#19481: No cardinality for virtual crystals
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Reporter: aschilling | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.10
Component: combinatorics | Resolution:
Keywords: crystals | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by tscrim):
Your first issue is that it should be
{{{#!diff
-G = crystals.LSPaths(La[1])
+G = crystals.LSPaths(La[1]).digraph()
}}}
The second is more of a problem, in that it doesn't know at present that
it is a finite crystal. So it should error out, but with a different error
of `NotImplementedError: unknown cardinality`. Part of it is that
`Subcrystal` (and hence `VirtualCrystal`) should be smarter about its
category. Another part is the desired interface (which, admittedly, is not
the most discoverable), which sets the correct category, is:
{{{
sage: LaC = RootSystem(['C',2]).weight_space().fundamental_weights()
sage: C = crystals.LSPaths(LaC[1])
sage: A = crystals.Tableaux(['A',3], shape=[2,1,1])
sage: phi = C.crystal_morphism(A.module_generators)
sage: V = phi.image()
sage: V
Virtual crystal of The crystal of tableaux of type ['A', 3] and shape(s)
[[2, 1, 1]] of type ['C', 2]
sage: V.cardinality()
4
sage: V.category()
Category of classical crystals
}}}
Yet another part is that this will have to raise an error message because
`(Enumerated)Sets` does not want a default `cardinality` to avoid
namespace pollution.
----
I also just ran across this problem today too:
{{{
sage: La = RootSystem(['A',3]).weight_space().fundamental_weights()
sage: LaC = RootSystem(['C',2]).weight_space().fundamental_weights()
sage: B = crystals.AlcovePaths(La[1]+La[3])
sage: V = crystals.AlcovePaths(LaC[1])
sage: phi = V.crystal_morphism(B.module_generators)
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
...
ValueError: (1, -1) is not in the coroot space
}}}
This comes from the fact that the weights of the alcove path model do not
lie in the weight lattice realization.
----
Fixes will follow shortly.
--
Ticket URL: <http://trac.sagemath.org/ticket/19481#comment:1>
Sage <http://www.sagemath.org>
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