Evaluating Taylor polynomials




-----maxima-bounces at math.utexas.edu wrote: -----


>With
>
>fT : taylor(f(x,y),[x,y],[0,0],2);
>
>I compute the Taylor expansion of a generic function f(x,y). Now, I
>would like to evaluate the Taylor polynomial at a given point: let's
>say x=-1 , y=1. How can I do this?

I think you need to use the function 'at.' Try this:

(%i6) fT : taylor(f(x,y),[x,y],[0,0],2)$

 (%i7) at(fT,x=-1 , y=1);
 (%o7)
 (f[(0,2)](0,0)*y^2-2*f[(1,1)](0,0)*y+f[(2,0)](0,0))/2+f[(0,1)](0,0)*y-f[(1,0)](0,0)+f(0,0)

To view the user documentation for 'at,' enter "? at" at an input prompt.

Alternatively, you can use the positional derivative package 'pdiff,' but
you'll still
need to use 'at'

 (%i8) load("pdiff")$
 (%i9) fT : taylor(f(x,y),[x,y],[0,0],2)$

 (%i10) at(%,x=-1 , y=1);
 (%o10)
 (f[(0,2)](0,0)*y^2-2*f[(1,1)](0,0)*y+f[(2,0)](0,0))/2+f[(0,1)](0,0)*y-f[(1,0)](0,0)+f(0,0)

Welcome to Maxima; let us know if you have more questions.

Barton