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EPUB Math: Best Practices for Mathematics in Ebooks

5/28/2009 First draft

Science, technical, engineering and medical (STEM) content presents unique challenges to publishers due to the fact that it contains a large amount of mathematical notation, tables and diagrams.  The Open Publication Structure v2.0 Specification, the standard for content in EPUB ebooks, handles tables and diagrams by relying on the table and image capabilities of XHTML.  However, OPS provides several ways in which equations might be addressed in EPUB ebooks.  The result has been that content providers and reader system vendors alike have been unsure as to what to produce and implement. In addition, publishers are interested in providing enhanced access to such content, including accessibility to readers with disabilities, copying of equations for use in analysis software, and making the mathematics visible to search. The purpose of this document is to propose a single set of conventions for incorporating mathematical content in EPUB ebooks that achieves these objectives. 


OPS offers basically two ways in which equations might be published in EPUB ebooks: raster images (PNG, GIF) or vector images (SVG). Each has its weaknesses. Raster images do not scale smoothly with the text. Neither raster or vector images represent the equation's mathematical structure, preventing useful reading system features such as accessiblity for readers with disabilities, copy to calculation and authoring applications, or math-based search. MathML is the standard XML format for representing mathematical notation and, therefore, associating MathML with the equation's visual description is an essential goal. In addition, there are other requirement for high-quality mathematics in ebooks, such as baseline alignment. This section identifies the goals for the ideal support for mathematical content in EPUB ebooks, so that there is a basis for assessing the the proposed format.

  • Math notation must render with typographic quality comparable to surrounding text.  In particular:
    • Equations should scale together with the surrounding text.
    • Inline expressions should properly align on the baseline of the surrounding text.  Here is an illustration:

      image of an equation properly positioned on the baseline
  • It must be possible to make math notation accessible in reading systems that wish to do so.
    • Readers should make MathML available to assistive technology (AT) applications.
  • Math notation should degrade gracefully in reading systems with limited capabilities, lacking SVG support for example.
  • It must be possible to implement enhanced functionality, such as math-aware search and clipboard copy of mathematical structure.
  • Implementation must be feasible for reading systems (both technically and economically)
    • it should be straightforward to implement minimum requirements
    • libraries should be readily available through licensing and open source
    • there should be sufficient conformant content to make the effort worthwhile
  • Implementation must be feasible for content producers (both technically and economically)
    • it should be possible to generate with available workflow and production software
  • Implementation must adhere to the OPS 2.0 specification.

Format for Mathematical Notation

Content should be encoded using the XHTML preferred vocabularies. Equations should adhere to the following format:

<ops:switch xmlns:ops="">

    <ops:case required-namespace="">
        <math xmlns="">

    <ops:case required-namespace="">
        <svg xmlns=""
                style="width:N.NNem; height:N.NNem;" ... >

         <img style=" {baseline-positioning-code} " src="..."
                  alt=" {math speech text} "/>


Key Considerations

The proposed format meets the functionality goals laid out above:

  • The proposal is valid under the current OPS 2.0 specification.
  • The MathML encoding provides  for accessibility and advanced functionality in rendering systems wishing to offer such functionality.
  • The SVG encoding provides a high-quality rendering, provided font-relative units (em) are respected for baseline alignment and size.
  • The <img> provides an acceptable fallback rendering, and is well-supported in current reading systems.
  • The <ops:switch> element provides for graceful fallback functionality across a range of reading systems.

The main considerations for implementation in reading systems are:

  • The <ops:switch> functionality is required by OPS 2.0, and it is simple to implement minimally compliant functionality.
  • Support for SVG is also required functionality for reading systems, and both open source and commercial implementations are readily available to reading systems. 
    • Note that the positioning attributes are given in font-relative units (em), and must be implemented that way for scaling and baseline alignment in order to achieve high-quality display.
  • Implementing advanced functionality using the MathML encoding is not required.  However, MathML support is widespread in math-aware software, and implementations for accessibility and other advanced functionality is readily available to reading systems through open source and commercial implementations. Consequently, reading systems should make <ops:switch> data (particularly MathML) programmatically available to 3rd-party software when possible.
  • Support for embedded fonts for use in SVG (or MathML) implementations is also a long term requirement, since fonts are a critical issue for math typography. 

The format is also possible to generate using industry standard tools:

  • MathML is widely supported in publishing workflow software.
  • Many tools can produce high-quality fallback images from MathML or other equation source
  • Support for SVG generation is increasing, with several converters  from MathML to SVG and other equation encodings available today.

Reading System Compliance

The following table may be used as a checklist to assess reading system compliance with this specification. Note that the items in the first section are requirements that would be met simply by fully implementing the EPUB standard. They are included here because they are important for math and, as of this writing, most EPUB reading systems do not fully implement the standard. In particular, they lack support for these important items. The items in the second section are allowed by the EPUB standard but required for good math support.

Pass/Fail Technical Requirement Reader Experience
EPUB Requirements:
  support for inline SVG text in math renders with same quality as body text
  <ops:switch> properly implemented only one math rendering appears when document includes fallback images
  support for embedded fonts no character dropouts on systems without math fonts pre-installed
EPUB Math Best Practice Requirements:
  support for font-relative sizing math scales with text
  support for font-relative baseline-shift math baseline aligns with the text baseline
  MathML programmatically available (recommended) math accessibility, copy and paste, math search, ...


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