Digital Repository of Mathematical Formulae

Cohl, Howard S.; McClain, Marjorie A.; Saunders, Bonita V.; Schubotz, Moritz; Williams, Janelle C.

doi:10.1007/978-3-319-08434-3_30

Cited by 8 publications

(11 citation statements)

References 12 publications

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“…To retrieve mathematical content on the structural level, researchers employed substitution tree data structures [11]. To access the semantic information of mathematical content, when it has not bee marked up explicitly [4], researchers proposed to adapt natural language processing methods to analyze the text that surrounds mathematical expressions [12,16,17]. While many research approaches have been proposed to perform similarity assessments on all three levels, Guidi and Sacerdoti Coen find that, as of 2016, only five systems or development frameworks were still available [9].…”

Section: Related Workmentioning

confidence: 99%

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Analyzing Mathematical Content to Detect Academic Plagiarism

Meuschke

Schubotz

Hamborg

et al. 2017

Proceedings of the 2017 ACM on Conference on Information and Knowledge Management

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This paper presents, to our knowledge, the first study on analyzing mathematical expressions to detect academic plagiarism. We make the following contributions. First, we investigate confirmed cases of plagiarism to categorize the similarities of mathematical content commonly found in plagiarized publications. From this investigation, we derive possible feature selection and feature comparison strategies for developing math-based detection approaches and a ground truth for our experiments. Second, we create a test collection by embedding confirmed cases of plagiarism into the NTCIR-11 MathIR Task dataset, which contains approx. 60 million mathematical expressions in 105,120 documents from arXiv.org. Third, we develop a first math-based detection approach by implementing and evaluating different feature comparison approaches using an open source parallel data processing pipeline built using the Apache Flink framework. The best performing approach identifies all but two of our real-world test cases at the top rank and achieves a mean reciprocal rank of 0.86. The results show that mathematical expressions are promising text-independent features to identify academic plagiarism in large collections. To facilitate future research on math-based plagiarism detection, we make our source code and data available.

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Section: Related Workmentioning

confidence: 99%

“…60 million formulae contained in 105,120 scientific papers from the fields computer science, mathematics, physics, and statistics retrieved from the arXiv preprint repository 4 . The papers were converted via LaTeXML 5 to XHTML.…”

Section: Test Collectionmentioning

confidence: 99%

Analyzing Mathematical Content to Detect Academic Plagiarism

Meuschke

Schubotz

Hamborg

et al. 2017

Proceedings of the 2017 ACM on Conference on Information and Knowledge Management

Self Cite

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“…-FunGrim shares many goals with the NIST Digital Repository of Mathematical Formulas (DRMF) [3], a companion project to the DLMF. We will not attempt to compare the projects in depth since DRMF is not fully developed, but we mention one important difference: DRMF represents formulas using a semantic form of LaTeX which is hard to translate perfectly to symbolic expressions, whereas FunGrim (like WFS) uses symbolic expressions as the source representation and generates LaTeX automatically for presentation.…”

Section: Related Projectsmentioning

confidence: 99%

FunGrim: A Symbolic Library for Special Functions

Johansson¹

2020

Lecture Notes in Computer Science

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“…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.…”

Section: Systems Representations Generic L a T E Xmentioning

confidence: 99%

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

Greiner-Petter

Schubotz

Cohl

et al. 2019

AJIM

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Purpose: Modern mathematicians and scientists of math-related disciplines often use Document Preparation Systems (DPS) to write and Computer Algebra Systems (CAS) to calculate mathematical expressions. Usually, they translate the expressions manually between DPS and CAS. This process is time-consuming and error-prone. Our goal is to automate this translation. This paper uses Maple and Mathematica as the CAS, and L A T E X as our DPS. Approach: Bruce Miller at the National Institute of Standards and Technology (NIST) developed a collection of special L A T E X macros that create links from mathematical symbols to their definitions in the NIST Digital Library of Mathematical Functions (DLMF). We are using these macros to perform rule-based translations between the formulae in the DLMF and CAS. Moreover, we develop software to ease the creation of new rules and to discover inconsistencies. Findings: We created 396 mappings and translated 58.8% of DLMF formulae (2,405 expressions) successfully between Maple and DLMF. For a significant percentage, the special function definitions in Maple and the DLMF were different. Therefore, an atomic symbol in one system maps to a composite expression in the other system. The translator was also successfully used for automatic verification of mathematical online compendia and CAS. Our evaluation techniques discovered two errors in the DLMF and one defect in Maple. Originality: This paper introduces the first translation tool for special functions between L A T E X and CAS. The approach improves error-prone manual translations and can be used to verify mathematical online compendia and CAS.

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Digital Repository of Mathematical Formulae

Cited by 8 publications

References 12 publications

Analyzing Mathematical Content to Detect Academic Plagiarism

Analyzing Mathematical Content to Detect Academic Plagiarism

FunGrim: A Symbolic Library for Special Functions

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

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