- #1
jackmell
- 1,807
- 54
Hi,
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
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
Last edited: