Hi Dominik, Chalk it up to different conventions. I am thinking of a typical modulus function for which the input is of the same type as the output; reals to reals, rationals to rationals, complex to complex, (Z/pZ) to (Z/pZ), etc. Then: Mod[2/5,23] = 2/5. There is another function QtoF[q,p] which takes input rational q and finds the correct element from (Z/pZ). This function QtoF composes three or four elemental functions, including the typical Mod function and an arithmetic table.
We can agree that lines wrap the torus nicely but cubic or quartic curves do not. Given three points on the same line, we can agree that these points may also be points on one elliptic curve up to a composition of Mod and QtoGF. My contention is that: If you want to represent the solutions as an intersection geometry on a torus over (Z/pZ)^2, in general you will need three elliptic curves f1, f2, f3 and two integers (n,m) related by f1 +n*p = f2 + m*p = f3. A torus drawing such as you propose could be nice if you are careful with this issue about Mod & QtoGF. The lines do wrap nicely. However you may encounter interdisciplinary difficulties with complex people who define elliptic curve tori in terms of the time-parameterization problem for reducing C^2 ----> C . Thanks for your interest, I will remember to send you a copy of my current writing effort when its finally finished. In these times interdisciplinary efforts do not happen quickly, especially as math, physics and computer science are all subjects with different languages and purposes. For the sake of developing perspective, it's nice to talk to another enthusiast who is involved with actual details of implementation. Back to writing . . . Cheers, you too! Brad
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