having fun with elliptic curves, matplotlib display and cypari2 use of ellratpoints()

[hermann@stamm-wilbrandt.de]

Soon I will have to give seminar talk "Elliptic curves and Fermat’s 
proof" (case n=4) in "Fermat and Number Theory" seminar at Heidelberg 
University. I have read much on elliptic curves on this mailing list 
before, but now after having learned what they are I see the beauty.

Today I realized (not part of book chapters for my talk) that given two 
rational points with different x axis determines unique elliptic curve 
through them. A three prompts 10 minute chat with free gemini.google.com 
gave me a simple viewer that displays the elliptic curve and the two 
points passed as parameters.

Now after 2 more hours with Gemini, the coordinates can be rational, are 
displayed rational, zoom in/out is aspect preserving with automatic 
redraw. Finally I asked Gemini to add "Find ellratpoints" checkbox that 
gets enabled if cypari2 module is installed (if marked all rational 
points up to a specified height are displayed), and instead of 
specifying "x1 y1 x2 y2" alternatively "a b" can be specified for 
elliptic curve y^2=x^3+ax+b.

More details, screenshots and animation, link to unique_ec_ℚ.py, ... can 
be found here:
https://github.com/Hermann-SW/uni-heidelberg#Observation

Regards,

Hermann.