sage.tensor.modules: Add SymPowerFreeModule

[mkoeppe]

FiniteRankFreeModule defines a method exterior_power, creating an instance of ExtPowerFreeModule.

We propose to add a method symmetric_power and class SymPowerFreeModule. (More generally, we could have submodules of tensors with prescribed symmetries; this is currently only available on the level of elements, not parents.)

They will be submodules of TensorFreeModules. (#30169 makes ExtPowerFreeModules quotients.)

The existing method FiniteRankFreeModule.sym_bilinear_form might be changed to produce elements of it for p=2.

Depends on #30229

CC: @egourgoulhon @dimpase @yuan-zhou @tscrim @mjungmath

Component: linear algebra

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/30095

[mkoeppe]

Dependencies: #30229

[mjungmath]

comment:7

I think one has to be very careful here, especially with the last proposal. If the base field has not characteristic zero, as described also on Wikipedia, a symmetric bilinear form cannot be identified with an element of the symmetric algebra.

Addendum: I just noticed, we are not even in the manifold setting.

[mkoeppe]

comment:8

Thanks. Yes, we'll have to be careful

[mkoeppe]

comment:10

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

[mkoeppe]

comment:14

Done as part of #30229

[dimpase]

Reviewer: Dima Pasechnik

[fchapoton]

comment:16

closing as duplicate, to test the new trac machine