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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.
mkoeppe
changed the title
Parent method support_order_section for ModulesWithBasis
Parent methods support_section, coordinate_section for ModulesWithBasis
Sep 4, 2022
Probably better to actually make this support_submodule, coordinate_submodule, with the morphisms just exposed as the lift/retract maps of the constructed submodule.
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_
inCubicHeckeAlgebra
; and it makes the morphism used by_vector_
explicit.Also for
ModulesWithBasis.FiniteDimensional
we can generalize the following methods ofFreeModule_generic
(fromsage.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
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