#21081: Cup product for cochains
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Reporter: vbraun | Type: enhancement
Status: new | Priority: major
Milestone: sage-7.3 | Component: algebraic topology
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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It would be nice to have the cup product available for arbitrary cochains,
without involving `homology_vector_space_with_basis`. Of course its not
well-defined on the level of cochains, but at least one could check that
products are non-zero if there is torsion over ZZ etc.
There are potentially two places where to put it:
* Method of `Chain.Element`, then chains would need to know about their
cell (sub)complex. Right now they don't reference their cell complex as
far as I can see.
* Method `GenericCellComplex.cup_product(self, left_cochain,
right_cochain)`. Then chains need to know their degree (dimension of
cells). Right now they don't store their degree, although the
documentation says that they must be of homogeneous degree.
Thoughts?
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Ticket URL: <https://trac.sagemath.org/ticket/21081>
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