[with patch, positive review] A correction to the weight of crystal elements for type A and a speedup for all types

[bump]

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.

[bump]

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

[mhansen]

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

[bump]

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

[mabshoff]

Replying to bump:

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

[bump]

> 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

[bump]

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

[mhansen]

Looks good to me. Apply just 2853.1.patch.

[mabshoff]

Merged in Sage 3.0.alpha3.