Re: accumulate coefficients of a polynomial

*To*: mathgroup at smc.vnet.net*Subject*: [mg102831] Re: [mg102813] accumulate coefficients of a polynomial*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Fri, 28 Aug 2009 05:43:04 -0400 (EDT)*References*: <200908280444.AAA28832@smc.vnet.net>

Hi, this will give you the general form of coefficients in terms of rules: In[1] = Clear[k]; coeffRules = List @@ ComplexExpand[Re[p[Exp[I Pi/k]]]] /. x_a*y : _ : 1 :> (x :> y) Out[1] = {a[10]:>1,a[9]:>Cos[\[Pi]/k],a[8]:>Cos[(2 \[Pi])/k],a[7]:>Cos[(3 \[Pi])/k],a[6]:>Cos[(4 \[Pi])/k],a[5]:>Cos[(5 \[Pi])/k],a[4]:>Cos[(6 \[Pi])/k],a[3]:>Cos[(7 \[Pi])/k],a[2]:>Cos[(8 \[Pi])/k],a[1]:>Cos[(9 \[Pi])/k],a[0]:>Cos[(10 \[Pi])/k]} This will compute the matrix of vectors of coefficients for 1<=k<=5 (5 instead of 20 just to keep the output size reasonable): In[2] = Table[Array[a, {10}] /. coeffRules, {k, 1, 5}] Out[2] = {{-1,1,-1,1,-1,1,-1,1,-1,1},{0,1,0,-1,0,1,0,-1,0,1},{-1,-(1/2),1/2,1,1/2,-(1/2),-1,-(1/2),1/2,1},{1/Sqrt[2],1,1/Sqrt[2],0,-(1/Sqrt[2]),-1,-(1/Sqrt[2]),0,1/Sqrt[2],1},{1/4 (1+Sqrt[5]),1/4 (-1+Sqrt[5]),1/4 (1-Sqrt[5]),1/4 (-1-Sqrt[5]),-1,1/4 (-1-Sqrt[5]),1/4 (1-Sqrt[5]),1/4 (-1+Sqrt[5]),1/4 (1+Sqrt[5]),1}} Regards, Leonid On Fri, Aug 28, 2009 at 8:44 AM, BHUPALA <bhupala at gmail.com> wrote: > I have generated a polynomial as > > p[z_] = Sum[a[k]*z^(10 - k), {k, 0, 10}] > > to give > > z^10 a[0] + z^9 a[1] + z^8 a[2] + z^7 a[3] + z^6 a[4] + z^5 a[5] + > z^4 a[6] + z^3 a[7] + z^2 a[8] + z a[9] + a[10] > > I want to substitute z = Exp[I Pi/k] where k varies from 1 to 20 and > for each k retain the coefficients of the real part as a vector. > > I used the following command for a single iteration (e.g k=6) > > ComplexExpand[Re[p[Exp[I Pi/6]]]]] > > But how to do it in a loop? > > Thanks for any help. > > Bhupala > >

**References**:**accumulate coefficients of a polynomial***From:*BHUPALA <bhupala@gmail.com>