#2808 closed defect (fixed)
[with patch, positive review] G2 fundamental weights were the negative of what they should be.
Reported by: | bump | Owned by: | bump |
---|---|---|---|
Priority: | major | Milestone: | sage-3.0 |
Component: | combinatorics | Keywords: | |
Cc: | sage-combinat | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
In combinat/root_system.py, the fundamental weights for the various root systems are entered by hand. For G2, the fundamental weights were the negatives of what they should be.
diff -r 80b506b8e07c sage/combinat/root_system.py --- a/sage/combinat/root_system.py Tue Apr 01 19:18:55 2008 -0700 +++ b/sage/combinat/root_system.py Sat Apr 05 08:40:46 2008 -0700 @@ -788,11 +788,11 @@ class AmbientLattice_g(AmbientLattice_ge """ EXAMPLES: sage: CartanType(['G',2]).root_system().ambient_lattice().fundamental_weights() - [(-1, 0, 1), (-2, 1, 1)] + [(1, 0, -1), (2, -1, -1)] """ return [ c0*self._term(0)+c1*self._term(1)+c2*self._term(2) \ for [c0,c1,c2] in - [[-1,0,1],[-2,1,1]]] + [[1,0,-1],[2,-1,-1]]] def WeylDim(type, coeffs):
Attachments (1)
Change History (7)
Changed 9 years ago by
comment:1 Changed 9 years ago by
- Owner changed from mhansen to bump
- Status changed from new to assigned
comment:2 Changed 9 years ago by
- Summary changed from G2 fundamental weights were the negative of what they should be. to [with patch, needs review] G2 fundamental weights were the negative of what they should be.
comment:3 Changed 9 years ago by
- Summary changed from [with patch, needs review] G2 fundamental weights were the negative of what they should be. to [with patch, positive review] G2 fundamental weights were the negative of what they should be.
Quoting from the email to sage-devel:
I should have added some justification for this conclusion in the trac report. Instead I'm giving it here. You can look the weights up in Bourbaki, Lie Groups and Lie Algebras Ch 4-6 (Appendix) and you can also check the inner products of the weights with the simple roots (which are correct). The inner product of the i-th fundamental weight with the j-th simple root should be positive if i=j and zero otherwise. I checked that all the other root systems are right by examining the output following program on the ambient lattices. This change had no effect on the output of the Weyl dimension formula. def test_lattice(L): rank = L.ct[1] roots = L.simple_roots() weights = L.fundamental_weights() return [[i,j, roots[i].inner_product(weights[j])] for i in range(rank) for j in range(rank)]
I am happy with this (small!) change.
comment:4 Changed 9 years ago by
- Resolution set to fixed
- Status changed from assigned to closed
Merged in Sage 3.0.alpha2.
comment:5 Changed 8 years ago by
- Cc sage-combinat added
comment:6 Changed 2 years ago by
- Description modified (diff)
- Report Upstream set to N/A
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patch correcting the G2 fundamental weights