Multivariate taylor



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

>I don't understand the result (or maybe only the notation) of
>multivariate taylor expansion of a formal function. I would expect the
>taylor expansion of f(x,y) to order 1 to be
>
>f(0,0) + x (df(x,y)/dx)(0,0) + y (df(x,y)/dy)(0,0)
>
>but what I understand of maxima's answer is
>
>f(0,0) + x (df(x,y)/dx)(0,y) + y (df(0,y)/dy)(0)

Maybe the at(xxx, y=0) in the last term alters the second term?

  (%i2) taylor(f(x,y),[x,y],[0,0],[1,1]);
  (%o2)
  f(0,0)+((at('diff(f(x,y),x,1),x=0))*x+(at('diff(f(0,y),y,1),y=0))*y)+...

Try loading pdiff --- things look different:

  (%i3) load(pdiff)$

  (%i4) taylor(f(x,y),[x,y],[0,0],[1,1]);
  (%o4) f(0,0)+(f[(1,0)](0,0)*x+f[(0,1)](0,0)*y)+...

Now everybody seems to be evaluated at (x = 0, y=0).

Barton