a summary of MathML use cases that don't work with Mathematica (stuff WRI should fix for the next go-round)

*To*: mathgroup at smc.vnet.net*Subject*: [mg69987] a summary of MathML use cases that don't work with Mathematica (stuff WRI should fix for the next go-round)*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Thu, 28 Sep 2006 06:18:25 -0400 (EDT)

See below for code, this is just the description: 1) It appears the ContentMathML part of a MathML export is based on some kind of parsing of the printed form of an expression. One would think that the content MathML would come directly from the Kernel representation/FullForm of an expression, but I demonstrate below that this is probably not the case. This is a particularly strange situation to be in for an implementation from WRI. Mathematica usually maintains very good simultaneous control of both the content of an expression and its presentation. As a result of the smearing together of content + presentation on MathML export, Mathematica can't reliably round-trip MathML. 2) Mathematica fails to import (as XML) its own MathML exports. 3) When Mathematica imports (as MathML) any MathML, even if it only contains content MathML, the resulting expression is a Box form. I would understand if that happened with presentation-only MathML, but content MathML should be imported as a kernel/FullForm expression. Imports of combination content + presentation MathML should take an option to allow the user to choose which result is desired. 4) When writing MathML, Mathematica screws up arbitrary precision numbers with accuracy less than 1.0. 5) It is very difficult to capture the SymbolicXML form of a namespace prefixed MathML expression due to lack of an appropriate option on XML`MathML`ExpressionToSymbolicMathML and, subsequently, various Import/Export shortcomings. This makes it hard to write it out in a compound document that can be transformed. Today's XSL 1.0 transformers are unable to handle compound documents with unprefixed namespaces. A typical case would be the transformation of DocBook + MathML into XHTML+MathML. An XSL 1.0 transformer can't do this without having a prefix on the MML elements. The code: 1) & 4) shows how content MathML is based, paradoxically, on the Box form of the exported expression & shows how 5.4 is actually written out as 5.0 (this bug is common to content and presentation MathML exports) In[1]:= MakeBoxes[YoungsModulus,_]="E"; MakeBoxes[SectionModulus,_]="I"; eqn[1]=\[Delta]==F*L^5.4``0.9/(3*YoungsModulus*SectionModulus); ex[1]=ExportString[eqn[1],"MathML",ConversionOptions->{"Formats"->"ContentMathML"}] Out[4]= <math xmlns='http://www.w3.org/1998/Math/MathML'> <apply> <eq/> <ci>δ</ci> <apply> <times/> <ci>F</ci> <apply> <power/> <ci>L</ci> <cn type='real'>5.0</cn> </apply> <apply> <power/> <apply> <times/> <cn type='integer'>3</cn> <imaginaryi/> <exponentiale/> </apply> <cn type='integer'>-1</cn> </apply> </apply> </apply> </math> 2) shows that Mathematica can't import its MathML as XML In[5]:= ex[2]=ExportString[eqn[1],"MathML"]; ImportString[ex[2],"XML"] Out[6]= System`Convert`MathMLDump`ImportMathML[C:\DOCUME~1\Chris\LOCALS~1\Temp\000\ 003a01664] 1) & 3) shows that Mathematica thinks that the content MathML should be represented by a box structure & also note the incorrect presence of \[ImaginaryI] and \[ExponentialE], as if they came from the printed form of the equation instead of the internal representation In[7]:= imp[1]=ImportString[ex[1],"MathML"] Out[7]= FormBox[TagBox[ RowBox[{\[Delta],\[LongEqual], FractionBox[RowBox[{F, ,SuperscriptBox[L,5.`]}], RowBox[{3, ,\[ImaginaryI], ,\[ExponentialE]}]]}],MathMLContentTag, AutoDelete\[Rule]True],TraditionalForm] 1) even after the Box form is turned into the expression that Mathematica should have automatically returned, it is not the same as the expression that we exported because of the presence of E and I: In[8]:= imp[2]=ImportString[ex[2],"MathML"]; ToExpression[imp[2]]===eqn[1] Out[9]= False 5) Where is the missing NamespacePrefixes option for ExpressionToSymbolicMathML?? And yes, I do know of a workaround, but it does not replace a direct option here. Notice that the option is present for ExpressionToMathML, even though it doesn't work right, since it also outputs a default namespace in addition to a prefixed namespace. In[10]:= Options@XML`MathML`ExpressionToSymbolicMathML Out[10]= {"Annotations"->{},"Formats"->{"PresentationMathML","ContentMathML"},"UseUnicodePlane1Characters"->True,"MathAttributes"->{},"IncludeMarkupAnnotations"->True} In[11]:= Options@XML`MathML`ExpressionToMathML Out[11]= {"Annotations"->{},"AttributeQuoting"->"'","CheckXML"->True,"ElementFormatting"->Automatic,"Entities"->None,"Formats"->{"PresentationMathML","ContentMathML"},"IncludeMarkupAnnotations"->True,"MathAttributes"->{},"NamespacePrefixes"->{},"UseUnicodePlane1Characters"->True} -- http://chris.chiasson.name/