Opened 7 years ago

Last modified 9 months ago

#10669 new enhancement

Implement MacMahon's partition analysis Omega operator

Reported by: nthiery Owned by: sage-combinat
Priority: major Milestone: sage-wishlist
Component: combinatorics Keywords:
Cc: sage-combinat, jbandlow, musiker, zaf Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by nthiery)

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:

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]
[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

Change History (3)

comment:1 Changed 7 years ago by nthiery

  • Description modified (diff)

comment:2 Changed 6 years ago by burcin

  • Cc zaf added

I have a Sage implementation of the Omega operator, mainly based on the Andrews/Paule/Riese? papers. (I haven't seen the MMA implementation). Maybe Zaf is interested in working on it so it can be included in Sage.

comment:3 Changed 9 months ago by dkrenn

An implementation can now be found at #22066.

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