#18644: Fix method is_real_root() in root_lattice_realizations.py
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Reporter: jonathan.judge | Owner: jonathan.judge
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: combinatorics | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Currently, the element method {{{is_real_root()}}} of
root_lattice_realizations.py is not quite correct. It checks only if
{{{norm_squared()}}} is positive. This is correct in a root system, but
not when in the root lattice. We can add an additional check in this
situation: see Proposition 5.10b in Kac's book.
{{{
sage: R = RootSystem(['A',1,1])
sage: Q = R.root_lattice()
sage: alpha = Q.simple_roots()
sage: beta = 3*alpha[0] + alpha[1] # not a root
sage: beta.norm_squared()
8
sage: beta.is_real_root()
True
}}}
{{{
sage: R = RootSystem("A2")
sage: Q = R.root_lattice()
sage: alpha = Q.simple_roots()
sage: beta = 2*alpha[1] + alpha[2] # not a root
sage: beta.norm_squared()
6
sage: beta.is_real_root()
True
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/18644>
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