2019-03-06 15:10:58 -0600 received badge ● Notable Question (source) 2019-03-06 15:10:58 -0600 received badge ● Famous Question (source) 2019-03-06 15:10:58 -0600 received badge ● Popular Question (source) 2015-06-06 05:45:46 -0600 answered a question Dimensions of modules in branching def branching_dimensions(chi): monomials = chi.monomials() coef = chi.coefficients() res = "" for i in range(len(coef)): res += str(coef[i]) + "*" + str(monomials[i].degree()) + " + " return res[:-3]  2015-06-03 09:55:46 -0600 asked a question Dimensions of modules in branching For example, consider the following branching: G2=WeylCharacterRing("G2",style="coroots") adj=G2(0,1) A1 = WeylCharacterRing("A1", style="coroots") adj.branch(A1,rule="levi")  How can I find the dimensions of all representations that occur? In this example, we obtain: 3*A1(0) + A1(2) + 2*A1(3)  and I would like to get: 3*1 + 3 + 2*4  (Note: If I try A1(1).degree() I obtain 1 which is wrong.) 2013-04-01 09:13:29 -0600 received badge ● Editor (source) 2013-04-01 08:02:03 -0600 commented question epsilon basis for roots (was graph edge labels) No the labels are in $\alpha$-notation in SAGE. The matter is a bit more complicated since the $\epsilon$-notation has to be computed from the $\alpha$-notation. It;s just a different notation really. The problem is, that there's no $\epsilon$-notation in SAGE, since the ambient space for RootSystem is implemented via tuples of numbers. 2013-04-01 04:43:19 -0600 asked a question epsilon basis for roots (was graph edge labels) I need an illustration of some (sub)poset of positive roots. I have a working code that produces correct labels, but they are written as sums of simple roots. I.e. the resulting graph (when exported to LaTeX) has labels such as $\alpha_1 + \alpha_2$. I would like to have these labels in $\epsilon$-notation. I.e. the previous example would read $\epsilon_1 - \epsilon_3$. RootSystem has an ambient_space method that provides an access epsilon basis, but I am not clear on converting between these two bases and output to LaTeX should really use $\epsilon_1 - \epsilon_3$ rather than $(1,0,-1)$.