On Jan 31, 12:29 am, "William Stein" <[EMAIL PROTECTED]> wrote:
> On Jan 30, 2008 3:48 PM, pgdoyle <[EMAIL PROTECTED]> wrote:
>
>
>
>
>
> > I would like to take the Taylor series of a matrix. But I find I
> > can't even put a Taylor polynomial into a matrix without its being
> > simplified.
>
> > sage: f=-x/(2*x-4); f
> > -x/(2*x - 4)
> > sage: g=taylor(f,x,1,1); g
> > 1/2 + x - 1
> > sage: matrix(1,[g])
> > [x - 1/2]
> > sage: m=matrix(1,[f]); m
> > [-x/(2*x - 4)]
> > sage: m.apply_map(lambda e: taylor(e,x,1,1))
> > [x - 1/2]
>
> > Any suggestions?
>
> You're already doing it exactly correctly. Try a higher degree
> approximation to avoid confusion:
>
> sage: m = matrix(1,[-x/(2*x-4)])
> sage: m.apply_map(lambda e: taylor(e,x,1,4))
> [x + (x - 1)^4 + (x - 1)^3 + (x - 1)^2 - 1/2]
William:
Sorry - I didn't make the issue clear enough. When I ask for the
Taylor polynomial at x=1, I want a polynomial in x-1. And that's what
I get, except that when I put this polynomial into a matrix, 1/2 + x -
1 gets simplified to x-1/2. Your example shows this behavior very
clearly.
I understand that a whole new approach to power series is in the
works, which will keep track of degrees of approximation, and I expect
this will include taking the power series of a matrix. But for now, I
just want to be able to use Sage instead of Mathematica for an
exposition of generating functions for Markov chains, where I need to
compute and display Taylor polynomials of matrices. Hopefully there
is some way I can keep a polynomial in x-1 from getting simplified
automatically when it's an element of a matrix.
Cheers,
Peter
Cheers,
Peter
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