Automated Symbolic and Numerical Testing of DLMF Formulae Using Computer Algebra Systems

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11006)


We have developed an automated procedure for symbolic and numerical testing of formulae extracted from the National Institute of Standards and Technology (NIST) Digital Library of Mathematical Functions (DLMF). For the NIST Digital Repository of Mathematical Formulae, we have developed conversion tools from semantic Open image in new window to the Computer Algebra System (CAS) MAPLE which relies on Youssef’s part-of-math tagger. We convert a test data subset of 4,078 semantic Open image in new window DLMF formulae extracted from the DLMF to the native CAS representation and then apply an automated scheme for symbolic and numerical testing and verification. Our framework is implemented using Java and MAPLE. We describe in detail the conversion process which is required so that the CAS is able to correctly interpret the mathematical representation of the formulae. We describe the improvement of the effectiveness of our automated scheme through incremental enhancement (making more precise) of the mathematical semantic markup for the formulae.


Digital Library Of Mathematical Functions (DLMF) National Institute Of Standards And Technology (NIST) Semantic Macros Infusion Scan Web Graphics Library (WebGL) 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We are indebted to Bruce Miller and Abdou Youssef for valuable discussions and for the development of the custom macro set of semantic mathematical Open image in new window macros used in the DLMF, and for the development of the POM tagger, respectively. We also thank the DLMF editors for their assistance and support. We also greatly appreciate valuable discussions with Jürgen Gerhard concerning MAPLE.


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Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2018

Authors and Affiliations

  1. 1.Applied and Computational Mathematics DivisionNational Institute of Standards and TechnologyMission ViejoUSA
  2. 2.Department of Computer and Information ScienceUniversity of KonstanzKonstanzGermany

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