First I want to thank Robert for clarifying the problem [to me].
Apart from that, if the explicit form of the function f(x,y) has been specified before, you can use an alternative method:
define(ft(x,y),taylor(f(x,y),[x,y],[0,0],2]));
Then you can evaluate the value of the function ft(x,y):
ft(-1,1);
~Shahir
------- Original Message -------
From: Barton Willis <willisb at unk.edu>
To: mrestelli at gmail.com
Sent: 06/04/08, 15:46:51
Subject: Re: [Maxima] 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
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