Here is the result of the first calculation (using the KR crystal) and its parent:
B[-9*Lambda[0] + 9*Lambda[1]] + (q^2+q)*B[-7*Lambda[0] + 7*Lambda[1]] + (q^4+q^3+q^2)*B[-5*Lambda[0] + 5*Lambda[1]] + (q^6+q^5+q^4+q^3)*B[-3*Lambda[0] + 3*Lambda[1]] + (q^5+q^4)*B[-Lambda[0] + Lambda[1]] Free module generated by Weight lattice of the Root system of type ['A', 1, 1] over Univariate Polynomial Ring in q over Integer Ring Here is the result of the first calculation (using the KR crystal) and its parent: (A1(3) + A1(5) + A1(9))*q^3 + (A1(1) + A1(3) + A1(5) + A1(7))*q^2 + (A1(1) + A1(3) + A1(5) + A1(7))*q + A1(3) Univariate Polynomial Ring in q over The Weyl Character Ring of Type ['A', 1] with Rational Field coefficients It is clear (to a human being) that we have the dictionary: B[-9*Lambda[0] + 9*Lambda[1]] is the same as A1(9) etc. I have just noticed that the coefficients are different but that is not the problem (at least not yet). On Friday, November 22, 2013 3:46:02 PM UTC, Nicolas M. Thiery wrote: > > Hi Bruce, > > On Fri, Nov 22, 2013 at 05:04:14AM -0800, Bruce wrote: > > I am trying to test a conjecture by comparing the results of two > > calculations. One calculation works with Kirillov-Reshetikhin > crystals and > > the result is an element of the free module on the Weight Lattice of > the > > affine root system (in one example ['A',1,1]). The other calculation > > returns an element of the WeylCharacterRing of the (finite) root > system > > (in the same example 'A1'). The ring of coefficients in both cases is > the > > same. This uses the ambient lattice. It is trivial to compare these > by > > hand but could I please have some suggestions how to get sage to > compare > > them? > > Can you send a quick sample of both? There is a conversion from the > weight lattice to the ambient lattice, so that should be easy, but > it's best to talk on a concrete example. > > Cheers, > Nicolas > -- > Nicolas M. Thi�ry "Isil" <nth...@users.sf.net <javascript:>> > http://Nicolas.Thiery.name/<http://www.google.com/url?q=http%3A%2F%2FNicolas.Thiery.name%2F&sa=D&sntz=1&usg=AFQjCNGCYA0-O_Memn-RaGRcLp0INyGziw> > > -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
