I just found this and it blew my mind (he gives an elliptical curve to do multiplication). If I understand correctly (from reading the link and other things) the Abelian group he is using is $\mathbb{R}^*/\{10^n | n \in \mathbb{N}\}$ under multiplication of coset representatives. I want to graph these using my computer. I am very willing to do all the programming my self but I don't know how he does this. He says that he used "a transcendental function related to the Weierstrass P-function" and he expounds as to the general well known techniques he used to approximate this function. That's all fine and good but he didn't really go much further into this.
To be more precise I want to do the following.
Given a group operation on the reals $* : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$ compute the constants $a, b$ in elliptical curve $y^2 = x^3 + a \cdot x + b$ corresponding to the group $\mathbb{R}^*/\{10^n | n \in \mathbb{N}\}$ with group operation $(x H) *' (y H) = (x*y H)$.
Now of course approximation will be used but I think that I am familiar enough with numerical methods to be able to approximate about what ever I need (or I can ask a different question if I can't figure that out). What I do not know is the math behind finding those constants
So basically what is the math behind finding those constants?
edit: As pointed out $\mathbb{R}/10\mathbb{R}$ makes no sense because $\mathbb{R} = 10\mathbb{R}$. I'm sure this is a factor group because I can tell you what the cosets look like $\{x \cdot 10^n\ | n \in \mathbb{N}\}$ but I can't seem to figure out a better way to express this. I.E. 10 and 1 are in the same coset so the should be represented by the same point on the elliptical curve.
edit2: I think I got it. I just had to specify the coset in an unnatural way.