#14347: Implement group cycle indices
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Reporter: agd | Owner: agd
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: cycle index, species | Merged in:
Authors: Andrew Gainer-Dewar | Reviewers:
Report Upstream: N/A | Work issues: coverage, doctest
Branch: | Commit:
Dependencies: #14751 #14846 | Stopgaps:
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Changes (by agd):
* dependencies: #14751 => #14751 #14846
Old description:
> Let G be a group. A G-cycle index is a map from G to the ring of cycle
> index series. These objects are useful for enumerating G-species (species
> equipped with an equivariant G-action), where they serve a role analogous
> to the cycle indices of species.
>
> This patch offers an implementation of G-cycle indices with their most
> important algebraic features (sum, product, and composition/plethysm).
> (The plethysm of G-cycle indices is defined in a funny way that really
> depends on having access to the whole G-cycle index at once; otherwise,
> there wouldn't be much point in having this code.)
>
> This code is (believed to be) complete and functional. It could use a bit
> of attention of someone who understand the coersion system better than I
> do, though.
New description:
Let G be a group. A G-cycle index is a map from G to the ring of cycle
index series. These objects are useful for enumerating G-species (species
equipped with an equivariant G-action), where they serve a role analogous
to the cycle indices of species.
This patch offers an implementation of G-cycle indices with their most
important algebraic features (sum, product, and composition/plethysm).
(The plethysm of G-cycle indices is defined in a funny way that really
depends on having access to the whole G-cycle index at once; otherwise,
there wouldn't be much point in having this code.)
This code is (believed to be) complete and functional. It could use a bit
of attention of someone who understand the coersion system better than I
do, though.
(This code weakly depends on #14846; the class implemented here has a
{{{derivative}}} method which calls down to
{{{CycleIndexSeries.derivative}}}, which does not currently do what it
should.)
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Ticket URL: <http://trac.sagemath.org/ticket/14347#comment:26>
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