ReductionPair

A maple package for computing reduction pairs and indefinite integrals in transcendental Liovillian extensions

Authors

Software URL

Transcendental Liouvillian extensions are differential fields, in which one can model poly-logarithmic, hyperexponential, and trigonometric functions, logarithmic integrals, and their (nested) rational expressions. For such an extension, we construct, over the subfield of constants, a complement of the subspace of derivatives. The Maple package ReductionPair not only delivers a finite representation of this complement but also decomposes any element of the field into the sum of a derivative and a component lying in the complement.

Co-Authors

Wenqiao Li (Chinese Academy of Sciences)
Ziming Li (Chinese Academy of Sciences)

Licence

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses.

Download

The package can be downloaded here: ReductionPair.zip and is also accessible online at http://mmrc.iss.ac.cn/~zmli/ISSAC2025.html.
For comprehensive usage instructions, please refer to the ReadMe.txt file included in the package. Additionally, a Maple worksheet ("demo.mws") and its corresponding PDF output ("demo.pdf") are supplied to illustrate typical usage scenarios of the ReductionPair package.

Literature

Shaoshi Chen, Hao Du, Yiman Gao, Hui huang, Wenqiao Li, Ziming Li. Complete Reduction for Derivatives in a Transcendental Liouvillian Extension.

Bugs

ReductionPair is developed for Maple 2021 and higher versions and might not run properly on earlier versions. Please report any bugs or other comments to Yiman Gao, Wenqiao Li, and Ziming Li.