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 c
n,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
