Elena Smirnova and Stephen M. Watt

Ontario Research Centre for Computer Algebra,
University of Western Ontario

MathML to TeX Conversion:
Conserving high-level semantics

** Demo description **

1. Main goals of the converter
2. Principal MathML to TEX conversion scheme
   • MathML Object Structure
   • TeX Object Structure
   • Mapping file
3. Three jobs for the converter
4. Three interfaces to the converter
5. Advanced possibilities
   • Linebreaking in long formulas
   • Settings for output TEX
   • Conversion XML with MathML to XML with TeX
6. Advantages of this converter
7. Choice of Java - program vs XSLT
8. Status

• This program converts a given MathML representation of some formula to an equivalent TeX expression.
• The MathML may be a part of an XML-file or may be given as an input string.
• One of the main goals of this converter is to conserve high-level semantics during translation.
• Using a mapping file allows us to transform high-level MathML extensions to TeX macros.

Figure 1. MathML to TeX converter scheme

A MathML-object is represented in the form of Document Object Model as specified by the W3C Recommendation http://www.w3.org/DOM .

<math> <mo> &sum; </mo> <msupsub> <mi> x </mi> <mn> 3 </mn> <mi> i </mi> </msupsub> </math>

A TeX - object is also represented by a tree, but the logic of its structure is different from that of a MathML DOM-tree. Each level of this tree corresponds to a TeX -group.

Example: the following TeX-expression $\sqrt {1-\alpha} + x^{3+a}$ is represented as

Figure 2. Structure of TeX-Object

• The mapping file is one of principle parts of converter: it describes the correspondence between MathML and TEX patterns.
• The mapping file has a XML-form and consists of templates, representing MathML - TEX patterns.
• Each template has a form

<pat:template>
  <pat:tex op="\[TeX macro]" parameters=" TEX expression"/>
  <pat:mml op="mml-element" mode="math|text|spec"
   . . .
   [MathML expression]
   . . .
  <pat:mml>
</pat:template>

• Namespaces:
  • local: xmlns:pat = "http://www.orcca.on.ca/mathml/tex2mml.xml"
  • general: xmlns:pat = http://www.w3.org/1998/Math/MathML
• Root element: pat:tex2mmlmap
• Allowed children of pat:tex2mmlmap:
  • pat:template
• Allowed children of pat:template :
  • pat:tex
  • pat:mml
  • pat:img
• Allowed children of pat:tex : none
• Allowed children of pat:mml:
  • MathML elements
  • pat:rep
  • pat:variable
• Allowed children of pat:img : none
• Table of attributes used with the above elements:

More information about our mapping file and its specification can be found on the ORCCA site.

1. for fraction:

   <pat:template>
     <pat:tex op="\frac" params="\patVAR!{num}\patVAR!{den}"/>
     <pat:mml op="mfrac">
       <mfrac>
         <pat:variable name="num"/>
         <pat:variable name="den"/>
       </mfrac>
     </pat:mml>
   </pat:template>
   

   ---

2. for fenced expression

   <pat:template>
    <pat:tex op="" params="\left\patVAR!{o} \patREP*{\patVAR*{b},}\patVAR{t} \right\patVAR!{c}"/>
     <pat:mml op="mfenced">
       <mfenced open="pat:variable=o" close="pat:variable=c">
        <pat:rep> <pat:variable name="b"/> </pat:rep>
        <pat:variable name="t"/>
       </mfenced>
     </pat:mml>
   </pat:template>
   

combinatorics.xsl

XSLT template for an element <mmlx:binom>:

<xsl:template match = "apply/mmlx:binom[position()=1][count(child::*)=2]">
  <mfrac thikness="0ex">
     <xsl:for-each select = 'mmlx:binom/child::*'>
	<xsl:copy-of select='.'/>
     </xsl:for-each>
  </mfrac>
</xsl:template>

\newcommand{\binom}[2]{left(\atop{#1}{#2}\right)}

Now we can put a template for convert <mmlx:binom> to \binom in the mapping file:

<pat:template>
   <pat:tex op="\binom"params="\patVAR!{a}\patVAR!{b}"/>
   <pat:mml op="apply-mmlx:binomial">
      <apply>
	 <mmlx:binomial>
	    <pat:variable name="a"/>
	    <pat:variable name="b"/>
	 </mmlx:binomial>
      </apply>
   </pat:mml>
</pat:template>

Then we would want to translate

<apply>
 <mmlx:binomial>
   <apply>
     <plus/>
     <ci> a </ci>
     <ci> b </ci>
   </apply>
   <mrow>
     <mi> c </mi>
     <mo> + </mo>
     <mi> d </mi>
   </mrow>
 </mmlx:binomial>
</apply>

1. File to file
   To convert an entire
   • MathML file into TEX document
   • XML file with MathML entries to XML document with embedded TEX
   
   
2. Expression to expression
   The system provides the possibility to convert any valid MathML expression, given as input string.
   
   
3. Object to object
   This possibility allows to user manipulate individual MathML and TEX -objects obtained from sources different from standard MathML or TEX files.

1. Command-line mode
   
   
2. GUI Framework
   
   
3. Servlet at ORCCA web site.

Converter provides a special algorithm for line breaking in TeX output.

Motivation: Standard MathML browsers (Amaya, Mozilla, MathPlayer) perform line breaking in mathematical formulas according to their own logic, but TeX does not. So long formulas, generated from MathML may not fit the page of TeX document.

The algorithm provides line breaking in long expression such as

• Plain formulas (like polynomials or simple summation),
• long text,
• long numbers,
• special cases like
  • radicals,
  • fractions,
  • matrix entries,
  • indexes,
  • under and over scripts

Examples of linebreaking in special cases:

1. Long expression under a radical		2. Long expression in a numerator
3. Long superscripts		4. Long underscripts

5. Long number

100! = 93326215443944152681699238856266700490715968264381621468592963895
       21759999322991560894146397615651828625369792082722375825118521091
       6864000000000000000000000000
  
 

• The converter allows the user to choose a text area width and font size for the output TEX file. These settings will be considered in the calculation of the optimal formula length.
  
  
• Line breaking usually occurs around mathematical operators, but is done differently in different cultures.
  There are three ways in which signs of these operators can be
  1. before the line break,
  2. after the line break,
  3. duplicated.
  
  Examples:

  1		2		3
  a + b + ... + k + m + n + ... + z		a + b + ... + k + m + n + ... + z		a + b + ... + k + + m + n + ... + z

  
  The user can choose the more convenient variant.
  
  
• The user may also set an option to indent after a line break.

The converter also provides the transformation of a XML file with MathML to XML file with TeX, embedded into CDATA section. This CDATA will be put under XML node <LaTeX> with special namespace.
Motivation: this possibility may be useful for HTML to TeX translation.

• The mapping file allows high-level translation of user-defined macros, to help preserve any semantic content of the original expression.
• Using a mapping file for conversion from MathML to TeX and back allows the converter-program to be flexible (i.e. not hard-coded).
• If the user needs to add a new TeX-macro or MathML element, he or she may put a new template into this mapping file.
• The algorithm for line breaking for TeX output lets one deal with mathematical expressions that cannot fit in one line in an output document.
• The user-friendly GUI lets users browse a file system to pick up an input MathML file, convert it to a DOM tree and easily explore it.

• to share technologies with TeX to MathML converter,
  • in particular mapping file can be used for conversion in both directions
• to use GUI
• to manipulate with separate TeX and MathML objects
• to compute linebreaking + other complex calculations are more natural

• Formulas
• Matrices
• Multi-line equations
• Equation arrays
• Commutative diagram