finite dimensional submodules of infinite dimensional ones

[Reimundo Heluani]

I am trying to reuse the code already in place in combinat/freemodule and
modules/with_basis/subquotients to construct a finite dimensional submodule of
an infinite dimensional one. I think that there are places where the basis of
the ambient space is assumed to be a list without needing it. The following is
a minimal example of what I mean:

sage: RPT = PartitionTuples(level=4)
sage: V = CombinatorialFreeModule(QQ, RPT)
sage: M = V.submodule([V.an_element()], already_echelonized=True)
sage: M.lift(M.an_element())
Traceback (most recent call last):
...
NotImplementedError: cannot list an infinite set

However this can be forced into working by simply:

sage: V._rank_basis = RPT.rank
sage: V._order = RPT.rank
sage: M.lift(M.an_element())
2*B[([], [], [], [])] + 6*B[([], [1], [], [])] + 2*B[([], [1], [2], [3])] + 4*B[([1], [], [], [])]

The exception is being raised because V._order is set to None and the first
call to get_order simply forces it to be self.basis().keys().list() which
fails on an infinite set.

A call to set_order() would also fail, because it sets correctly self._order
but then it calls rank_from_list on it to produce self._rank_basis.

I haven't tested much but it seems that just setting these two orders
correctly in the infinite set I can produce a working finite dimensional
submodule without trouble. This must be something that has arisen before, so
perhaps someone here can point me to some part of the library which deals with
these situations?

Best,

R.

[Matthias Koeppe]

See https://trac.sagemath.org/ticket/19448

[Reimundo Heluani]

On June 9, 2020 7:35:51 PM GMT-03:00, Matthias Koeppe <matthia...@gmail.com> wrote:
>See https://trac.sagemath.org/ticket/19448
>

Ohh wow! That's been active really recently! Thanks, I'll merge the ticket into my branch.

R.

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[Reimundo Heluani]

On Jun 09, Matthias Koeppe wrote:
>See [1]https://trac.sagemath.org/ticket/19448
>
With the patch in this ticket I find this:

sage: V = CombinatorialFreeModule(QQ, Partitions())
sage: M = V.submodule([V.an_element()])
sage: M.reduce(V.an_element())
0

so far so good.

sage: v = V([3,2,1]); v
B[[3, 2, 1]]
sage: M.reduce(v)

Traceback (most recent call last):
...

ValueError: tuple.index(x): x not in tuple

Without this patch but forcing the orders as in my previous e-mail this
worked:

sage: P = Partitions()
sage: V = CombinatorialFreeModule(QQ, P)
sage: V._order = P.rank
sage: V._rank_basis = P.rank

sage: M = V.submodule([V.an_element()], already_echelonized=True)

sage: v = V([3,2,1]); v
B[[3,2,1]]
sage: M.reduce(v)
B[[3,2,1]]
sage: M.reduce(V.an_element())
0

So I suppose the quotient could be implemented in some cases. Is the above
ValueError expected with this patch?

Best,

R.

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