Opened 10 years ago

Family over enumerated set has wrong category

Reported by: Owned by: cnassau nthiery minor sage-duplicate/invalid/wontfix categories Family, Category of finite enumerated sets, CartesianProduct N/A u/ncohen/14541 fd3d6d51a3251999e327cf18c38f3389b2ee2a1b

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
```

comment:1 follow-up:  3 Changed 10 years ago by 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?

comment:2 Changed 10 years ago by 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).

Last edited 10 years ago by cnassau (previous) (diff)

comment:3 in reply to:  1 Changed 10 years ago by cnassau

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.

comment:4 Changed 10 years ago by 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.

comment:5 Changed 10 years ago by cnassau

Authors: → Christian Nassau CartesianProduct added new → needs_review

comment:6 Changed 10 years ago by cnassau

Description: modified (diff)

comment:7 Changed 9 years ago by jdemeyer

Milestone: sage-5.11 → sage-5.12

comment:8 Changed 9 years ago by 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

comment:9 Changed 9 years ago by ncohen

Branch: → u/ncohen/14541

comment:10 Changed 9 years ago by ncohen

Authors: Christian Nassau → Christian Nassau, Nathann Cohen

comment:11 Changed 9 years ago by git

Commit: → fd3d6d51a3251999e327cf18c38f3389b2ee2a1b

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

 ​fd3d6d5 `trac #14541: Family over enumerated set has wrong category`

comment:12 Changed 9 years ago by vbraun_spam

Milestone: sage-6.1 → sage-6.2

comment:13 Changed 9 years ago by vbraun_spam

Milestone: sage-6.2 → sage-6.3

comment:14 Changed 9 years ago by rws

Status: needs_review → needs_work

patchbot:

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

comment:15 Changed 9 years ago by 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

comment:16 Changed 8 years ago by vbraun_spam

Milestone: sage-6.3 → sage-6.4

comment:18 Changed 7 years ago by 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.

comment:19 Changed 6 months ago by mkoeppe

The remaining issue is a dup of #18849

comment:20 Changed 6 months ago by mkoeppe

Milestone: sage-7.3 → sage-duplicate/invalid/wontfix needs_work → needs_review

comment:21 Changed 6 months ago by mkoeppe

Authors: Christian Nassau, Nathann Cohen
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