ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 22 Feb 2016 20:52:12 +0100Decomposing a Root vector into simple rootshttps://ask.sagemath.org/question/32630/decomposing-a-root-vector-into-simple-roots/
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.
Mon, 22 Feb 2016 18:22:02 +0100https://ask.sagemath.org/question/32630/decomposing-a-root-vector-into-simple-roots/Answer by FrédéricC for <p>Is there a sage functions which does the following: </p>
<p>Input = Root System / Ambient Lattice or Ambient space of irreducible (or even classical) Root System and a Root vector $v$</p>
<p>Output = a list containing the integers which expresses $v$ as a linear combination of simple roots. </p>
<p>Thank you for your help. </p>
https://ask.sagemath.org/question/32630/decomposing-a-root-vector-into-simple-roots/?answer=32635#post-id-32635Would 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)Mon, 22 Feb 2016 20:52:12 +0100https://ask.sagemath.org/question/32630/decomposing-a-root-vector-into-simple-roots/?answer=32635#post-id-32635