Re: four dimensioal polynomial composition

*To*: mathgroup at smc.vnet.net*Subject*: [mg57323] Re: four dimensioal polynomial composition*From*: dh <dh at metrohm.ch>*Date*: Wed, 25 May 2005 06:02:28 -0400 (EDT)*References*: <d6hfhg$dao$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Christoph, If I understand your question, then your problem is not the composition, but to extract all monomials with a given degree from a poly. Here is an example for this. We define some poly: p = Plus @@ Flatten@Table[(i + 0.3j)x^i y^j, {i, 0, 3}, {j, 0, 3}] and we want the coefficients of all monomials with degree: deg=2 First we extract all coefficients: cof = CoefficientList[p, {x, y}] The degree of a monomial is related to the position in the obove array. Note that position counts from 1 on: pos = Position[t, _?NumberQ] Now we select from pos those entries belonging to the given total degree: pos = Select[pos, ((Plus @@ # - 2) == deg) &] We must subtract 2 because degree counts from 0 and position from 1. Now we extract the coefficients: Extract[cof, pos] This gives the list of the searched coefficients. Note that the first entry belongs to x^0 y^deg, the second to x^1 y^deg-1 e.t.c. Sincerely, Daniel Christoph Lhotka wrote: > Hello ! > > I want to compose a four dimensional polynomial p(x,y,u,v) of some certain > degree N with four other polynomials x->px(x,y,u,v), y->py(x,y,u,v), > u->pu(x,y,u,v), v->pv(x,y,u,v) up to order N (p(px,py,pu,pv)) and extract all > monomials of some certain order, say M (with respect to lambda). For this > reason I introduce some artificial parameter lambda which holds terms together > of equal order. I implement the polynomials using the SeriesData (which now > has five expansion parameters) object and have the following question: > > Is there anywhere on the net some more detailed information of dealing with > multivariates Series in Mathematica, I have not found yet. > > Is there a better way, when dealing with polynomials? > > Christoph > > University of Vienna > Institute for Astronomy > mail. lhotka at astro.univie.ac.at >