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 (accessible via the `(about section)' links in the mockup)
and equations (accessible by clicking the equation or equation number).
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.
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 as 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).
For initial exploration of the site design, and to make the site portable
to facilitate evaluation, we have constructed a tree of static HTML pages.
In its current form, we have attempted to maximize portability and
accessiblity. Formulas have been presented as images, a non-ideal solution
but the best 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 in the mockup, although these will be useful
technologies in the future. In any case, accessibility for all users will
always be a primary concern.
Future Version
For the eventual DLMF, we will translate the LaTeX sources
into XML, with formulas being represented
by OpenMath.
This translation will, at best, be 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 expect that
most ambiguities in the sources can be resolved.
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.
