Making Presentation Math Computable: Proposing a Context Sensitive Approach for Translating LaTeX to Computer Algebra Systems

Greiner-Petter, André; Schubotz, Moritz; Aizawa, Akiko; Gipp, Béla

doi:10.1007/978-3-030-52200-1_33

Cited by 5 publications

(6 citation statements)

References 12 publications

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“…However, we discovered one example without integrals. For EulerE[n,0] from [11, (24.4.26)], we expected to extract {n} as the set of free variables but instead received a set of the unevaluated expression itself {EulerE[n,0]} 18 . Since the extended version of L A CAST handles operators, including bound variables of MEOMs, we drop the use of internal methods in CAS and extend L A CAST to extract identifiers from an expression.…”

Section: Numerical Evaluationmentioning

confidence: 99%

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

Greiner-Petter,

Cohl,

Youssef

et al. 2022

Preprint

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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 L A CAST) 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.

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Section: Numerical Evaluationmentioning

confidence: 99%

“…Hence, a transformation tool from DML to CAS must disambiguate mathematical expressions. While there is an ongoing effort towards such a process [18,27,37,38,39,41], there is no reliable tool available to disambiguate mathematics sufficiently to date.…”

Section: The Dlmf Datasetmentioning

confidence: 99%

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

Greiner-Petter,

Cohl,

Youssef

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…At first, the algorithm compares V E A and V E B to transform them into the same (ll. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Here, we define between-shared variables V bs as the variables shared between E A and E B , and within-shared variables V ws,E i as the variables shared between the equations within an equation group E i (ll.…”

Section: Equivalence Judgment Of Equation Groupsmentioning

confidence: 99%

“…The most effective way for computers to comprehend formulas' meanings is to use computer algebra systems (CASs). Formula transformations, for example, from L A T E X to the format usable in CASs, are well-studied in the CASs literature 18,19 . Further, CASs, such as Mathematica and Maple, have L A T E X input support.…”

Section: Introductionmentioning

confidence: 99%

Simple Algorithm for Judging Equivalence of Differential-Algebraic Equation Systems

Kato

Zhang

Kano

2022

Preprint

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Mathematical formulas play a prominent role in science, technology, engineering, and mathematics (STEM) documents; understanding STEM documents usually requires knowing whether equation groups containing multiple equations are equivalent. However, existing tools cannot judge the equivalence of two equation groups; thus, we develop an algorithm to judge such an equivalence using a computer algebra system. The proposed algorithm first eliminates variables appearing only in either equation group. It then checks the equivalence of the equations one by one. If each equation in one equation group is equivalent to an equation in the other, the equation groups are judged equivalent; otherwise, non-equivalent. We generated 50 pairs of equation groups for evaluation. The proposed method accurately judged the equivalence of all pairs. This method is expected to facilitate comprehension of a large amount of mathematical information in STEM documents. Furthermore, this is a necessary step for machines to understand equations, including process models.

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“…The most effective way for computers to comprehend formulas’ meanings is to use computer algebra systems (CASs). Formula transformations, for example, from LaTeX to the format usable in CASs, are well-studied in the CASs literature 18 , 19 . Further, CASs, such as Mathematica and Maple, have LaTeX input support.…”

Section: Introductionmentioning

confidence: 99%

Simple algorithm for judging equivalence of differential-algebraic equation systems

Kato

Zhang

Kano

2023

Sci Rep

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Mathematical formulas play a prominent role in science, technology, engineering, and mathematics (STEM) documents; understanding STEM documents usually requires knowing the difference between equation groups containing multiple equations. When two equation groups can be transformed into the same form, we call the equation groups equivalent. Existing tools cannot judge the equivalence of two equation groups; thus, we develop an algorithm to judge such an equivalence using a computer algebra system. The proposed algorithm first eliminates variables appearing only in either equation group. It then checks the equivalence of the equations one by one: the equations with identical algebraic solutions for the same variable are judged equivalent. If each equation in one equation group is equivalent to an equation in the other, the equation groups are judged equivalent; otherwise, non-equivalent. We generated 50 pairs of equation groups for evaluation. The proposed method accurately judged the equivalence of all pairs. This method is expected to facilitate comprehension of a large amount of mathematical information in STEM documents. Furthermore, this is a necessary step for machines to understand equations, including process models.

show abstract

Making Presentation Math Computable: Proposing a Context Sensitive Approach for Translating LaTeX to Computer Algebra Systems

Cited by 5 publications

References 12 publications

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

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

Simple Algorithm for Judging Equivalence of Differential-Algebraic Equation Systems

Simple algorithm for judging equivalence of differential-algebraic equation systems

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