I did not know about this "FreeAlgebra". Thank you for the example you included. I think this should work! -Elizabeth
On Apr 22, 12:41 am, Mike Hansen <mhan...@gmail.com> 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] > > --Mike > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group > athttp://groups.google.com/group/sage-support > URL:http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
