild(self._print(item))
            mrow.appendChild(self._r_paren())
            return mrow
        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)
        mat_delim = self._settings["mat_delim"]
        if mat_delim == '':
            return table
        left = self.dom.createElement('mo')
        right = self.dom.createElement('mo')
        if mat_delim == "[":
            left.appendChild(self.dom.createTextNode("["))
            right.appendChild(self.dom.createTextNode("]"))
        else:
            left.appendChild(self.dom.createTextNode("("))
            right.appendChild(self.dom.createTextNode(")"))
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(left)
        mrow.appendChild(table)
        mrow.appendChild(right)
        return mrow

    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)
        mrow.appendChild(self.parenthesize(e.function, precedence_traditional(e)))
        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 = self._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):
        frac = self.dom.createElement('mfrac')
        frac.setAttribute('linethickness', '0')
        frac.appendChild(self._print(expr.args[0]))
        frac.appendChild(self._print(expr.args[1]))
        brac = self.dom.createElement('mrow')
        brac.appendChild(self._l_paren())
        brac.appendChild(frac)
        brac.appendChild(self._r_paren())
        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):
        left = self.dom.createElement('mo')
        left.appendChild(self.dom.createTextNode('\u27e8'))
        right = self.dom.createElement('mo')
        right.appendChild(self.dom.createTextNode('\u27e9'))
        brac = self.dom.createElement('mrow')
        brac.appendChild(left)
        brac.appendChild(self._print(i.min))
        brac.appendChild(self._comma())
        brac.appendChild(self._print(i.max))
        brac.appendChild(right)
        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):
        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)))
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(x)
        mrow.appendChild(self._paren_comma_separated(*e.args))
        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('mrow')
        brac.appendChild(self._l_paren())
        brac.appendChild(self._print(expr.args[1]))
        brac.appendChild(self._r_paren())
        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)
        mrow.appendChild(self._paren_comma_separated(*e.args))
        return mrow

    def _print_Tuple(self, e):
        return self._paren_comma_separated(*e.args)

    def _print_Interval(self, i):
        right = self.dom.createElement('mo')
        if i.right_open:
            right.appendChild(self.dom.createTextNode(')'))
        else:
            right.appendChild(self.dom.createTextNode(']'))
        left = self.dom.createElement('mo')
        if i.left_open:
            left.appendChild(self.dom.createTextNode('('))
        else:
            left.appendChild(self.dom.createTextNode('['))
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(left)
        mrow.appendChild(self._print(i.start))
        mrow.appendChild(self._comma())
        mrow.appendChild(self._print(i.end))
        mrow.appendChild(right)
        return mrow

    def _print_Abs(self, expr, exp=None):
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(self._bar())
        mrow.appendChild(self._print(expr.args[0]))
        mrow.appendChild(self._bar())
        return mrow

    _print_Determinant = _print_Abs

    def _print_re_im(self, c, expr):
        brac = self.dom.createElement('mrow')
        brac.appendChild(self._l_paren())
        brac.appendChild(self._print(expr))
        brac.appendChild(self._r_paren())
        mi = self.dom.createElement('mi')
        mi.appendChild(self.dom.createTextNode(c))
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(mi)
        mrow.appendChild(brac)
        return mrow

    def _print_re(self, expr, exp=None):
        return self._print_re_im('\u211C', expr.args[0])

