Prime divisors hyperelliptic curves

1. Sep 15, 2011

yavanna

Every divisor $D$ associated to a hyperelliptic curve over $\mathbb{F}_q$ can be represented by a couple of polynomials $D=div(a(x),b(x))$ (Mumfor representation):

A divisor $D$ is prime if $a(x)$ is irreducible over $\mathbb{F}_q$.
I'm trying to prove that a semi-reduced divisor can be written as a combination of prime divisors factoring $a(x)$:
if $a(x)=\prod a_{i}(x)^{c_i}$, then $D=\sum c_i div(a_i(x),y-b_i(x))$, where $b_i \equiv b \textit{mod}a_i$

I've some problems with $y-b_i(x)$, any ideas?

(I think the author of the article had some notation problems, if we express $D=div(a(x),b(x))$ it should be $D=\sum c_i div(a_i(x),b_i(x))$, where $D=div(a(x),b(x))$ means $D=gcd (div(a(x)),div(y-b(x)))$ )

Last edited by a moderator: Apr 26, 2017