| 1234567891011121314151617181920212223242526272829 |
- # Lets show that div(f) = [P] - [∞]
- # So any divisor with supp(D) = {P},
- # with an effective size of 1 can be represented
- # by the horizontal line f = y - P.y
- q = 47
- K = GF(q)
- E = EllipticCurve(K, (0, 5))
- C = E.defining_polynomial()
- R.<x, y> = PolynomialRing(K)
- for i in range(100):
- P = E.random_point()
- Px, Py = P[0], P[1]
- # Skip points at infinity
- if P[2] == 0:
- continue
- assert P[2] == 1
- f = y - Py
- I = Ideal([C(x, y, 1), f])
- V = I.variety()
- print(P, V)
- assert len(V) == 1
- assert V[0][x] == Px
- assert V[0][y] == Py
|