    def _print_im(self, expr, exp=None):
        return self._print_re_im('\u2111', 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('mrow')
        brac.appendChild(self._l_brace())
        for i, item in enumerate(items):
            if i:
                brac.appendChild(self._comma())
            brac.appendChild(self._print(item))
        brac.appendChild(self._r_brace())
        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('mrow')
            brac.appendChild(self._l_paren())
            brac.appendChild(self._print(args[0]))
            brac.appendChild(self._r_paren())
            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('mrow')
                y.appendChild(self._l_paren())
                y.appendChild(self._print(arg))
                y.appendChild(self._r_paren())
            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('mrow')
                    mbrac.appendChild(self._l_paren())
                    mbrac.appendChild(self._print(v))
                    mbrac.appendChild(self._r_paren())
                    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('mrow')
            x.appendChild(self._l_paren())
            x.appendChild(self._print(e.args[0]))
            x.appendChild(self._r_paren())
        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"
        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)
        brac = self.dom.createElement('mrow')
        brac.appendChild(self._l_brace())
        for i, el in enumerate(printset):
            if i:
                brac.appendChild(self._comma())
            if el == dots:
                mi = self.dom.createElement('mi')
                mi.appendChild(self.dom.createTextNode(dots))
                brac.appendChild(mi)
            else:
                brac.appendChild(self._print(el))
        brac.appendChild(self._r_brace())
        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)
        mrow.appendChild(self._paren_comma_separated(*args))
        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]
        left = self.dom.createElement('mo')
        left.appendChild(self.dom.createTextNode('\u27e8'))
        right = self.dom.createElement('mo')
        right.appendChild(self.dom.createTextNode('\u27e9'))
        brac = self.dom.createElement('mrow')
        brac.appendChild(left)
        brac.appendChild(self._print(shift))
        brac.appendChild(right)
        sup = self.dom.createElement('msup')
        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
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(sub)
        mrow.appendChild(self._paren_comma_separated(*e.args[1:]))
        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('mrow')
            brac.appendChild(self._l_paren())
            brac.appendChild(self._print(mat))
            brac.appendChild(self._r_paren())
            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('mrow')
            brac.appendChild(self._l_paren())
            brac.appendChild(self._print(mat))
            brac.appendChild(self._r_paren())
            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('mrow')
            brac.appendChild(self._l_paren())
            brac.appendChild(self._print(mat))
            brac.appendChild(self._r_paren())
            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('mrow')
            brac.appendChild(self._l_paren())
            brac.appendChild(self._print(base))
            brac.appendChild(self._r_paren())
            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):
        left = self.dom.createElement('mo')
        left.appendChild(self.dom.createTextNode('\u230A'))
        right = self.dom.createElement('mo')
        right.appendChild(self.dom.createTextNode('\u230B'))
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(left)
        mrow.appendChild(self._print(e.args[0]))
        mrow.appendChild(right)
        return mrow

    def _print_ceiling(self, e):
        left = self.dom.createElement('mo')
        left.appendChild(self.dom.createTextNode('\u2308'))
        right = self.dom.createElement('mo')
        right.appendChild(self.dom.createTextNode('\u2309'))
        mrow = self.dom.createElement('mrow')
        mrow.appendChild(left)
        mrow.appendChild(self._print(e.args[0]))
        mrow.appendChild(right)
        return mrow

    def _print_Lambda(self, e):
        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(self._l_paren())
        mrow.appendChild(symbols)
        mo = self.dom.createElement('mo')
        mo.appendChild(self.dom.createTextNode('&#x21A6;'))
        mrow.appendChild(mo)
        mrow.appendChild(self._print(e.args[1]))
        mrow.appendChild(self._r_paren())
        return mrow

    def _print_tuple(self, e):
        return self._paren_comma_separated(*e)

    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('mrow')
        for i, arg in enumerate(e.indices):
            if i:
                brac.appendChild(self._comma())
            brac.appendChild(self._print(arg))
        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)
        x.appendChild(self._paren_bar_separated(*e.args))
        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)
        x.appendChild(self._paren_bar_separated(*e.args))
        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('mrow')
        y.appendChild(self._l_paren())
        if len(e.args) == 2:
            n, m = e.args
            y.appendChild(self._print(n))
            y.appendChild(self._bar())
            y.appendChild(self._print(m))
        else:
            n, m, z = e.args
            y.appendChild(self._print(n))
            y.appendChild(self._semicolon())
            y.appendChild(self._print(m))
            y.appendChild(self._bar())
            y.appendChild(self._print(z))
        y.appendChild(self._r_paren())
        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))
    pretty_xml = xml.toprettyxml()

    print(pretty_xml)


# For backward compatibility
MathMLPrinter = MathMLContentPrinter