Changes between Version 9 and Version 11 of Ticket #30229


Ignore:
Timestamp:
08/01/20 18:21:38 (16 months ago)
Author:
mkoeppe
Comment:

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  • Ticket #30229

    • Property Commit changed from 862aca828ac0228f11afee91a4388b54d4834c74 to 3bd0a8a8004df62ad2e332d198e3f0529afe1f9d
    • Property Summary changed from ExtPowerFreeModule, ExtPowerDualFreeModule, TensorFreeModule cannot create a basis to Submodules of TensorFreeModule defined by the symmetries of a Components object
  • Ticket #30229 – Description

    v9 v11  
    1 Setup:
     1Currently, `TensorFreeModule` does not have an interface to the bases that it uses implicitly, nor is it possible to create new bases for it.
    22{{{
    33sage: M = FiniteRankFreeModule(ZZ, 3, name='M')
    44sage: e = M.basis('e')
    5 }}}
    6 
    7 Problems:
    8 {{{
    9 sage: A = M.exterior_power(2); A
    10 2nd exterior power of the Rank-3 free module M over the Integer Ring
    11 sage: A.default_basis()
    12 No default basis has been defined on the 2nd exterior power of the Rank-3 free module M over the Integer Ring
    13 sage: A.basis('w')
    14 TypeError: __init__() missing 1 required positional argument: 'degree'
    15 }}}
    16 {{{
    175sage: T = M.tensor_module(1, 2); T
    186Free module of type-(1,2) tensors on the Rank-3 free module M over the Integer Ring
     
    2311}}}
    2412
    25 On this ticket, we add a class `FreeModuleCompTensorBasis` that implements the standard basis of a tensor module (given a basis of the base module), indexed by `Component.non_redundant_index_generator()`.
     13On this ticket, we add a subclass `TensorFreeSubmodule_comp` of `TensorFreeModule` that implements subspaces spanned by the tensors with prescribed symmetries.
    2614
     15It provides a `basis` method that returns an instance of the new class `TensorFreeSubmoduleBasis_comp`, which represents the standard basis corresponding to a given `Components` object.
     16
     17Also any `TensorFreeModule` provides a `basis` method that returns such a basis object.
     18