[Date Index]
[Thread Index]
[Author Index]
Replacing terms and expanding one at a time
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg1804] Replacing terms and expanding one at a time
*From*: Stephen Corcoran <corcoran at news.ox.ac.uk>
*Date*: Mon, 31 Jul 1995 23:08:04 -0400
*Organization*: Oxford University
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
--------------------------------------------------------------------------
Prev by Date:
**behaviour of N[0]**
Next by Date:
**Re: RealDigits**
Previous by thread:
**behaviour of N[0]**
Next by thread:
**Re: Replacing terms and expanding one at a time**
| |