mersenneforum.org - View Single Post - [Help] understanding about finding norm in non monic polynomials

canny · 2018-05-21, 03:11

Hi, I'm interested in algorithm, namely NFS (number field sieve).
So, the problem is that we're trying to sieve over the norm generated by a,b pairs in the form of algebraic number that is in the form of (a - bα) where α is the algebraic root of irreducible polynomial f. Say, in most of the references i've read, it's said that the norm will be F (a,b) = b^d*f(a/b). And as for monic polynomial, the norm isn't changing. However, if the polynomial isn't monic (say leading coefficient is some constant C), then the norm calculation would be different, in this case it will be N(a - bα) = (F(a,b))/c. I just wanted to make sure, is this true?

2018-05-21, 03:11	#1
canny "chun" May 2018 Indonesia 1 Posts	[Help] understanding about finding norm in non monic polynomials Hi, I'm interested in algorithm, namely NFS (number field sieve). So, the problem is that we're trying to sieve over the norm generated by a,b pairs in the form of algebraic number that is in the form of (a - bα) where α is the algebraic root of irreducible polynomial f. Say, in most of the references i've read, it's said that the norm will be F (a,b) = b^d*f(a/b). And as for monic polynomial, the norm isn't changing. However, if the polynomial isn't monic (say leading coefficient is some constant C), then the norm calculation would be different, in this case it will be N(a - bα) = (F(a,b))/c. I just wanted to make sure, is this true?