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/"Curve" function error: 'list' object is not callablehttps://ask.sagemath.org/question/57273/curve-function-error-list-object-is-not-callable/Hello!
I am trying to work with the curve constructor (particularly affine curves) in sage using their built in functions. I am using this page as reference: https://doc.sagemath.org/html/en/reference/curves/sage/schemes/curves/affine_curve.html
But when I try to define curves like below I get the `'list' object not callable` error message every time, even when I copy and paste code from the sage reference manual.
`A.<x,y> = AffineSpace(QQ, 2)`
`C = Curve(x^2 + y^2 -1)`
I understand that it probably thinks `Curve` is a list or something, but I'm not sure how to fix it?
Any help would be greatly appreciated!b17Tue, 25 May 2021 20:50:23 +0200https://ask.sagemath.org/question/57273/The modular tower of curves over a finite field.https://ask.sagemath.org/question/53092/the-modular-tower-of-curves-over-a-finite-field/I want to investigate the tower of modular curves $X(\ell^n) \to X(1)$ over a finite field $\mathbb F_q$ with $\ell \neq 0 0 \in \mathbb F_q$ and pullbacks of this tower by maps $C \to X(1)$.
In particular, I want to investigate the characteristic polynomial of the Frobenius on the $\ell$-adic cohomology. If I knew defining equations for $X(n)$ in terms of the parameter $t$ on $X(1)$, I guess I could do it but I am not sure... AsvinTue, 18 Aug 2020 07:55:32 +0200https://ask.sagemath.org/question/53092/