New class IntegerListLex for generating integer lists => much improved partition iterators

[nthiery]

IntegerListsLex refactoring, and application to Partitions

• Reworked the integer lists lexicographic generator into a full
  featured combinatorial class IntegerListsLex
• support for n in a set (or any iterable I implementing n in I)

Applications to Partitions:

• Systematic use of IntegerListsLex to get constant amortized time
  iterators (huge efficiency improvement).
• This includes PartitionsGreatestEQ and PartitionsGreatestLE which
  were previously implemented in GAP. This was inefficient due to
  the communication overhead, and not using an iterator.
  (backward compatible unpickling)
• Implements horizontal_border_strip.

CC: @sagetrac-sage-combinat

Component: combinatorics

Issue created by migration from https://trac.sagemath.org/ticket/4549

[nthiery]

comment:1

Attachment: integer_lists_lex-4549-nt.patch.gz

Reworked the integer lists lexicographic generator into a full featured combinatorial class IntegerListsLex
Use it systematically in Partitions to get constant amortized time iterators.
Also implements horizontal_border_strip.

Note: the attached patch does not contain the commit messages!

[saliola]

Replying to @nthiery:

See the title. Patch integer_lists_lex-nt in development in sage-combinat.

Note: this patch depends on #4371 and #5255.

[mwhansen]

Attachment: trac_4549-review.patch.gz

[mwhansen]

comment:5

I've added a patch which adds some doctests, adds a warning when min_part=0 is passed to partitions, and changed the default implementation of count to use Integers so that we don't have to reimplemented in IntegerListsLex

Assuming someone okay's my changes, I think both patches are good to go in.

[hivert]

comment:6

Replying to @mwhansen:
It's ok for me ! The warning is a good idea. Go ahead.