Hi,
Yep, there are definitely easy ways of doing this. Here's one way:
sage: var('a b c d')
(a, b, c, d)
sage: A = matrix(2,[2,1,1,1])
sage: B = matrix(2,[a,b,c,d])
sage: C = A*B - B*A
sage: [ e == 0 for e in C.list() ]
[c - b == 0, d + b - a == 0, -d - c + a == 0, b - c == 0]
sage: solve([ e == 0 for e in C.list() ], N.list())
[[a == r2 + r1, b == r2, c == r2, d == r1]]
-cc
On Sat, Feb 7, 2009 at 9:45 AM, mb <bestv...@gmail.com> wrote:
>
> Hi,
>
> Say I want to compute the centralizer of a matrix.
>
> sage: P.<a,b,c,d>=PolynomialRing(QQ)
> sage: A=matrix(P,2,2,[2,1,1,1])
> sage: B=matrix(P,2,2,[a,b,c,d])
> sage: C=A*B-B*A
> sage: C
>
> [ -b + c -a + b + d]
> [ a - c - d b - c]
> sage: var('a b c d')
> (a, b, c, d)
> sage: solve([-b + c==0,-a + b + d==0,a - c - d==0,b - c==0],[a,b,c,d])
> [[a == r2 + r1, b == r2, c == r2, d == r1]]
>
> Here I had to manually copy the entries of C into solve, which is a
> problem for larger matrices. Ideally, something like
>
> solve(C==0,[a,b,c,d])
>
> should work, but of course it doesn't. Is there any way of doing this?
>
> Mladen
> >
>
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