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CoefficientList[] option

• To: mathgroup@smc.vnet.net
• Subject: [mg12576] CoefficientList[] option
• From: Alex Bates <norman@galois.uoregon.edu>
• Date: Mon, 25 May 1998 14:24:47 -0400

Hello Mathgroup Users,

I want to print out the Q matrix used the the Berlecamp factorization
algorithm.  To generate the Matrix, I was using:

f[x_] := x^4 + x + 1	// the function I want to factor h[x_] := x^P-x	//
P large prime for x^P = x mode f

Table[CoefficientList[PolynomialMod[h[x^n], {f[x], P}], x], {n, 0, P}]

say P = 3

Then the Table prints out:

{{}, {0, 2, 0, 2}, {0, 0, 1, 2}, {0, 1, 2}}

But I want this to be a rectangular matrix (Q) so i can find the
NullSpace and find the irreducible factors (Berlecamp algorithm).

Is there a way to force CoefficientList[] to pad out its list to P+1
elements (so that the List it outputs corresponds to a rectangular
matrix?)
In other words, is there an option in CoefficientList[] to print out all
the coefficients up to a certain power of x even if they're zero?

Thanks,

Norman Bates

• Follow-Ups:
  • Re: CoefficientList[] option
    • From: Daniel Lichtblau <danl@wolfram.com>