Mathematical Content Conversions

Mathematical Content Conversions David McKain 9 th September 2009

Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Motivation: Philosophy ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Motivation: Practical examples ,[object Object],[object Object],[object Object],[object Object],[object Object],LaTeX PDF

Example: “Single Source, Multiple Output” ,[object Object],[object Object],[object Object],[object Object],PDF Slides LaTeX Web Pages XML

Example: Dynamic maths in a browser Server-side Converter Web Page with embedded LaTeX fragments $rac{1}{2}$ Embedded JavaScript Rendered Web Page LaTeX replaced by MathML, image or other trickery read LaTeX to MathML LaTeX to images Good for: diverse browser mix, constrained delivery conditions

Example: CAA question Student’s Browser Middleware Computer Algebra System Parse Response Process Response Show Feedback Get Outcome Render Question Randomise Start

Typical formats ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Both are schizophrenic, but in different ways! Will focus on this now!

Example: Conversion challenges ,[object Object],[object Object],Consider the following function application: f(x+2α)

LaTeX markup version ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Presentation MathML spectrum ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],<math> <mi>f</mi> <mo>⁡</mo> <mfenced open=“(“ close=“)”> <mrow> <mi>x</mi> <mo>+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>α</mi> </mrow> </mrow> </mfenced> </math> Similar to LaTeX! Renders the same but encapsulates lots more meaning More semantic Less Semantic

Content MathML version ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],This is not too far from the “semantic” PMathML version

Conversion challenges ,[object Object],[object Object],[object Object],[object Object],[object Object]

LaTeX <-> MathML possibilities LaTeX (Low Semantic) Presentation MathML (High Semantic) Presentation MathML OR Content MathML Routine, modulo equivalents Harder, requires context knowledge OK, but needs knowledge about preferred notation Most converters focus on this

Conversion guidelines ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Conversion tools ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Discriminating factors ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Thinking about these factors can help make the most appropriate decision for a given scenario

Some (La)TeX-y to XML Converters (1) Name Converts Maths Output Platform Config? License Notes TeX4ht Whole doc MathML, Images TeX Very LPPL TtM Doc MathML, Images C “ Free” PlasTeX Doc Images Python “ Renderers” Good for Python platforms LaTeXML Doc MathML, Images Perl Post-processor Public Domain SnuggleTeX Doc (almost) or Fragments MathML, Images, XHTML+CSS Java Java API, XSLT, DOM hooks BSD GELLMU Doc with special LaTeX markup MathML, LaTeX ELISP Generates intermediate XML GPL Interesting approach Tralics Doc MathML C++ Custom

Some (La)TeX-y to XML Converters (2) Name Converts Maths Platform Config? License Notes MathTran Fragments Images Web Service Not sure Useful SOA idea ORCCA Fragments XML Java Via Mapping file ??? LaTeXMathML Fragments MathML Browser JavaScript As above LGPL Based on ASCIIMath ASCIIMathML Fragments MathML Browser JavaScript Not really LGPL

Conversion techniques (geeky!) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Mathematical Content Conversions

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