-----maxima-bounces at math.utexas.edu wrote: -----
>Can I use taylor(...) with extra massaging to
>generate a formal expansion like;
>
>f(x + e) --> f(x) + e* 'diff( f(x), x, 1)
> + e^2 * 'diff( f(x), x, 2) / 2 + ...
>
>?? or can this be done with pdiff ?
I think pdiff makes these kind of calculations nicer, but depending on what
you need, maybe you don't need pdiff. Example:
(%i1) taylor(f(x + e),e,0,2);
(%o1)
f(x)+(at('diff(f(x+e),e,1),e=0))*e+((at('diff(f(x+e),e,2),e=0))*e^2)/2+...
Substituting a value for 'e' gives an error (maybe atvalue allows you to
do such things, I don't know).
(%i2) subst(e=1,%);
Attempt to differentiate with respect to a number: 1
Try again using pdiff:
(%i4) load(pdiff)$
(%i5) taylor(f(x + e),e,0,2);
(%o5) f(x)+f[(1)](x)*e+(f[(2)](x)*e^2)/2+...
(%i6) subst(e=1,%);
(%o6) f[(2)](x)/2+f[(1)](x)+f(x)
>What about 2D?
Multi-variable expansions aren't all that different:
(%i7) taylor(f(x + e1,y+e2),[e1,e2],0,1);
(%o7) f(x,y)+(f[(1,0)](x,y)*e1+f[(0,1)](x,y)*e2)+...
Barton (author of pdiff)