#14348: Implement cycle index of combinatorial logarithm (virtual) species
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Reporter: agd | Owner: agd
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.10
Component: combinatorics | Resolution:
Keywords: cycle index, species | Work issues:
Report Upstream: N/A | Reviewers: Frédéric Chapoton
Authors: Andrew Gainer-Dewar | Merged in:
Dependencies: | Stopgaps:
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Old description:
> The semiring of species can be completed to form the ring of "virtual
> species", which are certain equivalence classes of formal differences of
> species. Among other benefits, this allows the "compositional inverse" of
> a species to be defined. It turns out that virtual species have well-
> defined cycle index series (which may have negative coefficients).
>
> This patch adds code to compute the cycle index of the "combinatorial
> logarithm" virtual species, which is the compositional inverse of the
> species of nonempty sets. Among other things, this can be used to extract
> the cycle index of a species of "connected F-structures" from the cycle
> index for the species F. (The standard example is the case of the species
> G of simple graphs.)
>
> I believe this code is functional and complete.
>
> Apply:
> * [attachment:combinatorial_logarithm-agd.patch]
> * [attachment:trac_14348_combinatorial_logarithm-review-fc.patch]
New description:
The semiring of species can be completed to form the ring of "virtual
species", which are certain equivalence classes of formal differences of
species. Among other benefits, this allows the "compositional inverse" of
a species to be defined. It turns out that virtual species have well-
defined cycle index series (which may have negative coefficients).
This patch adds code to compute the cycle index of the "combinatorial
logarithm" virtual species, which is the compositional inverse of the
species of nonempty sets. Among other things, this can be used to extract
the cycle index of a species of "connected F-structures" from the cycle
index for the species F. (The standard example is the case of the species
G of simple graphs.)
I believe this code is functional and complete.
Apply:
* [attachment:trac_14348_combinatorial_logarithm.patch]
--
Comment (by chapoton):
yes, its ok (but it was not necessary) to include my changes in your
patches.
for the patchbot:
aaply trac_14348_combinatorial_logarithm.patch
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14348#comment:13>
Sage <http://www.sagemath.org>
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