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show how to calculate intersection_multiplicity of point on elliptic curve: otherwise known as the order of vanishing - ord_P(f)

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narodnik
2022-07-20 12:56:12 +02:00
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script/research/ec/intersection-multiplicity.sage Normal file
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# Calculate intersection multiplicity of a point in sage
q = 47
K = GF(q)
E = EllipticCurve(K, (0, 5))
Q = E(10, 26)
C = E.defining_polynomial()
R.<x, y, z> = PolynomialRing(K)
f = y - Q[1] * z
P.<x,y,z> = ProjectiveSpace(K, 2)
X = P.subscheme([C(x, y, z)])
Y = P.subscheme([f(x, y, z)])
Q = X([Q[0], Q[1]])
print(Q.intersection_multiplicity(Y))