#12667: category root lattice realization issue: infinite loop while trying to
reflect to the positive chamber
------------------------------+---------------------------------------------
Reporter: mshimo | Owner: sage-combinat
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: combinatorics | Keywords: root system
Work_issues: | Upstream: N/A
Reviewer: Anne Schilling | Author: Mark Shimozono
Merged: | Dependencies: #6588
------------------------------+---------------------------------------------
Description changed by mshimo:
Old description:
> version 5.0 beta7
>
> sage/combinat/root_system/root_lattice_realizations.py
> element methods to_positive_chamber, reduced_word
> may give infinite loops for affine root systems
>
> {{{
> R=sage.combinat.root_system.all.RootSystem(['A',1,1])
> rl = R.root_lattice()
> mu = rl.from_vector(vector([0,1]))
> mu.to_positive_chamber()
> }}}
New description:
version 5.0 beta7
sage/combinat/root_system/root_lattice_realizations.py
element methods to_positive_chamber, reduced_word
may give infinite loops for affine root systems
{{{
R=sage.combinat.root_system.all.RootSystem(['A',1,1])
rl = R.root_lattice()
mu = rl.from_vector(vector([0,1]))
mu.to_positive_chamber()
}}}
For elements of a root lattice realization:
1. Added method reflect which reflects across a hyperplane orthogonal
to a (co)root.
2. Renamed to_positive_chamber to to_dominant_chamber, and added case
checking
for affine root systems which prevents infinite looping. Root systems
that are not finite and not affine are not checked.
3. Added method weyl_action which acts on a vector by a Weyl group
element.
4. Added method weyl_stabilizer which returns indices of simple
reflections
fixing a weight.
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12667#comment:9>
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