Jason Grout <[EMAIL PROTECTED]> writes:
> Martin Rubey wrote:
> > I tried to demonstrate Cayley Hamilton in Sage, but failed. Here is what I
> > tries:
> >
> > sage: f = function('f')
> > sage: m = matrix([[f(i,j) for j in range(2)] for i in range(2)])
> > sage: p=SR[x](m.characteristic_polynomial('x'))
> > sage: p.subs(x=m)
> >
> > [(f(0, 0) - x)*(f(1, 1) - x) - f(0, 1)*f(1, 0)
> > 0]
> > [ 0 (f(0, 0) - x)*(f(1, 1) - x) -
> > f(0, 1)*f(1, 0)]
> >
> > Of course, the result *should* be the zero matrix. It seems that the value
> > of
> > p is not what I'd expect:
> >
> > sage: p.coefficients()
> > [(f(0, 0) - x)*(f(1, 1) - x) - f(0, 1)*f(1, 0)]
> >
> > So, probably the question is: how do I create a polynomial over Symbolic
> > Ring
> > properly?
>
> To answer your original question:
>
>
>
> sage: f = function('f')
> sage: m = matrix([[f(i,j) for j in range(2)] for i in range(2)])
> sage: p=m.charpoly('x')
> sage: p
> (f(0, 0) - x)*(f(1, 1) - x) - f(0, 1)*f(1, 0)
> sage: p.coefficients(x)
> [[f(0, 0)*f(1, 1) - f(0, 1)*f(1, 0), 0], [-f(1, 1) - f(0, 0), 1], [1, 2]]
>
> However, we run into problems. Any comments on these, anyone?
Why is your coefficients different from mine?
Martin
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