Source code for sympy.printing.mathml

"""
A MathML printer.
"""

from sympy import sympify, S, Mul
from sympy.core.function import _coeff_isneg
from sympy.simplify import fraction
from .printer import Printer
from .conventions import split_super_sub


[docs]class MathMLPrinter(Printer): """Prints an expression to the MathML markup language Whenever possible tries to use Content markup and not Presentation markup. References: http://www.w3.org/TR/MathML2/ """ printmethod = "_mathml" _default_settings = { "order": None, "encoding": "utf-8" } def __init__(self, settings=None): Printer.__init__(self, settings) from xml.dom.minidom import Document self.dom = Document()
[docs] 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
[docs] 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 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 # thing 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 _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.lines): 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))) #denomenator 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 http://www.w3.org/2003/entities/2007doc/isogrk1.html""" x = self.dom.createElement('cn') x.appendChild(self.dom.createTextNode("\u03c6")) 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_Negative_Infinity(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 # taken from http://www.w3.org/2003/entities/2007doc/isogrk1.html unitr = { 'Alpha' : '\u0391', 'Beta' : '\u0392', 'Gamma' : '\u0393', 'Delta' : '\u0394', 'Epsilon' : '\u0395', 'Zeta' : '\u0396', 'Eta' : '\u0397', 'Theta' : '\u0398', 'Iota' : '\u0399', 'Kappa' : '\u039A', 'Lambda' : '\u039B', 'Mu' : '\u039C', 'Nu' : '\u039D', 'Xi' : '\u039E', 'Omicron' : '\u039F', 'Pi' : '\u03A0', 'Rho' : '\u03A1', 'Sigma' : '\u03A3', 'Tau' : '\u03A4', 'Upsilon' : '\u03A5', 'Phi' : '\u03A6', 'Chi' : '\u03A7', 'Psi' : '\u03A8', 'Omega' : '\u03A9', 'alpha' : '\u03B1', 'beta' : '\u03B2', 'gamma' : '\u03B3', 'delta' : '\u03B4', 'epsilon' : '\u03B5', 'zeta' : '\u03B6', 'eta' : '\u03B7', 'theta' : '\u03B8', 'iota' : '\u03B9', 'kappa' : '\u03BA', 'lambda' : '\u03BB', 'mu' : '\u03BC', 'nu' : '\u03BD', 'xi' : '\u03BE', 'omicron' : '\u03BF', 'pi' : '\u03C0', 'rho' : '\u03C1', 'varsigma' : '\u03C2', 'sigma' : '\u03C3', 'tau' : '\u03C4', 'upsilon' : '\u03C5', 'phi' : '\u03C6', 'chi' : '\u03C7', 'psi' : '\u03C8', 'omega' : '\u03C9', } def translate(s): if s in unitr: return unitr[s] else: return s name, supers, subs = split_super_sub(sym.name) name = translate(name) supers = [translate(sup) for sup in supers] subs = [translate(sub) for sub in subs] mname = self.dom.createElement('mml:mi') mname.appendChild(self.dom.createTextNode(name)) if 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.p == 1: x = self.dom.createElement('apply') x.appendChild(self.dom.createElement('root')) if e.exp.q != 2: xmldeg = self.dom.createElement('degree') xmlci = self.dom.createElement('ci') xmlci.appendChild(self.dom.createTextNode(str(e.exp.q))) 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') x.appendChild(self.dom.createElement(self.mathml_tag(e))) 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: 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: 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 apply_patch(self): # Applying the patch of xml.dom.minidom bug # Date: 2011-11-18 # Description: http://ronrothman.com/public/leftbraned/xml-dom-minidom-\ # toprettyxml-and-silly-whitespace/#best-solution # Issue: http://bugs.python.org/issue4147 # Patch: http://hg.python.org/cpython/rev/7262f8f276ff/ from xml.dom.minidom import Element, Text, Node, _write_data def writexml(self, writer, indent="", addindent="", newl=""): # indent = current indentation # addindent = indentation to add to higher levels # newl = newline string writer.write(indent+"<" + self.tagName) attrs = self._get_attributes() a_names = list(attrs.keys()) a_names.sort() for a_name in a_names: writer.write(" %s=\"" % a_name) _write_data(writer, attrs[a_name].value) writer.write("\"") if self.childNodes: writer.write(">") if (len(self.childNodes) == 1 and self.childNodes[0].nodeType == Node.TEXT_NODE): self.childNodes[0].writexml(writer, '', '', '') else: writer.write(newl) for node in self.childNodes: node.writexml(writer, indent+addindent, addindent, newl) writer.write(indent) writer.write("</%s>%s" % (self.tagName, newl)) else: writer.write("/>%s"%(newl)) self._Element_writexml_old = Element.writexml Element.writexml = writexml def writexml(self, writer, indent="", addindent="", newl=""): _write_data(writer, "%s%s%s"%(indent, self.data, newl)) self._Text_writexml_old = Text.writexml Text.writexml = writexml def restore_patch(self): from xml.dom.minidom import Element, Text Element.writexml = self._Element_writexml_old Text.writexml = self._Text_writexml_old
[docs]def mathml(expr, **settings): """Returns the MathML representation of expr""" return MathMLPrinter(settings).doprint(expr)