Re: extracting powers and coefficients from a polynomial

*To*: mathgroup at smc.vnet.net*Subject*: [mg49064] Re: [mg49040] extracting powers and coefficients from a polynomial*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 30 Jun 2004 05:34:11 -0400 (EDT)*References*: <200406290850.EAA18783@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 29 Jun 2004, at 17:50, AngleWyrm wrote: > I have made a formula that produces a polynomial expansion, and I wish > to > extract the powers and coefficients into a list. > > Expand[(Sum[x^i, {i, 6}])^3] > 1x^3 + 3x^4 + 6x^5 + 10x^6 + 15x^7 + 21x^8 + 25x^9 + 27x^10 + 27x^11 > + 25x^12 > + 21x^13 + 15x^14 + 10x^15 + 6x^16 + 3x^17 + 1x^18 > > How do I make a table of the powers and coefficents? > 3, 1 > 4, 3 > 5, 6 > 6, 10 > .... > > -- > AngleWyrm > The C++ hat random selection container: > http://home.comcast.net/~anglewyrm/hat.html > > > If you do not mind using an undocumented function then probably the simplest way is: Reverse[Flatten/@First[Internal`DistributedTermsList[f,x]]] {{3,1},{4,3},{5,6},{6,10},{7,15},{8,21},{9,25},{10,27},{11,27},{12,25},{ 13,21},{14,15},{15,10},{16,6},{17,3},{18,1}} Or you can use CoefficientList as follows: With[{l=CoefficientList[f,x]},Transpose[{Range[0,Length[l]-1],l}]] {{0,0},{1,0},{2,0},{3,1},{4,3},{5,6},{6,10},{7,15},{8,21},{9,25},{10,27} ,{ 11,27},{12,25},{13,21},{14,15},{15,10},{16,6},{17,3},{18,1}} Note that the first three terms given above have coefficient 0. One could drop all leading 0 coefficient terms like this: Flatten[Rest[Split[With[{ l=CoefficientList[f,x]},Transpose[{Range[0,Length[l]-1],l}]],#1[[ 2]]==#2[[2]]&]],1] {{3,1},{4,3},{ 5,6},{6,10},{7,15},{8,21},{9,25},{10,27},{11,27},{12,25},{13,21},{ 14,15},{15,10},{16,6},{17,3},{18,1}} Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**extracting powers and coefficients from a polynomial***From:*"AngleWyrm" <no_spam_anglewyrm@hotmail.com>