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?
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