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sage.tensor.modules: Add SymPowerFreeModule #30095
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Dependencies: #30229 |
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. |
comment:8
Thanks. Yes, we'll have to be careful |
comment:10
Setting new milestone based on a cursory review of ticket status, priority, and last modification date. |
comment:14
Done as part of #30229 |
Reviewer: Dima Pasechnik |
comment:16
closing as duplicate, to test the new trac machine |
FiniteRankFreeModule
defines a methodexterior_power
, creating an instance ofExtPowerFreeModule
.We propose to add a method
symmetric_power
and classSymPowerFreeModule
. (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
TensorFreeModule
s. (#30169 makesExtPowerFreeModule
s 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
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