Sometime recently, possibly because of python3, the required argument
`support_order` was been added to the class
`sage.modules.with_basis.subquotient.SubmoduleWithBasis`.
The documentation says:
``support_order`` -- an ordering of the support of ``basis`` expressed in
``ambient`` given as a list
I have a derived class of `SubmoduleWithBasis` that used to work and I am
trying to understand what is required here. I am a little surprised that a
list is expected because it can be expensive to compute indexing sets for
bases, but perhaps this is deemed acceptable when constructing submodules?
More to the point, can someone tell me what the documentation for
`support_order` actually means? If the ambient space has indexing set
{1,2,3} and basis {x1,x2,x3} and my submodule is spanned by {x1+x2} then I
would think that the support should be {1,2}. Is `support_order` meant to
tell me what order I should walk through the indexing set when rewriting
elements of the submodule in terms of its basis? I honestly don't know is
required except that `support_order` must have an `index` method.
As far as I can see the only place that `support_order` is used is ub the
method `_support_key`where it becomes the `key` in a `module_morphism` in
the `list` method of `SubmoduleWithBasis`.
Andrew
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