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

We have developed an automated procedure for symbolic and numerical testing of formulae extracted from the NIST Digital Library of Mathematical Functions (DLMF). For the NIST Digital Repository of Mathematical Formulae, we have developed conversion tools from semantic LaTeX 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 LaTeX 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 can 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.