Example: Smooth quartic over a finite field
We construct the Jacobian J of the curve
C : x4
+ 2y4
+ x3
− 3xy − 2 = 0
over F293 , and generate a random point on J.
J = smoothplanepicinit(x^4+2*y^4+x^3-3*x*y-2,29,3)
W = picrand(J)
picmember(J,W)
piciszero(J,W)
W2 = picrand(J);
piceq(J,W,W2)
picadd(J,W,W2)
Hyperelliptic and superelliptic curves are also available.
We plan to implement general curves; the only missing
ingredient is Riemann-Roch spaces.
Nicolas Mascot p-adic computation of Galois representations