Re: accumulate coefficients of a polynomial

*To*: mathgroup at smc.vnet.net*Subject*: [mg102832] Re: [mg102813] accumulate coefficients of a polynomial*From*: Adriano Pascoletti <adriano.pascoletti at dimi.uniud.it>*Date*: Fri, 28 Aug 2009 05:43:15 -0400 (EDT)*References*: <200908280444.AAA28832@smc.vnet.net>

Create a list of replacement rules: Table[{Rule[z, Exp[I Pi/k]]}, {k, 1, 20}] perform the replacements: Sum[a[k]*z^(10 - k), {k, 0, 10}] /. Table[{Rule[z, Exp[I Pi/k]]}, {k, 1, 20}] and take the real parts: ComplexExpand[ Re[Sum[a[k]*z^(10 - k), {k, 0, 10}] /. Table[{Rule[z, Exp[I Pi/k]]}, {k, 1, 20}]]] Adriano Pascoletti 2009/8/28 BHUPALA <bhupala at gmail.com> > 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>