Enumerate integer vectors modulo the action of a Permutation Group

[sagetrac-nborie]

The goal of this ticket is to enumerate integer vectors up to the action of a Permutation Group.

This will produced a Parent : infinite enumerated set whose element are integer vectors (as list of integer)

Apply

• attachment: trac_6812_integer_vectors_mod_permgroup-final.patch
• attachment: trac_6812-reviewer.patch

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: enumeration, integer, list, permutation, group

Author: Nicolas Borie, Simon King

Reviewer: Karl-Dieter Crisman, Simon King, Nicolas Borie

Merged: sage-5.1.beta4

Issue created by migration from https://trac.sagemath.org/ticket/6812

[sagetrac-nborie]

comment:3

I fixed some language mistakes. I already tell reviewers that there are probably still some typos, misunderstood or mistakes. I am sorry for that... It's hard!

[sagetrac-nborie]

Description changed:

--- 
+++ 
@@ -4,4 +4,4 @@
 
 There is a lot of test on this module( strong_generating_system() are also test indirectly in this module... )
 
-depends on #6647
+depends on #6647 and the category framework #5891

[sagetrac-nborie]

comment:5

Refactoring :
-> I move the code in sage/combinat/invariant_ring_perm_gps (advise form Nicolas Thiéry)
-> I implemented a new class InfiniteEnumeratedSet (with category)

There is no a shortcut in sage to IntegerVectorsUptoPermGroup which is a user friendly parent (with hope).
This code stay really strongly connected to the Invariant theory and connected with a the graded algebras of multivariate polynomial view as combination of orbit sum. This really why the code enter this new folder : sage/combinat/invariant_ring_perm_gps (other things have to come here....)