Algebraic Relations of C-Finite Sequences and Multi-Sequences
Short Description
For any tuple
f1,
f2,...
fr of sequences,
the set of multivariate polynomials
p such that
p(f1(n),
f2(n), ...,
fr(n))=0
for all points n
forms an ideal of the polynomial ring.
The package provides a function for computing a basis for that ideal in the case where
f1,
f2,...
fr are C-finite
sequences (or multi-sequences), i.e., they satisfy homogeneous linear recurrence equations
with constant coefficients.
The package was written by
Manuel Kauers
and
Burkhard Zimmermann.
Registration and Legal Notices
The source code for this package is password protected. To get the password
send an email to
Peter Paule.
It will be given for free to all researchers and non-commercial users.
Copyright © 1999–2008 The RISC Combinatorics Group, Austria — all rights reserved.
Commercial use of the software is prohibited without prior written permission.
The Package
The package is contained in the Mathematica input file
and is accompanied by the Mathematica notebook
Literature
To use the implementation it should be sufficient to study the notebook
demo.nb. It contains a few examples to start with.
A description of the underlying algorithm can be found in the following
paper.
M. Kauers and B. Zimmermann,
Computing the Algebraic Relations of C-Finite Sequences and Multisequences,
Technical Report 2006-24, SFB F013, September 2006.
[pdf]
Versions and Bugs
Right now you are using Version 0.30 last updated on March 18, 2010.
Please report any bugs and comments to
Manuel Kauers.