#19830: Classification of finite and affine Coxeter groups
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Reporter: stumpc5 | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.0
Component: combinatorics | Resolution:
Keywords: coxeter system, root system | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nthiery):
Replying to [comment:6 stumpc5]:
> Sorry for adding more and more questions here: The documentation of the
method {{{roots}}} states
> {{{
> These are roots in the Coxeter sense, that all have the
> same norm. They are given by their coefficients in the
> base of simple roots, also taken to have all the same
> norm.
> }}}
> How is this true if the sum of the coefficients is not one? As in
> {{{
> sage: W = CoxeterGroup(['A',2])
> sage: W.roots()
> [(1, 0), (1, 1), (0, 1), (-1, 0), (-1, -1), (0, -1)]
> }}}
The basis of the simple roots is not orthonormal. So one can't read of the
norm of vectors expressed there right away.
--
Ticket URL: <http://trac.sagemath.org/ticket/19830#comment:10>
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