# Revision history [back]

### 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 $f^* : \rightarrow \mathbb{F}_q (Y) \rightarrow \mathbb{F}_q (X)$ defined by $f^(\alpha) = \alpha \circ f$. The degree of $f$ is then defined to be $[\mathbb{F}_q (X) : f^ (\mathbb{F}_q (Y))]$. 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$f^*$ and degree of $f$? 2 None

### 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^* $$f^\ast : \rightarrow \mathbb{F}_q (Y) \rightarrow \mathbb{F}_q (X)$$ defined by$f^(\alpha) $f^\ast(\alpha) = \alpha \circ f$. The degree of $f$ is then defined to be $[\mathbb{F}_q (X) : f^ (\mathbb{F}_q f^\ast(\mathbb{F}_q (Y))]$. 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$f^*$ map $f^\ast$ and degree of $f$? 3 None

### 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 $$f^\ast : \rightarrow \mathbb{F}_q (Y) \rightarrow \mathbb{F}_q (X)$$ 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 $f$?