A correction to the weight of crystal elements for type A and a speedup for all types

[dwbump]

For Cartan Types 'A' a problem with the weight function of crystals was described here:

http://groups.google.com/group/sage-combinat-devel/browse_thread/thread/7cdfe075257ba963?hl=en

The method of correcting this problem was to hard-code the weight in the crystals of letters,
and to have the crystals of tensors get the weight of a tensor element by summing the weights
of its constituents. This alters the weight for Type A (correcting the defect) and returns the
same weight as the old algorithm for other Cartan types.

When the patch was implemented it was found to be 2-3 times faster than the old algorithm.

CC: @sagetrac-sage-combinat

Component: combinatorics

Issue created by migration from https://trac.sagemath.org/ticket/2853

[dwbump]

patch correcting problem with weights for crystal graphs of type A and speeding up all Cartan types.

[sagetrac-mabshoff]

comment:1

Attachment: crystal_weights.patch.gz

[mwhansen]

Attachment: 2853.patch.gz

[mwhansen]

comment:2

Hi Dan,

I've updated a patch to move the tests for .weight() to the docstring for the definition of weight. There is an issue with ['G',2] though:

Before the patch:

sage: C = CrystalOfLetters(['G',2])
sage: hwvs = C.highest_weight_vectors()
sage: wlr = C.weight_lattice_realization()
sage: v = hwvs[0]; v
1
sage: v.weight()
(1, 0, -1)
sage: wlr.weyl_dimension(v.weight())
7

After the patch:

sage: C = CrystalOfLetters(['G',2])
sage: wlr = C.weight_lattice_realization()
sage: hwvs = C.highest_weight_vectors()
sage: hwvs
[1]
sage: v = hwvs[0]; v
1
sage: v.weight()
(-1, 0, 1)
sage: wlr.weyl_dimension(v.weight())
0

[dwbump]

comment:3

I was unable to confirm the problem with G2. I applied the patch in the modified form
that you posted, and sage: wlr.weyl_dimension(v.weight()) returns 7 for me.

Dan

[sagetrac-mabshoff]

comment:4

Replying to @dwbump:

I was unable to confirm the problem with G2. I applied the patch in the modified form
that you posted, and sage: wlr.weyl_dimension(v.weight()) returns 7 for me.

Dan

Hi Dan,

I can confirm that with 3.0.alpha2 and your patch applied wlr.weyl_dimension(v.weight()) returns 0. With what build did you try? Are there any other patches you have in your tree?

Cheers,

Michael

[dwbump]

comment:5

Hi Dan,

I can confirm that with 3.0.alpha2 and your patch applied wlr.weyl_dimension(v.weight()) returns 0. With what build did you try? Are there any other patches you have in your tree?

Cheers,

Michael

I did this with 3.0-alph0 and no other patches. I can install 3.0.alpha2 and debug the patch.

Dan

[dwbump]

comment:6

Attachment: 2853.1.patch.gz

It turns out that I had forgotten the G2 patch that went in on Saturday.

I corrected the patch and added it as 2853.1.patch. I believe it is now
correct.

Dan