Reducing Hyperexponential Functions over Monomial Extensions
Shaoshi Chen, Hao Du, Yiman Gao, Ziming Li
TL;DR
This paper introduces a unified algorithm for reducing hyperexponential functions over monomial extensions, enabling the computation of elementary integrals that existing computer algebra systems may not evaluate.
Contribution
It extends shell and kernel reductions to monomial extensions and combines them into a single algorithm for improved integral computation.
Findings
Unified algorithm for hyperexponential reductions over monomial extensions
Able to compute some elementary integrals missed by current software
Provides an alternative method for integral decomposition in hyperexponential towers
Abstract
We extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, we present an additive decomposition in rationally hyperexponential towers. The decomposition yields an alternative algorithm for computing elementary integrals over such towers. The alternative can find some elementary integrals that are unevaluated by the integrators in the latest versions of Maple and Mathematica.
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Taxonomy
TopicsPolynomial and algebraic computation · Numerical Methods and Algorithms · Modeling and Simulation Systems