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Parent methods support_section, coordinate_section for ModulesWithBasis #34487

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mkoeppe opened this issue Sep 3, 2022 · 4 comments
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mkoeppe commented Sep 3, 2022

This returns a partial module morphism from a free module with basis to an ambient free module, indexed according to the support order.

Calling the morphism is like calling the element method IndexedFreeModuleElement._vector_, but it would also work with elements of infinite-dimensional modules because an appropriate finite-dimensional submodule will be used.

This generalizes the interaction of _dense_free_module, get_order, and _vector_ in CubicHeckeAlgebra; and it makes the morphism used by _vector_ explicit.

Also for ModulesWithBasis.FiniteDimensional we can generalize the following methods of FreeModule_generic (from sage.modules):
coordinates, coordinate_vector, coordinate_module.

Depends on #33431

CC: @tscrim @soehms

Component: linear algebra

Issue created by migration from https://trac.sagemath.org/ticket/34487

@mkoeppe mkoeppe added this to the sage-9.8 milestone Sep 3, 2022
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@mkoeppe mkoeppe changed the title Parent method support_order_section for ModulesWithBasis Parent methods support_section, coordinate_section for ModulesWithBasis Sep 4, 2022
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mkoeppe commented Sep 4, 2022

comment:4

Probably better to actually make this support_submodule, coordinate_submodule, with the morphisms just exposed as the lift/retract maps of the constructed submodule.

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mkoeppe commented Sep 4, 2022

Dependencies: #33431

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