ReductionPair
Short Description
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 ReductionPair package, developed by
Yiman Gao,
Wenqiao Li,
Ziming Li,
not only provides 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.
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.
The Package
The package can be downloaded here:
And it is also accessible online at
For comprehensive usage instructions, please refer to
Additionally, we provide a Maple worksheet and its corresponding PDF output, which present some examples illustrating the usage of ReductionPair.
Literature
-
Shaoshi Chen, Hao Du, Yiman Gao, Hui Huang, Wenqiao Li, Ziming Li.
Complete Reduction for Derivatives in a Transcendental Liouvillian Extension. Preprint, arXiv:2602.03592.
[url]
Bugs
ReductionPair is developed for Maple 2021 and higher versions and may not run properly on earlier versions.
Please report any bugs and comments to
Yiman Gao,
Wenqiao Li, and
Ziming Li.
