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Purpose: Modern mathematicians and scientists of math-related disciplinesoften use Document Preparation Systems (DPS) to write and Computer AlgebraSystems (CAS) to calculate mathematical expressions. Usually, they translatethe expressions manually between DPS and CAS. This process is time-consumingand error-prone. Our goal is to automate this translation. This paper usesMaple and Mathematica as the CAS, and LaTeX as our DPS.  Design/methodology/approach: Bruce Miller at the National Institute ofStandards and Technology (NIST) developed a collection of special LaTeX macrosthat create links from mathematical symbols to their definitions in the NISTDigital Library of Mathematical Functions (DLMF). We are using these macros toperform rule-based translations between the formulae in the DLMF and CAS.Moreover, we develop software to ease the creation of new rules and to discoverinconsistencies.  Findings: We created 396 mappings and translated 58.8% of DLMF formulae(2,405 expressions) successfully between Maple and DLMF. For a significantpercentage, the special function definitions in Maple and the DLMF weredifferent. Therefore, an atomic symbol in one system maps to a compositeexpression in the other system. The translator was also successfully used forautomatic verification of mathematical online compendia and CAS. Our evaluationtechniques discovered two errors in the DLMF and one defect in Maple.  Originality: This paper introduces the first translation tool for specialfunctions between LaTeX and CAS. The approach improves error-prone manualtranslations and can be used to verify mathematical online compendia and CAS.

Semantic Preserving Bijective Mappings for Expressions involving Special Functions in Computer Algebra Systems and Document Preparation Systems