Hyperelliptic Integrals to Elliptic Integrals

Thierry Combot

Consider a hyperelliptic integral $I=\int P/(Q\sqrt{S})dx$, $P,Q,S\in \mathbb{K}[x]$, with $[\mathbb{K}:\mathbb{Q}]<\infty$. When $S$ is of degree $\le 4$, such integral can be ca…