On 04/22/2010 12:41 AM, Mike Hansen wrote:
On Wed, Apr 21, 2010 at 8:06 PM, Elizabeth<papag...@earthlink.net> wrote:
I'd like to know if there is a way to define a variable in Sage as non-
commuting.
I am trying to multiply a few matrices together and take the trace,
*but* the matrix entries are non-commuting elements. So, I need Sage
to leave a term like a*x*a as-is and not change it to x*a^2.
You could work over the FreeAlgebra:
sage: R.<a,b> = FreeAlgebra(QQ, 2)
sage: a*b + b*a
a*b + b*a
sage: s = matrix(R)
sage: s = matrix(R, [[a,b],[b,a]]); s
[a b]
[b a]
sage: s*s
[a^2 + b^2 a*b + b*a]
[a*b + b*a a^2 + b^2]
sage: b*s*s
[ b*a^2 + b^3 b*a*b + b^2*a]
[b*a*b + b^2*a b*a^2 + b^3]
Nice! I've added the above example to the FAQ.
Thanks,
Jason
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