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You guys know of any (software) function which accepts as input an aribtrary algebraic function, then computes the genus as output?

Here's an aribtrary one:

[tex](-9+8 z^2-6 z^4)\text{}+(6 z-6 z^4)w+(-6+2 z^3)w^2+(1-7 z+5 z^5)w^3+(-7 z-8 z^2-3 z^3-7 z^5)w^4+(9-8 z-z^2-9 z^3+5 z^4)w^5=0[/tex]

What's the genus? I don't know.

I count 43 singular points and I suppose if I had to, I could manually (numerically) compute the ramification around each to determine the genus. Is this the only way to compute the genus for this function?

Edit:

I did that numerical computation, and using

[tex]g=1/2 \sum (r-1)-n+1[/tex]

arrived at a genus of 16. Anyone feel like checking this for me?

Thanks,

Jack

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# Genus of aribtrary algebraic function

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