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 --------------------------------------------------------------------------