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- K.<x, y> = GF(11)[]
- EC_A, EC_B = 4, 0
- C = y^2 - x^3 - EC_A*x - EC_B
- S = K.quotient(C).fraction_field()
- X, Y = S(x), S(y)
- foo = (X^2 - Y) / (X - 2)
- f, g = foo.numerator().lift(), foo.denominator().lift()
- I = ideal(C, f)
- J = ideal(C, g)
- load("ordp.sage")
- total_k = 0
- for info in I.variety():
- Px, Py = P = info[x], info[y]
- k = ordp(P, f)
- print(f"ordp(({Px}, {Py}), {f}) = {k}")
- total_k += k
- for info in J.variety():
- Px, Py = P = info[x], info[y]
- k = ordp(P, g)
- print(f"ordp(({Px}, {Py}), 1/({g})) = -{k}")
- total_k -= k
- print(f"ordp(∞, ({f})/({g}) = -{total_k}")
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