Allow for tensor product of a FiniteRankFreeModule dual

[egourgoulhon]

Since Sage 9.7.rc0, FiniteRankFreeModule's are endowed with a tensor_product method, thanks to #31276. However, this does not work with the dual:

sage: M = FiniteRankFreeModule(ZZ, 2, name='M')
sage: M.tensor_product(M.tensor_module(1,1))  # OK
Free module of type-(2,1) tensors on the Rank-2 free module M 
 over the Integer Ring
sage: M.tensor_product(M.dual())
...
AttributeError: 'ExtPowerDualFreeModule_with_category' object has 
 no attribute 'tensor_type'

The method ExtPowerDualFreeModule.tensor_type is implemented here,
which fixes the issue:

sage: M.tensor_product(M.dual())
Free module of type-(1,1) tensors on the Rank-2 free module M 
 over the Integer Ring

Depends on #30241

CC: @mkoeppe @tscrim

Component: linear algebra

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/34471

[egourgoulhon]

Branch: public/manifolds/tensor_product_dual-34471

[egourgoulhon]

New commits:

f6d1598

Add tensor_type to ExtPowerFreeModule and ExtPowerDualFreeModule (#34471)

[egourgoulhon]

Commit: f6d1598

[mkoeppe]

comment:3

Is this needed when #34474 is merged?

[mkoeppe]

comment:4

I'd suggest to do #30241 (a separate implementation class for the dual) instead.

[egourgoulhon]

comment:5

Replying to @mkoeppe:

Is this needed when #34474 is merged?

Only if you plan to do M.tensor_product(M.tensor_module(0, 1)).
You well get an error then.

[sagetrac-git]

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

31b0c07

Use of ExtPower(Dual)FreeModule.tensor_type in TensorFreeModule._coerce_map_from_

[sagetrac-git]

Changed commit from f6d1598 to 31b0c07

[egourgoulhon]

comment:7

Replying to @mkoeppe:

I'd suggest to do #30241 (a separate implementation class for the dual) instead.

This makes sense. On the other hand, it does not harm to endow the classes ExtPowerFreeModule and ExtPowerDualFreeModule with a method tensor_type(). Even, this permits a slight simplification of the code of TensorFreeModule._coerce_map_from_, as shown in the latest commit.

[mkoeppe]

comment:8

Replying to @egourgoulhon:

On the other hand, it does not harm to endow the classes ExtPowerFreeModule and ExtPowerDualFreeModule with a method tensor_type().

It does make tensor_product return a wrong result instead of giving an error when one of the factors is an exterior power

[mkoeppe]

comment:9

I would propose to close this in favor of #30241

[mkoeppe]

Dependencies: #30241

[egourgoulhon]

comment:10

Replying to @mkoeppe:

Replying to @egourgoulhon:

On the other hand, it does not harm to endow the classes ExtPowerFreeModule and ExtPowerDualFreeModule with a method tensor_type().

It does make tensor_product return a wrong result instead of giving an error when one of the factors is an exterior power

Ah yes!

[egourgoulhon]

Changed commit from 31b0c07 to none

[egourgoulhon]

Changed branch from public/manifolds/tensor_product_dual-34471 to none

[egourgoulhon]

comment:11

Replying to @mkoeppe:

I would propose to close this in favor of #30241

Agreed

[egourgoulhon]

Changed author from Eric Gourgoulhon to none

[egourgoulhon]

Reviewer: Eric Gourgoulhon