epsilon basis for roots (was graph edge labels)

asked 2013-04-01 11:43:19 +0200

vit.tucek gravatar image

updated 2015-01-13 18:04:25 +0200

FrédéricC gravatar image

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

  1. I am not clear on converting between these two bases


  1. output to LaTeX should really use $\epsilon_1 - \epsilon_3$ rather than $(1,0,-1)$.
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Are the labels in the graph in $\epsilon$-notation? Just want to know if the edge labels are changed when exporting to LaTeX. Could you post an example so we can see where in the process the labels are being changed? A quick solution for this (if there aren't any other objects labelled $\alpha$) would be to take the `str` returned by the `latex` method and use string replacement to change `alpha` to `epsilon`.

fidbc gravatar imagefidbc ( 2013-04-01 12:18:17 +0200 )edit

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.

vit.tucek gravatar imagevit.tucek ( 2013-04-01 15:02:03 +0200 )edit

Oh, I see. So then the problem is not really the edge labels in the graph, but converting between notations. Perhaps it would be convenient to rename this question.

fidbc gravatar imagefidbc ( 2013-04-01 15:14:31 +0200 )edit