#14543: Implement compositional inverses of cycle index series
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Reporter: agd | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: species, cycle indices | Merged in:
Authors: Andrew Gainer-Dewar | Reviewers: Darij Grinberg
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by agd):
Replying to [comment:14 darij]:
Thanks for your suggestions! I've uploaded a new version of my patch which
incorporates some of your changes and applies on top of the current
5.12-beta3 source; see comments below.
> And I have not filled in the definition of functorial composition since
I don't fully understand it myself (I don't have the [BLL] reference, only
[BLL-Intro]), but I've added a #TODO because it should eventually be
filled in.
I cleaned this up in #14809, which will go live when 5.12 ships.
> In the stretch doctest, I replaced {{{f = CIS([p([1])])}}} by {{{f =
CIS([p([]), p([1]), p([2]), p.zero()])}}} because, as far as I understand,
when you write a cycle index series as a power series in t, the
coefficient before {{{t^n}}} has to be a symmetric polynomial homogeneous
of degree n.
This sounds right to me, but I haven't rolled it in because it's not
related to compositional inverses. I also left out your other small tweaks
to other docstrings It looks like all of this documentation could use an
overhaul, though.
> I have removed the reference to [BLL] from your method because the same
reference appears in another method. Generally, every reference needs to
exist only once in the source.
Whoops!
> I added the {{{res._name = 'res'}}} line because the examples in the
{{{define}}} method in {{{series.py}}} do that. Maybe it is cargo cult. I
hope you can shed light on this.
I don't claim to understand this entirely either, but I believe
(presumably cultishly) that the _name field is meant for user-facing
output and shouldn't be set to something not user-useful like "res".
Perhaps one day we'll all ascend to the inner temple of {{{define}}} and
gain true wisdom.
--
Ticket URL: <http://trac.sagemath.org/ticket/14543#comment:19>
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