2.3 Challenges

Other elements remain difficult, however.

What might be called `live mathematics', direct manipulation of the formula within the browser, has been explored in teaching materials, where it is quite appropriate. But in our case, the capability to transform a given identity into an arbitrary form of the user's choosing is an open-ended task. Any non-trivial usage would require access to the full power of a computer algebra system. Although presenting limited alternative views of formulas is reasonable, providing completely live on-line manipulations of them is quite beyond the scope of the planned DLMF.

On the other hand, providing mathematical reference data is clearly within our role at NIST. The right representation of the mathematics will allow inclusion in user documents, or insertion into a user's computer algebra system. The problem is thus transformed into the problem of extracting a sufficiently generic, semantic representation of the mathematics, say in OpenMath [21] or Content MathML [23], from what the authors have written.

While a mathematical structure editing application, say with buttons for every conceivable mathematical concept, might be a good solution for the future, it is not an answer for us at present. The chapter authors were chosen for their mathematical expertise. They are experienced mathematicians who already have their preferred authoring tools, their favorite operating system. For the most part, they do not want to be retrained for new tools, nor do we want to retrain them -- we want them to focus on the mathematical content.

In fact, most (but not all!) of these authors are comfortable with TEX or L^ATEX[10]. While L^ATEX markup is significantly more content oriented than many systems, it still allows for a great many ambiguities. It has been suggested that one should develop a L^ATEX package providing completely unambiguous mathematics markup. Again, although this may be a good goal for future work -- and future authors -- it would not be workable here for the same reasons given above; it would be too unfamiliar and too verbose, and would not get used.

Search, virtual documents and layered information require the support of a variety of metadata. Annotations are needed to provide layered information. An abundance of references and indexing keywords are called for; some would appear in the regular bibliography or index, but others used solely for layered information or for the search engine. Constructing sensible virtual documents would need some knowledge of the `role' of sections and formulas, e.g. does it represent a definition, or notation. Unless one is willing to impose a rigid organization on all chapters, one must also include metadata to indicate this role.

These items are fairly unusual requests to make of an author, and yet the authors are the best sources. So, while we accept that we will have to augment and rationalize the metadata that they do provide, we must make it as easy as possible for them to include that information. Furthermore, since metadata is generally hidden from view, we must provide feedback to the authors, and also to the editors, for proofreading purposes of what data is present.

Even with extensive indexing metadata, users must be able to search in the mathematical content itself. Search and retrieval technology has been developing for several decades, and has reached a high level of maturity for text search [9,17]. The formulas, equations, and other mathematical constructs present in the DLMF, however, are symbolic and highly structured. Current search systems and technology do not provide the means for formulating math queries and for searching for equations and other mathematical constructs. Many equivalences, such as commutativity and associativity, are simply not recognized.

Finally, there is the issue of targeting the material to different media. Even were it not for our emphasis on semantic markup, we wish to discourage presentation markup. Not only does it obfuscate the content and waste the author's time, it tends to be specific to a certain medium, layout or dimensions.