Family over enumerated set has wrong category

[cnassau]

This happens with Sage 5.10beta3:

sage: P=Permutations()
sage: print P.category()
Category of sets
sage: print P.cardinality()
+Infinity
sage: F=Family(Permutations(), lambda i:i)
sage: print F.category()
Category of finite enumerated sets

But clearly F is not finite...

Another bug, (also fixed in the attached patch):

sage: Family(CartesianProduct(ZZ,ZZ),lambda (x,y) : (x+y,x-y)).cardinality()
...
TypeError: cardinality does not fit into a Python int.

update: following example is still wrong (see second comment)

sage: X=CombinatorialFreeModule(ZZ,ZZ)
sage: print X
Free module generated by Integer Ring over Integer Ring
sage: print X.basis().category()
Category of enumerated sets
sage: TX = tensor((X,))
sage: print TX.basis().cardinality()
+Infinity
sage: print TX.basis().category()
Category of finite enumerated sets

[nthiery]

Thanks for the report!

Hmm, that's annoying indeed. This stems from the fact that Permutations still uses the old CombinatorialClass?, and for those it's not so easy to detect easily whether they are known to be finite.

As a workaround, line 832 of Family, when the input is a CombinatorialClass?, we could ask whether x.cardinality() != infinity. The risk is to trigger the enumeration of the elements of the combinatorial class which might take a while ... Or check if cardinality actually is implemented (i.e. is not the default _cardinality_from_iterator), and if yes call it.

Of course, the proper fix would be to revamp permutations to be an enumerated set like has been done recently for tableaux.

Would you be willing to handle any of the above?

[cnassau]

I actually don't care about Permutations() a lot - I just picked those to come up with an easily reproducible problem. I should have given this example:

sage: X=CombinatorialFreeModule(ZZ,ZZ)
sage: print X
Free module generated by Integer Ring over Integer Ring
sage: print X.basis().category()
Category of enumerated sets
sage: TX = tensor((X,))
sage: print TX.basis().category()
Category of finite enumerated sets

I believe I fixed this in #13979 for Sage 5.7.b4 (which was neither merged nor even considered).

[cnassau]

Replying to nthiery:

As a workaround, line 832 of Family, when the input is a CombinatorialClass?, we could ask whether x.cardinality() != infinity. The risk is to trigger the enumeration of the elements of the combinatorial class which might take a while ... Or check if cardinality actually is implemented (i.e. is not the default _cardinality_from_iterator), and if yes call it.

This sounds like a solution that might fix the issue that I'm seeing with my (still nascent) Steenrod algebra module package. I'll try to prepare a patch along these lines.

[cnassau]

The attached patch changes the category initialization of LazyFamily objects: if the keys K are an instance of CombinatorialClass the category choice now depends on "K.cardinality() < Infinity" in the obvious way.

(I have not tried to inspect the keys K further, because I could not find a CombinatorialClass without custom cardinality method.)

I have also added another exception to LazyFamily.cardinality(): the code used to check for AttributeError and NotImplementedError, but CartesianProduct(...).__len__ raises a TypeError instead. I've added a doctest that fails otherwise.

[ncohen]

The bug reported has been fixed in the meantime by #14772 : permutations do not use CombinatorialClass anymore. This does not fix the general problem however, and indeed one should not force the computation of the cardinality of this set unless this operations has been explicitly requested.

Thus, I upload a git branch which just removes CombinatorialClass from the list of exceptions. There is apparently no reason why all instances of CombinatorialClass should represent finite sets.

(and I personally don't even see why an uncountable set should be said to be "enumerable", but that's another problem)

Nathann

[git]

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

​fd3d6d5

trac #14541: Family over enumerated set has wrong category

[rws]

patchbot:

sage -t --long src/sage/combinat/free_module.py  # 1 doctest failed

[ncohen]

Okay Ralf, I don't know how to fix that. I give up. If you understand category code please give it a try, I don't.

Nathann

[tscrim]

The first and second issues are fixed

sage: F = Family(Permutations(), lambda i: i)
sage: F.category()
Category of infinite enumerated sets
sage: Family(cartesian_product([ZZ,ZZ]),lambda (x,y) : (x+y,x-y)).cardinality()
+Infinity

However, the last issue is still outstanding:

sage: X=CombinatorialFreeModule(ZZ,ZZ)
sage: X.basis().category()
Category of infinite enumerated sets
sage: TX = tensor((X,))
sage: TX.basis().cardinality()
+Infinity
sage: TX.basis().category()
Category of finite enumerated sets

This seems to be due to falling into a default of finite (enumerated) sets instead of just pulling the information from the category of the keys:

sage: TX.basis().keys()
Image of Cartesian product of Integer Ring by <type 'tuple'>
sage: TX.basis().keys().category()
Category of sets

Also, the stopgap field is to be used for ticket(s) for the stopgaps.

[mkoeppe]

The remaining issue is a dup of #18849