ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 13 Jul 2022 08:56:42 +0200Degree of a rational map and the corresponding map between function fieldshttps://ask.sagemath.org/question/63229/degree-of-a-rational-map-and-the-corresponding-map-between-function-fields/Let $X$ and $Y$ be two curves defined over $\mathbb{F}_q $ and $f:X \rightarrow Y$ be a separable rational map. Then there is field embedding
$$
f^\ast : \mathbb{F}_q (Y) \rightarrow \mathbb{F}_q (X)
$$ defined by
$f^\ast(\alpha) = \alpha \circ f$.
The degree of $f$ is then defined to be $[\mathbb{F}_q (X) : f^\ast(\mathbb{F}_q (Y))]$.
If I take two curves $X$ and $Y$ in sagemath over some $\mathbb{F}_q $ in sagemath, is there any way to automatically get the map $f^\ast$ and degree of $f$?DodulWed, 13 Jul 2022 08:56:42 +0200https://ask.sagemath.org/question/63229/