Re: Rebuilding polygon from CoefficientList?

*To*: mathgroup at smc.vnet.net*Subject*: [mg20193] Re: [mg20164] Rebuilding polygon from CoefficientList?*From*: BobHanlon at aol.com*Date*: Tue, 5 Oct 1999 04:04:23 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Holger, reconstructPolynomial[coefMatrix_List, vars_List] := Module[{maxPwrs = Dimensions[coefMatrix] - 1, factors, k}, factors = Table[#[[1]]^k, {k, 0, #[[2]]}] & /@ Transpose[{vars, maxPwrs}]; Flatten[coefMatrix].Flatten[Outer[Times, Apply[Sequence, factors]]]]; poly = a*x^3*y + b*x^2*y^2*z + c*x*y^3*z^2 + d*z^2 + e*t*x*y*z; var = {x, y, z}; coef = CoefficientList[poly, var]; reconstructPolynomial[coef, var] == poly True var = {t, x, y, z}; coef = CoefficientList[poly, var]; reconstructPolynomial[coef, var] == poly True Bob Hanlon In a message dated 10/4/1999 3:10:53 AM, strauss at ika.ruhr-uni-bochum.de writes: >I have a mixed polynomial poly in several variables vars. > >cl = CoefficientList[poly, vars] > >gives a multi-dimensional matrix of coefficients. > >Can anyone help with an algorithm/expression that >re-constructs the original poly given cl and vars? >(In practice, I'd like to manipulate the coefficients before >reconstructing the polynomial; otherwise this wouldn't >make sense). >The algorithm must be able to handle any number of vars. >I've found a solutions for a small and fixed number of vars >using some ugly nested For loops. However, I suppose >that there must be a more efficient solution using some cute >matrix operations. >