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, 04 Sep 2016 15:19:15 +0200how to sum up the function over all permutations of variables in associative non-commutative algebrahttps://ask.sagemath.org/question/34714/how-to-sum-up-the-function-over-all-permutations-of-variables-in-associative-non-commutative-algebra/ hello, i need to sum up $\lambda_{\sigma}(a_{\sigma(1)}a_{\sigma(2)}a_{\sigma(3)}-a_{\sigma(3)}a_{\sigma(4)}a_{\sigma(5)})$ over all $\sigma\in S_5$ where $a_i$ are elements of associative non-commutative algebra.
the result should be $E_1a_1a_2a_3a_4a_5+\cdots+E_{120}a_5a_4a_3a_2a_1$
and i need to express $E_i$ in terms of $\lambda_{\sigma}$.
actualy my tartget is to find non-zero solution of $E_i=0$ for all $i$.RadmirSun, 04 Sep 2016 15:19:15 +0200https://ask.sagemath.org/question/34714/non-commutative algebra with formal functionshttps://ask.sagemath.org/question/9595/non-commutative-algebra-with-formal-functions/I'd like to look at the following: the set of formal functions with 2 variables f(x,y) and the real numbers a,b,c..., including an addition and a non-commutative multiplication, such that things like
expand((a+f(x,y))*(b+c*f(u,v))) = a*b + a*c*f(u,v) + b*f(x,y) + c*f(x,y)*f(u,v)
are possible (and vice versa), and with the multiplication of the functions
f(x,y)*f(u,v) != f(u,v)*f(x,y)
being non-commutative, however with the multiplication of the functions by the real scalars
a*f(x,y) == f(x,y)*a
still commutative. Can I construct something like that with sage?
MarkSat, 01 Dec 2012 18:37:19 +0100https://ask.sagemath.org/question/9595/Factorization of non-commutative Laurent polynomialshttps://ask.sagemath.org/question/8417/factorization-of-non-commutative-laurent-polynomials/Hi, can Sage factorize non-commutative Laurent polynomials in several variables?
By those polynomials I mean elements in the group algebra Z[F(n)], where Z is the integers and F(n) is the free group on n letters.
(The case with Z/2- instead of Z-coefficients would also be interesting.)
Thank you!bmWed, 26 Oct 2011 02:37:53 +0200https://ask.sagemath.org/question/8417/