Here is my beginner attempt on computing algebraic structures.
Pain point: I'm stupid. While reading [The Arithmetic of Elliptic Curves by Silverman], I saw a lot of computations involving rational maps, order, etc. My goal is to write a helper to help me compute rational maps. (Or at least to see why it doesn't work.)
In ratmap.pl, the goal is to check whether a morphism is an isogeny, i.e. whether it maps $\mathcal{O}$ to $\mathcal{O}$.
Example. (III.4.5.)
Consider the following elliptic curves
$$ E_1 \colon y^2 = x^3 + ax^2 + bx, $$
and
$$ E_2 \colon Y^2 = X^3 - 2aX^2 + rX. $$
Define a map $\phi \colon (x, y) \to \left(\frac{y^2}{x^2}, \frac{y(b-x^2)}{x^2}\right)$ from $E_1$ to $E_2$. Then $\phi$ is an isogeny.