2nd try: Number of monomials in discriminant of a polynomial of degree n.

T. D. Noe noe at sspectra.com
Sat Dec 16 07:56:32 CET 2006


At 11:30 PM -0500 12/15/06, Victor S. Miller wrote:
>According to Magma, the sequence starts
>
>foo := > foo := [#Monomials(Numerator(Disc(n))) : n in [1..6]];
>
>[ 1, 2, 5, 16, 59, 246, 1103 ]
>
>I got this withe following program
>
>function Disc(n)
>	F := FunctionField(Rationals(),n);
>	R<x> := PolynomialRing(F);
>	f := x^n + &+[(F.i)*x^(n-i) : i in [1..n]];
>	return Discriminant(f);
>end function;
>
>[#Monomials(Numerator(Disc(n))) : n in [1..7]]


Victor has found A007878, the correct version of A039744.

Tony







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