Automated simplification of large symbolic expressions

Authors:
David H. Bailey;Jonathan M. Borwein;Alexander D. Kaiser
Affiliations:
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States;Centre for Computer Assisted Research Mathematics and its Applications (CARMA), Laureate Professor, Univ. of Newcastle, Callaghan, NSW 2308, Australia;Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States
Venue:
Journal of Symbolic Computation
Year:
2014

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Abstract

We present a set of algorithms for automated simplification of symbolic constants of the form @?"i@a"ix"i with @a"i rational and x"i complex. The included algorithms, called SimplifySum and implemented in Mathematica, remove redundant terms, attempt to make terms and the full expression real, and remove terms using repeated application of the multipair PSLQ integer relation detection algorithm. Also included are facilities for making substitutions according to user-specified identities. We illustrate this toolset by giving some real-world examples of its usage, including one, for instance, where the tool reduced a symbolic expression of approximately 100@?000 characters in size enough to enable manual manipulation to one with just four simple terms.