Discovering Mathematical Objects of Interest—A Study of Mathematical Notations

Abstract

Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today's systems. In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical reviewing service for pure and applied mathematics zbMATH (61M mathematical objects). Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. Further, we demonstrate the relevance of our results to a variety of use-cases. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems.The contributions of our presented research are as follows: (1) we present the first distributional analysis of mathematical formulae on arXiv and zbMATH; (2) we retrieve relevant mathematical objects for given textual search queries (e.g., linking P (α,β) n (x) with 'Jacobi polynomial'); (3) we extend zbMATH's search engine by providing relevant mathematical formulae; and (4) we exemplify the applicability of the results by presenting auto-completion for math inputs as the first contribution to math recommendation systems. To expedite future research projects, we have made available our source code and data.

Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems

“…With the WED and the new support for Mathematica in L A CAST, we perform the symbolic and numeric tests for Mathematica as well. The symbolic evaluation in Mathematica relies on the full simplification 17 . For Maple and Mathematica, we defined the global assumptions x,y ∈R and k,n,m∈N.…”

“…For Mathematica, we define 279 new translation patterns which enables L A CAST to perform translations to Mathematica. Even though the DLMF uses 675 distinguished semantic macros, we cover ∼70% of all DLMF equations with our extended list of translation patterns (see Zipf's law for mathematical notations [17]). In addition, we implemented rules for translations that are applicable in the context of the DLMF, e.g., ignore ellipsis following floating-point values or \choose always refers to a binomial expression.…”

A Survey on Semantics in Automated Data Science

“…In a data science context, it would be more useful for searching relevant expressions to surface to a data scientist, or to extract features if the terms of the equation can be mapped to columns successfully. [Greiner-Petter et al, 2020] describe the use of modified information retrieval techniques on an extracted database of several million equations; they, for instance, find equations associated with Jacobi Polynomial, or complete equations. Once again, from a data science perspective, [Greiner-Petter et al, 2020] connect equations to textual topics, but its utility in an entirely automated feature engineering mechanism is still an open question.…”

Comprehensive Review and Future Research Directions on Dynamic Faceted Search

“…The articles [146,147] extended traditional FS to support more prosperous information discovery tasks over more complex data models. The ability to view flexible and dynamic aggregations over faceted data as typically found in business intelligence applications over structured data would allow users to make more informed drill-down and roll-up choices, which will support them in making better decisions.…”