id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
4513 Action of MatrixGroup on a MPolynomialRing SimonKing SimonKing "A group of n by n matrices over a field K acts on a polynomial ring with n variables over K. However, this is not implemented yet.
The following should work:
{{{
sage: M = Matrix(GF(3),[[1,2],[1,1]])
sage: N = Matrix(GF(3),[[2,2],[2,1]])
sage: G = MatrixGroup([M,N])
sage: m = G.0
sage: n = G.1
sage: R. = GF(3)[]
sage: m*x
x + y
sage: x*m
x - y
sage: (n*m)*x == n*(m*x)
True
sage: x*(n*m) == (x*n)*m
True
}}}
On the other hand, we still want to have the usual action on vectors or matrices:
{{{
sage: x = vector([1,1])
sage: x*m
(2, 0)
sage: m*x
(0, 2)
sage: (n*m)*x == n*(m*x)
True
sage: x*(n*m) == (x*n)*m
True
}}}
{{{
sage: x = matrix([[1,2],[1,1]])
sage: x*m
[0 1]
[2 0]
sage: m*x
[0 1]
[2 0]
sage: (n*m)*x == n*(m*x)
True
sage: x*(n*m) == (x*n)*m
True
}}}" enhancement needs_work major sage-6.4 commutative algebra matrix group, action, polynomial ring wdj malb Simon King David Loeffler, William Stein N/A