Igor Schein on Tue, 1 Dec 1998 14:16:02 -0500

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nfdisc() performance


after Karim's latest patch fixed nfdisc(x^18+16) problem, I looked
into other polynomials of form x^18+n.  It turned out nfdisc is
extremely slow for n=(9*m)^2, where n is NOT a cube of an integer ( if
n is a cube, then x^18+n is reducible ). 

The first few *bad* polynomials are:
x^18+81 	(m=1)
x^18+324 	(m=2)
x^18+1296 	(m=4)
x^18+2025 	(m=5)

I looked at the \g output, it deals with polynomials with huge
coefficients in the process, but I don't really know the algorithm to
make an educated guess.  I was wondering if it's a short-coming of the
algorithm and can be improved, or it's expected and cannot be improved.



P.S.  BTW, I use this little hack to check whether the integer is a

iscube(n)=vecmax(Vec(factor(n))[2]%3)==0 \\ n>1

Is there a better way in GP to do that?