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Re: series expansions in two variables problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg39528] Re: series expansions in two variables problem
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Fri, 21 Feb 2003 04:08:23 -0500 (EST)
*Organization*: The University of Western Australia
*References*: <b329vc$b2q$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <b329vc$b2q$1 at smc.vnet.net>, mc799 at ic.ac.uk (Martin) wrote:
> I'm expanding an expression in two variables (sigma and epsilon, say),
> but am having trouble persuading Mathematica to chuck away terms of
> form epsilon*sigma.
>
> ie I'm getting
>
> A + B*sigma + C*epsilon + D*sigma*epsilon + O(sigma^2) + O(epsilon^2)
>
> and I'd like very much to lose the D terms.
The trick (which you will find in the MathGroup archive) is not to
expand in a series in both sigma and epsilon but to instead rescale the
variables by a parameter, say q, and then expand into a series in q,
truncating, and then setting q ->1. Here is a routine that does this:
Truncate[x_, p_List, n_] :=
Module[{q}, Normal[(x /. Thread[p -> q p]) + O[q]^n] /. q -> 1]
Here x is the expression, p is the List of variables and n is the
truncation order.
Truncate[a+ b sigma + c epsilon + d sigma epsilon, {sigma,epsilon},2]
Cheers,
Paul
--
Paul Abbott Phone: +61 8 9380 2734
School of Physics, M013 Fax: +61 8 9380 1014
The University of Western Australia (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009 mailto:paul at physics.uwa.edu.au
AUSTRALIA http://physics.uwa.edu.au/~paul
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