- #1
aheight
- 321
- 109
I believe the function ##w(z)## defined implicitly below has genus 116. Is there a means of independently confirming this? I believe the software Maple has a genus calculation but I don't have Maple. Is Maple the only other option?
Thanks.
$$
\begin{align*}
f(z,w)&=(8 z-4 z^2+5 z^7-4 z^{10}+4 z^{11}-8 z^{12})\\
&+(-7+6 z-5 z^2+8 z^5-9 z^7+2 z^{12})w\\
&+(-5 z^4-3 z^{10})w^2\\
&+(8-9 z+3 z^3+3 z^5+8 z^8+4 z^{12})w^3\\
&+(7-8 z^3+6 z^7+4 z^{10}-4 z^{11})w^4\\
&+(-4 z+6 z^4+6 z^5+9 z^6+6 z^9+9 z^{11}-7 z^{12})w^5\\
&+(-2+8 z-3 z^3-5 z^4+z^6+9 z^7+5 z^{11})w^6\\
&+(3 z^3+9 z^5+5 z^6+9 z^8)w^7\\
&+(8+2 z^2+3 z^7+8 z^8-2 z^{11}+7 z^{12})w^8\\
&+(z-2 z^3-2 z^4+7 z^5-6 z^9)w^9\\
&+(9 z-9 z^2+z^4+z^6+9 z^8-7 z^9-7 z^{11})w^{10}\\
&+(-4-3 z^2+3 z^3+z^5+3 z^6+7 z^8)w^{11}\\
&+(-8 z+z^4)w^{12}=0
\end{align*}
$$
Thanks.
$$
\begin{align*}
f(z,w)&=(8 z-4 z^2+5 z^7-4 z^{10}+4 z^{11}-8 z^{12})\\
&+(-7+6 z-5 z^2+8 z^5-9 z^7+2 z^{12})w\\
&+(-5 z^4-3 z^{10})w^2\\
&+(8-9 z+3 z^3+3 z^5+8 z^8+4 z^{12})w^3\\
&+(7-8 z^3+6 z^7+4 z^{10}-4 z^{11})w^4\\
&+(-4 z+6 z^4+6 z^5+9 z^6+6 z^9+9 z^{11}-7 z^{12})w^5\\
&+(-2+8 z-3 z^3-5 z^4+z^6+9 z^7+5 z^{11})w^6\\
&+(3 z^3+9 z^5+5 z^6+9 z^8)w^7\\
&+(8+2 z^2+3 z^7+8 z^8-2 z^{11}+7 z^{12})w^8\\
&+(z-2 z^3-2 z^4+7 z^5-6 z^9)w^9\\
&+(9 z-9 z^2+z^4+z^6+9 z^8-7 z^9-7 z^{11})w^{10}\\
&+(-4-3 z^2+3 z^3+z^5+3 z^6+7 z^8)w^{11}\\
&+(-8 z+z^4)w^{12}=0
\end{align*}
$$