Digital Library of Mathematical Functions
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About the Mockup
 NIST
     

Design Considerations

We have prepared this mockup of the Digital Library of Mathematical Functions (DLMF) in order to develop and refine our ideas about how the site will be created and how it will operate, and, of course, for evaluation purposes.

LaTeX as source

It is clear that LaTeX is the most appropriate original source for the mathematical material; most authors will be familiar with it, and it is very expressive for mathematics, allowing authors to write, edit and print their material. However, it can also be ambiguous, and although much mathematics can be expressed, it does not directly provide means to express much information we will need for the DLMF. We are therefore using an augmented LaTeX for the DLMF, together with a set of Authors Guidelines and support for the augmented LaTeX in the form of style files and external support programs.

Annotations

An example of the extra information we embed are the annotations of sectional units and equations (accessible via the links in the mockup). They provide an extra layer of information that may not be of interest to casual users, and would perhaps be distracting, but which may be important for various specialized purposes. Of particular note:
Notes, References
Authors provide additional notes on the material, such as the specific source for an equation or how it can be derived.
LaTeX, OpenMath
In the mockup DLMF, we have simply provided a cut-and-paste means for a user to obtain the LaTeX source for each formula. This is intended to demonstrate the intent; in the eventual DLMF we will make better provision for users to obtain an appropriately packaged set of formulas as LaTeX, and more importantly as OpenMath.

OpenMath is a developing standard for unambiguous representation of mathematics which will allow importation into a wide spectrum of applications: typesetting, numerical, visualization and computer algebra, to name a few. At the least, it will be possible to `cut and paste' a formula from the DLMF into a computer algebra system for further manipulations. It may also be possible for us to provide a number of transformations on-line; for example, including higher terms in a series expansion, or the capability of numerically testing or comparing formula.

Attributes
Attributes will be assigned to sections and formulas. These will be the foundation of the search and indexing capabilities, along with an integrated glossary and table of notation. As examples of attributes, we have in mind indicators that a given formula may be considered to define a particular function, or that the formula is an addition theorem. Only a few attributes have been assigned at this point; As part of the Authors Guidelines, we will be designing a controlled vocabulary for use in a multi-level permuted index.

Mockup Version

The mockup has been constructed in two version: HTML and XML/MathML. The former is generated by a combination of hand written HTML, and HTML generated from LaTeX. The translation from LaTeX was made using a customized version of LaTeX2HTML. (We wish to thank Ross Moore (Macquarie University, Sydney, Australia) for his assistance in solving problems with LaTeX2HTML). The latter is generated by a translator (LaTeXML) conceived, designed and constructed as part of the DLMF project.

In the HTML version, we have attempted to maximize portability and accessibility. Formulas have been presented as images, a non-ideal solution but the most portable solution at this time; MathML will be prefered once it is widely implemented. We have also declined to make use of Java, Javascript or Dynamic HTML, although these will be useful technologies in the future.

For the XML/MathML version, we translate the LaTeX sources into XML, with formulas being represented by Content MathML. This translation is, at best, semi-automatic; by augmenting the LaTeX with declarations of variable types for example, as well as by encouraging a more semantic as opposed to presentational style of markup, we find that most ambiguities in the sources can be resolved.

Accessibility for all users will always be a primary concern. The mockup attempts to determine the capabilities of the user's browser, and sends the appropriate version.

Future Version

For the eventual DLMF we will investigate use of OpenMath as a more satisfactory representation of formulas in comparison to MathML. The XML/ OpenMath representations will be stored in a database. They will be used as the source for generating HTML, MathML, LaTeX, postscript and other forms as needed. This approach will allow us to automatically construct a variety of specialized documents, for example as a result of a search query. By storing the data in an unambiguous form, emphasizing the structure and semantics rather than just the appearance, we will have greater flexibility in using the material and will maximize the useful lifetime of the authors' work. It will simplify the customization of the HTML that is delivered to users depending on the capabilities of their browser and platform.

We will also be adding more dynamic elements to the DLMF. One example is automatic generation of tables for user-specified ranges and accuracies; this may be either client-side (eg. using Java) or server-side. Automatic generation of visualizations is another example.


Last Modified Sat, Oct 22, 2005