Opened 12 years ago

Closed 5 years ago

Implement MacMahon's partition analysis Omega operator

Reported by: Owned by: Nicolas M. Thiéry Sage Combinat CC user major sage-duplicate/invalid/wontfix combinatorics Sage Combinat CC user, Jason Bandlow, musiker, Zafeirakis Zafeirakopoulos N/A

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
```

comment:1 Changed 12 years ago by Nicolas M. Thiéry

Description: modified (diff)

comment:2 Changed 11 years ago by Burcin Erocal

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 6 years ago by Daniel Krenn

An implementation can now be found at #22066.

comment:4 Changed 5 years ago by Frédéric Chapoton

Milestone: sage-wishlist → sage-duplicate/invalid/wontfix new → needs_review

comment:5 Changed 5 years ago by Frédéric Chapoton

Status: needs_review → positive_review

comment:6 Changed 5 years ago by Vincent Delecroix

Resolution: → wontfix positive_review → closed

closing positively reviewed duplicates

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