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@@ -0,0 +1,48 @@
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+p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
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+Fp = GF(p)
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+E = EllipticCurve(Fp, [0, 7])
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+
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+K.<x> = PolynomialRing(Fp, implementation="generic")
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+L.<y> = PolynomialRing(K, implementation="generic")
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+
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+def call(f, P):
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+ Px, Py = P.xy()
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+ return f(x=Px, y=Py)
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+
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+def slope_intercept(P0, P1):
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+ P0x, P0y = P0.xy()
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+ P1x, P1y = P1.xy()
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+ m = (P1y - P0y) / (P1x - P0x)
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+ c = P1y - m*P1x
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+ return m, c
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+
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+inf = E(0, 1, 0)
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+
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+P0 = E(2638891549212558194816434702774699814912586136468438548683319413291233982670, 10140456388517236016202114238224306675726576846632714430386916682749918607464)
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+P1 = E(17532914127565625088989484000002092349237591241902561765149751398626236254705, 88418181982451178952779569856811854926376929222674054022068577993668451054968)
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+P2 = -(P0 + P1)
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+assert P0 + P1 + P2 == inf
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+
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+m, c = slope_intercept(P0, P1)
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+f = y - m*x - c
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+assert call(f, P0) == 0
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+assert call(f, P1) == 0
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+assert call(f, P2) == 0
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+
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+A0 = E(71667150045698532747085079020221438975232032539323499361837608460679887058944, 112531462156938649599975140073878402074313288452223046891973447679626205036672)
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+A1 = E(24400044380857008437858416414134907169391225728426050882076550827717815954208, 31119844425475844378953714282286295361574062544261840901985213408230446258932)
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+A2 = -(A0 + A1)
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+assert A0 + A1 + A2 == inf
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+
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+λ, μ = slope_intercept(A0, A1)
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+g = y - λ*x - μ
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+assert call(g, A0) == 0
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+assert call(g, A1) == 0
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+assert call(g, A2) == 0
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+
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+s = call(f, A0) * call(f, A1) * call(f, A2)
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+t = call(g, P0) * call(g, P1) * call(g, P2)
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+assert s == -t
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+print(s)
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+print(-t)
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+
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