This is the element class of a CombinatorialFreeModule.

Its implementation of __iter__, __contains__, __len__ are not compatible with anything in the collections.abc protocols. Specifically,

sage: F = CombinatorialFreeModule(QQ, ['a','b','c'])
sage: B = F.basis()
sage: f = B['a'] + 3*B['c']; f
sage: import collections.abc
sage: isinstance(f, collections.abc.Collection)
True

but __iter__ating over this collection gives objects that are not __contain__ed in it.

To improve interoperability, we propose to make the following changes:

• Deprecate the __contains__ method (currently testing whether a given index is in the support). After its removal, the class would no longer be considered by Python to be a subclass of collections.abc.Collection, but merely a Sized Iterable.
• As a replacement for this functionality, revise the method support to return an instance of a new class SupportView, which provides a fast __contains__ method, instead of a list.

(Similarly, in #24815, it was proposed to make the elements of free modules from sage.modules a collections.abc.Sequence.)

Part of Meta-ticket #30309: Unify free module elements API: methods dict, monomial_coefficients, etc.

Depends on #34505

CC: @fchapoton @tscrim @mwageringel @nthiery @anneschilling

Component: linear algebra

Author: Matthias Koeppe

Branch/Commit: 2fe3b98

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/34509