Opened 2 years ago

Closed 3 months ago

#30095 closed enhancement (duplicate)

sage.tensor.modules: Add SymPowerFreeModule

Reported by: Matthias Köppe Owned by:
Priority: major Milestone: sage-duplicate/invalid/wontfix
Component: linear algebra Keywords:
Cc: Eric Gourgoulhon, Dima Pasechnik, Yuan Zhou, Travis Scrimshaw, Michael Jung Merged in:
Authors: Reviewers: Dima Pasechnik
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #30229 Stopgaps:

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Description (last modified by Matthias Köppe)

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.

Change History (16)

comment:1 Changed 2 years ago by Matthias Köppe

Cc: Travis Scrimshaw added

comment:2 Changed 2 years ago by Matthias Köppe

Description: modified (diff)

comment:3 Changed 2 years ago by Matthias Köppe

Cc: Michael Jung added

comment:4 Changed 2 years ago by Matthias Köppe

Description: modified (diff)

comment:5 Changed 2 years ago by Matthias Köppe

Description: modified (diff)

comment:6 Changed 2 years ago by Matthias Köppe

Dependencies: #30229

comment:7 Changed 2 years ago by Michael Jung

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.

Last edited 2 years ago by Michael Jung (previous) (diff)

comment:8 Changed 2 years ago by Matthias Köppe

Thanks. Yes, we'll have to be careful

comment:9 Changed 2 years ago by Matthias Köppe

Milestone: sage-9.2sage-9.3

comment:10 Changed 22 months ago by Matthias Köppe

Milestone: sage-9.3sage-9.4

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

comment:11 Changed 17 months ago by Matthias Köppe

Milestone: sage-9.4sage-9.5

comment:12 Changed 12 months ago by Matthias Köppe

Milestone: sage-9.5sage-9.6

comment:13 Changed 9 months ago by Matthias Köppe

Milestone: sage-9.6sage-9.7

comment:14 Changed 3 months ago by Matthias Köppe

Milestone: sage-9.7sage-duplicate/invalid/wontfix
Status: newneeds_review

Done as part of #30229

comment:15 Changed 3 months ago by Dima Pasechnik

Reviewers: Dima Pasechnik
Status: needs_reviewpositive_review

comment:16 Changed 3 months ago by Frédéric Chapoton

Resolution: duplicate
Status: positive_reviewclosed

closing as duplicate, to test the new trac machine

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