# I Is there an on-line table of genus of algebraic functions?

1. Mar 5, 2017

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Hi,

Given the algebraic function $w(z)$ defined implicitly as $f(z,w)=a_0(z)+a_1(z)w+a_2(z)w^2+\cdots+a_n(z)w^n=0$,
is there any on-line table of genus for them? Haven't been able to find anything. I am writing some code and would like to check it against a standard source. For example,
$f(z,w)=(z^4)+(2 z^2+z^4)w+(1+z^2+z^3)w^2+(z)w^3+(1/4-z/2)w^4+(-(1/2))w^5$ has genus of 1 according to my calculations. And $f(z,w)=(2+3 z-z^2)+(z^3+9 z^4)w+(-z-7 z^4)w^2+(-3 z)w^3+(2+4 z-4 z^3)w^4+(-8+z^2-7 z^3+3 z^4)w^5$ has genus of 12. Not sure my calculations are correct. I am using the formula:

$g=1/2 \sum_{p} (r-1) -n+1$

Might be useful to have an on-line table I think. What do you guys think?

Thanks,

Last edited: Mar 5, 2017
2. Mar 5, 2017

3. Mar 5, 2017