Growing the Digital Repository of Mathematical Formulae with Generic LaTex Sources

Abstract

One initial goal for the DRMF is to seed our digital compendium with fundamental orthogonal polynomial formulae. We had used the data from the NIST Digital Library of Mathematical Functions (DLMF) as initial seed for our DRMF project. The DLMF input L A T E X source already contains some semantic information encoded using a highly customized set of semantic L A T E X macros. Those macros could be converted to content MathML using L A T E xml. During that conversion the semantics were translated to an implicit DLMF content dictionary. This year, we have developed a semantic enrichment process whose goal is to infer semantic information from generic L A T E X sources. The generated context-free semantic information is used to build DRMF formula home pages for each individual formula. We demonstrate this process using selected chapters from the book "Hypergeometric Orthogonal Polynomials and their q-Analogues" (2010) by Koekoek, Lesky and Swarttouw (KLS) as well as an actively maintained addendum to this book by Koornwinder (KLSadd). The generic input KLS and KLSadd L A T E X sources describe the printed representation of the formulae, but does not contain explicit semantic information. See http://drmf.wmflabs.org.

Semantic preserving bijective mappings for expressions involving special functions between computer algebra systems and document preparation systems

“…Each macro ties specific character sequences to a well-defined mathematical object and is linked with the corresponding definition in the Digital Library of Mathematical Functions (DLMF). The Digital Repository of Mathematical Formulae (DRMF) is an outgrowth of the DLMF with the goal to facilitate interaction among a community of mathematicians and scientists (Cohl, McClain, et al, 2014;Cohl, Schubotz, McClain, et al, 2015). The DRMF extends the set of semantic macros.…”

Four Decades of TeX at zbMATH

“…By using these macros, with minimal overhead, information retrieval systems would be able to better disambiguate the syntax and semantics for mathematical expressions. Eventually, this will provide better search and recommendation functionality for users of mathematical digital libraries [2]. To some extent, such approaches have already been applied to realise the zbMATH formula search [4,3], but having standardised L A T E X sources at hand will certainly make further developments in this direction much more feasible.…”

Mathematical Research Data – An Analysis Through zbMATH References

“…Moreover, we connect our datasets to external datasets such as Wikidata or MathOverflow [23,24]. Additionally, after having switched to a LaTeX the input format for zbMATH reviews [22], we are considering to allow for semantically enriched LaTeX dialects as used in the DLMF and DRMF [21] projects, or optional semantic annotations for mathematical formulae via graphical tools [20]. ory in physics.…”