nthiery
commented
13 years ago Description changed:
---
+++
@@ -10,26 +10,24 @@
Implementations and algorithms:
-- [Mathematica implementation](http://www.risc.jku.at/research/combinat/software/Omega/) by Andrews/Paule/Riese:
+- [http://www.risc.jku.at/research/combinat/software/Omega/ Mathematica implementation](http://www.risc.jku.at/research/combinat/software/Omega/ Mathematica implementation) by Andrews/Paule/Riese:
Non-Free. Sources available upon request.
-- [[Maple implementation]]
+- [http://www.combinatorics.net.cn/homepage/xin/maple/Ell.rar Maple implementation](http://www.combinatorics.net.cn/homepage/xin/maple/Ell.rar Maple implementation)
by Guoce Xin who realized that Laurent series were the appropriate
setup for this problem, both conceptually and to derive efficient
algorithms using explicit partial fraction decomposition, together
with subtle heuristics for controlling the number of terms ([2];
see also Zeilberger opinion [3]).
-- [Maple implementation](http://www-irma.u-strasbg.fr/~guoniu/software/)
+- [http://www-irma.u-strasbg.fr/~guoniu/software/ Maple implementation](http://www-irma.u-strasbg.fr/~guoniu/software/ Maple implementation)
by Guo-Niu Han, who generalized Xin's algorithm from Eliot
fractions to any rational fraction [3]
-- [Mathematica implementation](http://www.risc.jku.at/research/combinat/software/GenOmega/index.php) by Wiesinger of Han's algorithm
+- [http://www.risc.jku.at/research/combinat/software/GenOmega/index.php Mathematica implementation](http://www.risc.jku.at/research/combinat/software/GenOmega/index.php Mathematica implementation) by Wiesinger of Han's algorithm
The link also point to Wiesinger's master thesis on the topic.
-- MuPAD crude implementation of Xin's algorithm by Thiéry:
-
- http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk/MuPAD-Combinat/experimental/2006-06-27-Omega.mu
+- [http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk/MuPAD-Combinat/experimental/2006-06-27-Omega.mu MuPAD crude implementation](http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk/MuPAD-Combinat/experimental/2006-06-27-Omega.mu MuPAD crude implementation) of Xin's algorithm by Thiéry:
The only reason to mention it here is for the attempts at using
proper data structures and object orientation; it is my bet that
@@ -37,9 +35,14 @@
also eventually faster. However at this point the heuristics are
improperly fine tuned, and the code darn slow.
-- Sage prototype (Bandlow/Musiker) written at Sage Days 7
+- Links with Schur functions, by Fu and Lascoux [4]
+- Sage prototype (Bandlow/Musiker) written at Sage Days 7: ...
+
+```
[1] http://arxiv.org/abs/math.CO/0408377
[2] http://www.math.rutgers.edu/~zeilberg/Opinion74.html
[3] http://www-irma.u-strasbg.fr/~guoniu/papers/p36omega.pdf
+[4] http://arxiv.org/abs/math/0404064
+```
burcin
dkrenn
videlec
Consider a multivariate fraction F, mixing parameters and variables (or possibly just an Eliot fraction, where the denonimators are binomials). The Omega operator applied on F returns the constant term of F, under the form of a fraction in the parameters.
A typical application of this tool is to build the generating function for all the solutions to a system of Diophantine linear equation. It has also been used in many papers to build closed form formula for generating series.
Implementations and algorithms:
[http://www.risc.jku.at/research/combinat/software/Omega/ Mathematica implementation](http://www.risc.jku.at/research/combinat/software/Omega/ Mathematica implementation) by Andrews/Paule/Riese: Non-Free. Sources available upon request.
[http://www.combinatorics.net.cn/homepage/xin/maple/Ell.rar Maple implementation](http://www.combinatorics.net.cn/homepage/xin/maple/Ell.rar Maple implementation) by Guoce Xin who realized that Laurent series were the appropriate setup for this problem, both conceptually and to derive efficient algorithms using explicit partial fraction decomposition, together with subtle heuristics for controlling the number of terms ([2]; see also Zeilberger opinion [3]).
[http://www-irma.u-strasbg.fr/~guoniu/software/ Maple implementation](http://www-irma.u-strasbg.fr/~guoniu/software/ Maple implementation) by Guo-Niu Han, who generalized Xin's algorithm from Eliot fractions to any rational fraction [3]
[http://www.risc.jku.at/research/combinat/software/GenOmega/index.php Mathematica implementation](http://www.risc.jku.at/research/combinat/software/GenOmega/index.php Mathematica implementation) by Wiesinger of Han's algorithm The link also point to Wiesinger's master thesis on the topic.
[http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk/MuPAD-Combinat/experimental/2006-06-27-Omega.mu MuPAD crude implementation](http://mupad-combinat.svn.sourceforge.net/viewvc/mupad-combinat/trunk/MuPAD-Combinat/experimental/2006-06-27-Omega.mu MuPAD crude implementation) of Xin's algorithm by Thiéry:
The only reason to mention it here is for the attempts at using proper data structures and object orientation; it is my bet that those could eventually yield not only much more readable code, but also eventually faster. However at this point the heuristics are improperly fine tuned, and the code darn slow.
Links with Schur functions, by Fu and Lascoux [4]
Sage prototype (Bandlow/Musiker) written at Sage Days 7: ...
CC: @sagetrac-sage-combinat @jbandlow @sagetrac-gmusiker @zafeirakopoulos
Component: combinatorics
Issue created by migration from https://trac.sagemath.org/ticket/10669