Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Mar 5, 2017 #1
    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. jcsd
  3. Mar 5, 2017 #2

    fresh_42

    Staff: Mentor

  4. Mar 5, 2017 #3
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Is there an on-line table of genus of algebraic functions?
Loading...