Re: [sage-combinat-devel] Weight lattices
Sorry about being difficult. Here is one command: lie.p_tensor(3,[2],'A1') Here is an alternative: C = KirillovReshetikhinCrystal(['A',1,1],1,2) L = CombinatorialFreeModule(ZZ,C.weight_lattice_realization()) T = TensorProductOfCrystals(*[C]*3) hw = [ a for a in T if a.e(1) == None ] sum( L.term( a.weight(), 1 ) for a in hw ) I would like to convince sage (in this simplified example) that these are the same. Thank you for your patience. On Saturday, November 23, 2013 7:28:26 AM UTC, Nicolas M. Thiery wrote: On Fri, Nov 22, 2013 at 08:09:25AM -0800, Bruce wrote: Here is the result of the first calculation (using the KR crystal) and its parent: Please, not the result but the command (or a simplified version) producing the result! Otherwise one has to reconstruct the command to play with the objects :-) 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%2Fsa=Dsntz=1usg=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.
Re: [sage-combinat-devel] Weight lattices
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. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- 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.
Re: [sage-combinat-devel] Weight lattices
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%2Fsa=Dsntz=1usg=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.
Re: [sage-combinat-devel] Weight lattices
On Fri, Nov 22, 2013 at 08:09:25AM -0800, Bruce wrote: Here is the result of the first calculation (using the KR crystal) and its parent: Please, not the result but the command (or a simplified version) producing the result! Otherwise one has to reconstruct the command to play with the objects :-) Cheers, Nicolas -- Nicolas M. Thiéry Isil nthi...@users.sf.net http://Nicolas.Thiery.name/ -- 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.
