In *Tools and Algorithms for the Construction and Analysis of Systems - 28th International Conference, (TACAS)*, of *Lecture Notes in Computer Science*, pages 87–105, Munich, Germany, April, 2022. Springer. Core Rank A

Paper doi abstract bibtex

Paper doi abstract bibtex

Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research applications rely more and more on computational solutions, which are often calculated and verified by computer algebra systems. Hence, the correctness, accuracy, and reliability of both digital mathematical libraries and computer algebra systems is a crucial attribute for modern research. In this paper, we present a novel approach to verify a digital mathematical library and two computer algebra systems with one another by converting mathematical expressions from one system to the other. We use our previously developed conversion tool (referred to as LaCASt) to translate formulae from the NIST Digital Library of Mathematical Functions to the computer algebra systems Maple and Mathematica. The contributions of our presented work are as follows: (1) we present the most comprehensive verification of computer algebra systems and digital mathematical libraries with one another; (2) we significantly enhance the performance of the underlying translator in terms of coverage and accuracy; and (3) we provide open access to translations for Maple and Mathematica of the formulae in the NIST Digital Library of Mathematical Functions.

@inproceedings{BibbaseGreinerPetter21b, address = {Munich, Germany}, series = {Lecture {Notes} in {Computer} {Science}}, title = {Comparative {Verification} of the {Digital} {Library} of {Mathematical} {Functions} and {Computer} {Algebra} {Systems}}, url = {https://arxiv.org/abs/2201.09488}, doi = {10.1007/978-3-030-99524-9_5}, abstract = {Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research applications rely more and more on computational solutions, which are often calculated and verified by computer algebra systems. Hence, the correctness, accuracy, and reliability of both digital mathematical libraries and computer algebra systems is a crucial attribute for modern research. In this paper, we present a novel approach to verify a digital mathematical library and two computer algebra systems with one another by converting mathematical expressions from one system to the other. We use our previously developed conversion tool (referred to as LaCASt) to translate formulae from the NIST Digital Library of Mathematical Functions to the computer algebra systems Maple and Mathematica. The contributions of our presented work are as follows: (1) we present the most comprehensive verification of computer algebra systems and digital mathematical libraries with one another; (2) we significantly enhance the performance of the underlying translator in terms of coverage and accuracy; and (3) we provide open access to translations for Maple and Mathematica of the formulae in the NIST Digital Library of Mathematical Functions.}, booktitle = {Tools and {Algorithms} for the {Construction} and {Analysis} of {Systems} - 28th {International} {Conference}, ({TACAS})}, publisher = {Springer}, author = {Greiner-Petter, André and Cohl, Howard S. and Youssef, Abdou and Schubotz, Moritz and Trost, Avi and Dey, Rajen and Aizawa, Akiko and Gipp, Bela}, month = apr, year = {2022}, note = {Core Rank A}, pages = {87--105}, }

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