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accumulate coefficients of a polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102813] accumulate coefficients of a polynomial
  • From: BHUPALA <bhupala at gmail.com>
  • Date: Fri, 28 Aug 2009 00:44:18 -0400 (EDT)

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


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