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.Sun, 17 Nov 2019 14:43:19 +0100Entries in canonical_matrix for Coxeter groupshttps://ask.sagemath.org/question/48649/entries-in-canonical_matrix-for-coxeter-groups/Can anyone please tell me what *a* is doing in the following output? (Depending on the ordering of the Dynkin diagram, I believe it should be either 1 or 3.)
<code> sage: W = WeylGroup(["G",2]) ; s = W.simple_reflections() ; s[2].canonical_matrix() <br >
[ 1 0] <br >
[ a -1] </code>
Wed, 06 Nov 2019 18:05:59 +0100https://ask.sagemath.org/question/48649/entries-in-canonical_matrix-for-coxeter-groups/Answer by tmonteil for <p>Can anyone please tell me what <em>a</em> is doing in the following output? (Depending on the ordering of the Dynkin diagram, I believe it should be either 1 or 3.)</p>
<p><code> sage: W = WeylGroup(["G",2]) ; s = W.simple_reflections() ; s[2].canonical_matrix() <br></code></p><code>
</code> https://ask.sagemath.org/question/48649/entries-in-canonical_matrix-for-coxeter-groups/?answer=48655#post-id-48655`a` is the square root of 3, as the coefficients of this matrix are defined on the number field with defining polynomial x^2 - 3, see:
sage: M = s[2].canonical_matrix()
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Number Field in a with defining polynomial x^2 - 3 with a = 1.732050807568878?
sage: M
[ 1 0]
[ a -1]
sage: M[1,0]
a
sage: M[1,0]^2
3Wed, 06 Nov 2019 20:23:30 +0100https://ask.sagemath.org/question/48649/entries-in-canonical_matrix-for-coxeter-groups/?answer=48655#post-id-48655Comment by Bob67846 for <p><code>a</code> is the square root of 3, as the coefficients of this matrix are defined on the number field with defining polynomial x^2 - 3, see:</p>
<pre><code>sage: M = s[2].canonical_matrix()
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Number Field in a with defining polynomial x^2 - 3 with a = 1.732050807568878?
sage: M
[ 1 0]
[ a -1]
sage: M[1,0]
a
sage: M[1,0]^2
3
</code></pre>
https://ask.sagemath.org/question/48649/entries-in-canonical_matrix-for-coxeter-groups/?comment=48787#post-id-48787Woops, thanks!Sun, 17 Nov 2019 14:43:19 +0100https://ask.sagemath.org/question/48649/entries-in-canonical_matrix-for-coxeter-groups/?comment=48787#post-id-48787