In the third one, try using the polynomial quotient ring with modulus x^2 + x + 1; the reason you aren't getting the output you expect is because x^3 - 1 is reducible over QQ, and QQ[x] / (x^3 - 1) isn't an integral domain. See below.
(Or you could use number field arithmetic; Sage has a special optimised set of routines specifically for doing linear algebra over cyclotomic fields.) sage: R.<x> = QQ[] sage: S.<y> = R.quotient(x^2 + x + 1) sage: M = matrix([[(y^i)^j for j in range(3)] for i in range(3)]) sage: M [ 1 1 1] [ 1 y -y - 1] [ 1 -y - 1 y] sage: N = M.matrix_from_rows([0,2,1]) sage: M * N [3 0 0] [0 3 0] [0 0 3] David --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
