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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]
- # Homogenize f
- f = z^f.degree() * f(x/z, y/z, 1)
- 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))
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