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Instead of symbolic variables you can use the generators of a polynomial ring:
sage: R.<x,y,z> = PolynomialRing(GF(2))
sage: v = vector([x, y, z])
sage: M = matrix(GF(2), [[0, 1, 0], [0, 0, 1], [1, 0, 0]])
sage: M*v
(y, z, x)
Like symbolic expressions, polynomials allow substitution/evaluation with the subs method.
