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MathGroup Archive 2003

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Re: polynomial operations through CoefficientList

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44758] Re: polynomial operations through CoefficientList
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 25 Nov 2003 00:45:27 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <bps3jo$9pu$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

CoefficientAdd[lst1_, lst2_] /; Length[lst1] == Length[lst2] := lst1 +
lst2

CoefficientAdd[lst1_, lst2_] /; Length[lst1] > Length[lst2] :=
    CoefficientAdd[lst1, PadRight[lst2, Length[lst1], 0]]

CoefficientAdd[lst1_, lst2_] := CoefficientAdd[lst2, lst1]

and

p1[x_] := 1 + k1 x - 2 k2 x^2
p2[x_] := -2 - k3 x

lst1 = CoefficientList[p1[x], x];
lst2 = CoefficientList[p2[x], x];

CoefficientAdd[lst1, lst2]


will help you.

Regards
  Jens

Paolo Bientinesi wrote:
> 
> Hello,
> does anybody have 2 functions ready to multiply and add
> 2 polynomials directly from their CoefficientList's?
> 
> example: the polynomials I'm considering are
> p1[x_] := 1 + k1 x - 2 k2 x^2
> p2[x_] := -2 -k3 x
> 
> Given
> cf1 = {1,k1,-2 k2}
> and
> cf2 = {-2,-k3}
> 
> I would like to get the list
> {-2,-2 k1-k3,4 k2-k1 k3,2 k2 k3}
> for p1[x]*p2[x]
> 
> and the list
> {-1,k1-k3,-2 k2}
> for p1[x]+p2[x]
> 
> without performing operations like
> 
> CoefficientList[
>  cf1.Table[x^i,{i,0,Length[cf1]-1}]*
>  cf2.Table[x^i,{i,0,Length[cf2]-1}], x]
> 
> Thanks!
> --
> Paolo
> 
> pauldj at cs.utexas.edu                    paolo.bientinesi at iit.cnr.it


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