Advanced Computer Algebra for Determinants

The material on this webpage accompanies the article Advanced Computer Algebra for Determinants by Christoph Koutschan and Thotsaporn "Aek" Thanatipanonda.

We provide a Mathematica notebook

containing all computations that constitute the proofs of the three determinant evaluations in our article. Some comments in the notebook may help to understand the technical details of the computations, but we recommend to consult our article to understand the general strategy of the proofs. For the execution of the notebook Determinants.nb, the following RISC combinatorics software packages are required: HolonomicFunctions, Guess, and Hyper.

Additionally, we provide some precomputed results, namely the recursive descriptions of most auxiliary functions cn,j that appear in the proofs (the only exception is Theorem 1 where we show explicitly how the guessing is done). On the other hand, finding the creative telescoping relations which constitute the proof of the analogue of Identity (2c) in Theorem 3 requires quite some time for which reason the result of this computation can be downloaded as well (its correctness is verified in the notebook and this is relatively easy). Just unpack the zip files into the current working directory of Mathematica.

Christoph Koutschan and Thotsaporn Thanatipanonda