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