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MathGroup Archive 1995

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Re: Replacing terms and expanding one at a time

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1841] Re: Replacing terms and expanding one at a time
  • From: derwent.1 at nd.edu (John E. Derwent)
  • Date: Mon, 7 Aug 1995 20:25:19 -0400
  • Organization: University of Notre Dame

PolynomialRemainder[e /. rep, y^16, y] is flexible, pretty fast, and puts
the answer in a nice form.
John

In article <DCBxwo.75w at wri.com>, Stephen Corcoran <corcoran at news.ox.ac.uk>
wrote:

> Suppose I have an expression like
> 
> e = x^10,
> 
> where I want to replace x by something like
> 
> rep = {x-> a1 y + a2 y^2 + a3 y^3 + a4 y^4}
> 
> I then want to expand e, keeping terms up to say , order 15. I can do this
> by using:
> 
> e2 = Normal[Series[ e /. rep,{y,0,15}]]
> 
> Presumably, however, this is a relatively inefficient way of proceeding as it
> involves manipulation of the product of 10 4th degree polynomials.  Is there
> a way to replace one of the x's at a time, and then do the expansions,i.e.
> something like:
> 
> e2 = x^9 (a1 y + a2 y^2 + a3 y^3 + a4 y^4)
> e3 = x^8 (a1^2 y^2 + ..... + a4^2 y^8)
> e4 = x^7 (a1^3 y^3 + ..... + a4^3 y^12)
> e5 = x^6 (a1^4 y^4 + ..... + 4 a3 a4^3 y^15)
> ...
> and so on ?
> 
> If so, is there any better in terms of speed and/or memory usage?  Is this
> more or less what Mathematica does anyway?
> 
> Thanks.
> -------------------------------------------------------------------------
> Stephen Corcoran,               email:  corcoran at stats.ox.ac.uk (internet)
> Dept. of Statistics,                    corcoran at uk.ac.ox.stats (janet)
> University of Oxford,
> 1, South Parks Road             phone:  (01865) 272879
> OXFORD, OX1 3TG                 fax:    (01865) 272595
> --------------------------------------------------------------------------


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