Meta-ticket: Unify free module elements API: methods dict, monomial_coefficients, etc.

[mkoeppe]

FreeModule and CombinatorialFreeModule elements support methods monomials, coefficients, monomial_coefficients, and FreeModule has the alias dict for the latter.

FiniteRankFreeModule elements could support these methods too (with an optional basis argument), and Components as well.

Tickets:

• Refined protocol for _element_constructor_ in element classes with mutability #29101 Refined protocol for _element_constructor_ in element classes with mutability
• Tensor product and coefficients #24900 Tensor product and coefficients
• _vector_, vector and vector_space #21737 _vector_, vector and vector_space
• Submodules of a MatrixSpace #31995 Submodules of a MatrixSpace
• Matrix and Components should have a sparse iterator #29619 tensors should have a sparse iterator
• Fix monomial_coefficients for submodules of free modules from sage.modules #34455 Fix monomial_coefficients for submodules of free modules from sage.modules
• Improve monomial_coefficients for Lie algebras when they are known to be finite dimensional #25033 Improve monomial_coefficients for Lie algebras when they are known to be finite dimensional
• vector.length() should be number of nonzero entries #29218 vector.length() should be number of nonzero entries
• Make IndexedFreeModuleElement compatible with collections.abc, change method support to return a SupportView #34509 Make IndexedFreeModuleElement compatible with collections.abc, add method items
• Register FreeModuleElement to the Sequence ABC #24815 Register FreeModuleElement to the Sequence ABC
• CombinatorialFreeModule._element_constructor_: Deprecate initialization from a given index #34507 CombinatorialFreeModule._element_constructor_: Deprecate initialization from a given index
• Parent methods support_section, coordinate_section for ModulesWithBasis #34487 Parent methods support_section, coordinate_section for ModulesWithBasis
• CombinatorialFreeModule.is_ambient, add element methods items and nonzero_positions #34511 CombinatorialFreeModule.is_ambient, add element methods items and nonzero_positions
• Generalize SubspaceFunctor to CombinatorialFreeModule #34475 Generalize SubspaceFunctor to CombinatorialFreeModule

CC: @mwageringel @mjungmath @tscrim @videlec @egourgoulhon @fchapoton

Component: linear algebra

Issue created by migration from https://trac.sagemath.org/ticket/30309

[mkoeppe]

comment:7

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