#17998: is_dominant methods of weight lattices should ignore vectors orthogonal
to
coroots
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Reporter: bump | Owner: bump
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: combinatorics | Keywords: dominant, days64
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Weight lattices have definitions in `root_lattice_realizations.py` and in
`weight_space.py`. Adding a vector that is orthogonal to the simple
coroots should not affect whether a weight is dominant. Furthermore there
is a separate function called is_dominant_weight defined in
root_lattice_realizations. There are reasons for having separate
implementations: the realization in weight_space.py is more efficient
since it avoids taking scalar products. Instead, it just looks at the
coefficients to see if they are positive. But this method only works if
the basis consists of the fundamental weights. Moreover in an extended
affine weight lattice the basis consists of the fundamental weights plus
the null root 'delta'. The coefficient of 'delta' should be ignored, so
currently this method can give wrong results.
{{{
sage: P=RootSystem(['A',2,1]).weight_lattice(extended=true)
sage: delta=P.null_root(); delta
delta
sage: Lam = P.fundamental_weights()
sage: Lam[0].is_dominant()
True
sage: (Lam[0]-delta).is_dominant()
False
}}}
Consequently we need to revise a remark in the docstring for
is_dominant_weight, and refine the definition in `weight_lattice.py` to
ignore the coefficient of `'delta'`
--
Ticket URL: <http://trac.sagemath.org/ticket/17998>
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