RE: extracting powers and coefficients from a polynomial
- To: mathgroup at smc.vnet.net
- Subject: [mg49066] RE: [mg49040] extracting powers and coefficients from a polynomial
- From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
- Date: Wed, 30 Jun 2004 05:34:13 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
>-----Original Message----- >From: AngleWyrm [mailto:no_spam_anglewyrm at hotmail.com] To: mathgroup at smc.vnet.net >Sent: Tuesday, June 29, 2004 10:50 AM >To: mathgroup at smc.vnet.net >Subject: [mg49066] [mg49040] extracting powers and coefficients from a polynomial > > >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 > > In[9]:= s = Sum[x^i, {i, 6}]^3 In[10]:= {Coefficient[s, x, #], #} & /@ Range[0, Exponent[s, x]] Out[10]= {{0, 0}, {0, 1}, {0, 2}, {1, 3}, {3, 4}, {6, 5}, {10, 6}, {15, 7}, {21, 8}, {25, 9}, {27, 10}, {27, 11}, {25, 12}, {21, 13}, {15, 14}, {10, 15}, {6, 16}, {3, 17}, {1, 18}} Perhaps delete the elements with 0 coefficient and apply TableForm. -- Hartmut Wolf