category of lazy family wrong if infinite combinatorial class used as index

[cnassau]

sage: from sage.sets.set_from_iterator import EnumeratedSetFromIterator
sage: C=CombinatorialFreeModule(ZZ,EnumeratedSetFromIterator(Integers)) ; C
Free module generated by {0, 1, -1, 2, -2, ...} over Integer Ring
sage: U = tensor((C,)) ; U
Free module generated by {0, 1, -1, 2, -2, ...} over Integer Ring
sage: C.basis().category()
Category of enumerated sets
sage: U.basis().category()
Category of finite enumerated sets

But clearly the basis of U is not finite.

Depends on #19195

CC: @tscrim

Component: categories

Author: Christian Nassau

Branch/Commit: u/cnassau/18849 @ 09f97fa

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/18849

[cnassau]

Author: Christian Nassau

[cnassau]

comment:1

Source of this problem is that the tensor product uses a sage.combinat.combinat.MapCombinatorialClass for the cartesian product, and the LazyFamily constructor assumed all CombinatorialClass objects to be finite. An extra check for is_finite has been added in this case. The check is caught since is_finite might not be implemented.

Note that it's important not to treat the negative answer of is_finite as affirmation that the class is actually infinite; whether the set is finite or not might just not be known, or to expansive to check.

---

New commits:

b553884

fix category detection for LazyFamily objects

[cnassau]

Branch: u/cnassau/18849

[cnassau]

Commit: b553884

[sagetrac-git]

Changed commit from b553884 to 82849a0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

82849a0

fix category detection for LazyFamily objects

[sagetrac-git]

Changed commit from 82849a0 to 09f97fa

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

09f97fa

fix category detection for LazyFamily objects

[cnassau]

comment:4

A first patchbot run gave this error:

**********************************************************************
File "src/sage/interfaces/expect.py", line 825, in sage.interfaces.expect.Expect._eval_line
Failed example:
    singular.interrupt(timeout=3)  # sometimes very slow (up to 60s on sage.math, 2012)
Expected:
    False
Got:
    True
**********************************************************************
1 item had failures:
   1 of  15 in sage.interfaces.expect.Expect._eval_line
    [89 tests, 1 failure, 9.38 s]
----------------------------------------------------------------------
sage -t --long --warn-long 69.5 src/sage/interfaces/expect.py  # 1 doctest failed
----------------------------------------------------------------------

I think this is completely unrelated and random; I have cleaned up an empty line in the commit, so a new run should be triggered soon.

[videlec]

comment:5

Hello,

1. Why a special care for CombinatorialClass is even needed at all? The following would be much simpler

category = EnumeratedSets()
if set in Sets().Finite() or isinstance(set, (list,tuple)):
    category = category.Finite()
elif set in Sets().Infinite():
    category = category.Infinite()

2. Your documentation lines are too long.

Vincent

[videlec]

Reviewer: Vincent Delecroix

[mkoeppe]

comment:7

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

comment:8

Setting a new milestone for this ticket based on a cursory review.

[mkoeppe]

comment:11

The bug illustrated by the example in the ticket description is still present in 9.7.beta8

The underlying implementation has changed. CombinatorialClass is no longer involved. The bug is now in sage.misc.mrange._is_finite (used by sage.combinat.cartesian_product):

sage: from sage.misc.mrange import _is_finite
sage: from sage.sets.set_from_iterator import EnumeratedSetFromIterator
sage: EnumeratedSetFromIterator(ZZ).category()
Category of facade enumerated sets
sage: _is_finite(EnumeratedSetFromIterator(ZZ))
True

[mkoeppe]

comment:12

A comment in _is_finite: "We usually assume L is finite for speed reasons"

[mkoeppe]

comment:13

This can be solved by #19195: getting rid of the ancient class sage.combinat.cartesian_product

[mkoeppe]

Dependencies: #19195