#12940: Combinatorial implementation of the affine symmetric group
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Reporter: sdenton | Owner: tom denton
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.4
Component: combinatorics | Resolution:
Keywords: affine, combinatorics, days38 | Work issues:
Report Upstream: N/A | Reviewers:
Authors: tom denton | Merged in:
Dependencies: | Stopgaps:
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Comment (by sdenton):
Ok, changed the documentation, updated the patch in the combinat queue,
and added some new functions.
There are two ways to pull a dominant element out of an affine
permutation: one is to sort the Lehmer code, and the other is to write
x=g*f, where g is dominant and f is finite type (0-parabolic). The
to_dominant method does the sorting, and the grassmannian_quotient()
method returns the pair (g,f). (Or (f,g) if you specify side='left'.) I
also put in a to_core method, which uses the sorting approach. One can
get the core for the quotient element by doing
x.grassmannian_quotient()[0].to_core().
Best,
-tom
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12940#comment:6>
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