Decomposing a Root vector into simple roots

DBS
45 ●2 ●2 ●8

Is there a sage functions which does the following:

Input = Root System / Ambient Lattice or Ambient space of irreducible (or even classical) Root System and a Root vector $v$

Output = a list containing the integers which expresses $v$ as a linear combination of simple roots.

Thank you for your help.

1 Answer

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5125 ●3 ●43 ●111

Would you please provide an example of what you fail to do ?

sage: v
2*alpha[1] + 2*alpha[2] + 3*alpha[3]
sage: v.to_vector()
(2, 2, 3, 0)

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Asked: 2016-02-22 18:22:02 +0200

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Last updated: Feb 22 '16