The Virtues of Collect[--]
- To: mathgroup at smc.vnet.net
- Subject: [mg35239] The Virtues of Collect[--]
- From: AES <siegman at stanford.edu>
- Date: Wed, 3 Jul 2002 05:14:55 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Appended below is an example of what Collect[expr, h, Simplify] just
did for me.
Thanks to David Park and Andrzej Kozlowski for teaching me about this.
I wish Collect[--] was mentioned as one of the "See Also"'s under the
Series Help message -- and I wonder a bit why Mathematica doesn't do
this kind of elementary simplification of the Series coefficients
automatically.
In[30]:=
fS[d_,h_] = Series[ f[d, h], {h,0,2} ] // Normal
Out[30]=
((((2 + d)*(d - d^2))/(-d + d^2) + (1/2)*(-d + d^2)*((4*d)/(-d + d^2)^2
+ (2*(2 + d))/(-d + d^2)))*h)/(2*d) +
(-(((-1 - d)*(((2 + d)*(d - d^2))/(-d + d^2) + (1/2)*(-d + d^2)*
((4*d)/(-d + d^2)^2 + (2*(2 + d))/(-d + d^2))))/(2*d^2)) +
((-d + d^2)*((4*(-1 - d))/(-d + d^2)^2 + (2 + d)^2/(-d + d^2)^2 -
(1/4)*((4*d)/(-d + d^2)^2 + (2*(2 + d))/(-d + d^2))^2))/(4*d))*h^2
In[32]:=
Collect[ fS[d, h], h, Simplify ]
Out[32]=
(1 / (-d + d^2)) * h - ((-1 + d + d^2) / (-1 + d)^3*d^2)) * h^2