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TransitiveIdeal -> RecursivelyEnumeratedSet in the sage library #16352

@seblabbe

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@seblabbe

TransitiveIdeal and TransitiveIealGraded are used in the code of sage/combinat, sage/categories and sage/groups at least. These should be replaced by RecursivelyEnumeratedSet for speed improvements and also to avoid issues explained in #6637.

This is a follow up of #6637 where TransitiveIdeal and TransitiveIealGraded have been deprecated.

More precisely, occurences of

TransitiveIdeal(succ, seeds)
TransitiveIdealGraded(succ, seeds, max_depth)

are replaced (respectively) by:

RecursivelyEnumeratedSet(seeds, succ, structure=None, enumeration='naive')
RecursivelyEnumeratedSet(seeds, succ, structure=None, enumeration='breadth', max_depth=max_depth)

Indeed, deprecated TransitiveIdealGraded class was not using the hypothesis of being graded in its code. This is why the structure is set to None for now. Of course, if people have really a graded structure, then the structure argument should be set to 'graded'... For now, I am keeping the behavior like it was before and I am assuming the structure is not graded.

CC: @anneschilling @tscrim

Component: combinatorics

Keywords: sd66

Author: Sébastien Labbé

Branch/Commit: 0beb042

Reviewer: Vincent Delecroix, Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/16352

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