Every divisor [itex]D[/itex] associated to a hyperelliptic curve over [itex]\mathbb{F}_q[/itex] can be represented by a couple of polynomials [itex]D=div(a(x),b(x))[/itex] (Mumfor representation):(adsbygoogle = window.adsbygoogle || []).push({});

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A divisor [itex]D[/itex] is prime if [itex]a(x)[/itex] is irreducible over [itex]\mathbb{F}_q[/itex].

I'm trying to prove that a semi-reduced divisor can be written as a combination of prime divisors factoring [itex]a(x) [/itex]:

if [itex]a(x)=\prod a_{i}(x)^{c_i} [/itex], then [itex]D=\sum c_i div(a_i(x),y-b_i(x))[/itex], where [itex]b_i \equiv b \textit{mod}a_i[/itex]

I've some problems with [itex]y-b_i(x)[/itex], any ideas?

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

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# Prime divisors hyperelliptic curves

Can you offer guidance or do you also need help?

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