Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). These representations include presentation MathML, content MathML, generic LaTeX, semantic LaTeX, and now CAS representations as well. The overall goal of these efforts is to provide semantically enriched standard conforming MathML representations to the public for formulae in digital mathematics libraries. We have also developed tools for translating the entire Wolfram Encoding Continued Fraction Knowledge and University of Antwerp Continued Fractions for Special Functions datasets, for use in the NIST Digital Repository of Mathematical Formulae. By taking advantage of Youssef's Part-of-Math tagger and CAS internal representations, we develop algorithms to translate mathematical expressions represented in semantic LaTeX to corresponding CAS representations and vice versa. Computer algebra systems (CAS) such as Maple and Mathematica use alternative markup to represent mathematical expressions. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical LaTeX markup (semantic LaTeX) is achieved by using a semantic macro set. Our long-term goal is to populate Wikidata, such that it can serve a variety of automated math reasoning tasks and AI systems.ĭocument preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Finally, we discuss community feedback and issues related to integrating Mathematical Entity Linking (MathEL) into Wikidata and Wikipedia, which was rejected in 33% and 12% of the test cases, for Wikidata and Wikipedia respectively.
Furthermore, some data mining methods (supervised formula annotation and concept retrieval) and applications (question answering and classification explainability) of the mathematical information are outlined. This paper summarizes the current state, challenges, and discussions related to this endeavor. In the last years, there have been efforts to define several properties and seed formulae together with their constituting identifiers into Wikidata. Therefore, the mathematical information needs to be stored in items. Some Mathematical Information Retrieval (MathIR) systems, e.g., Mathematical Question Answering (MathQA), exploit knowledge from Wikidata. Documents from Science, Technology, Engineering, and Mathematics (STEM) disciplines usually contain a significant amount of mathematical formulae alongside text.
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