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@@ -0,0 +1,96 @@
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+def is_normal(f):
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+ a, b, c = f
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+ return -a < b <= a
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+
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+def is_reduced(f):
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+ a, b, c = f
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+ return is_normal(f) and (a < c or (a == c and b >= 0))
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+
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+def reduce(f):
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+ a, b, c = f
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+ while not is_reduced((a, b, c)):
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+ if a > c or (a == c and b < 0):
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+ a, b, c = c, -b, a
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+ elif a < c:
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+ if b <= -a:
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+ a, b, c = a, b + 2*a, c + b + a
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+ else:
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+ assert b > a
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+ a, b, c = a, b - 2*a, c - b + a
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+ else:
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+ assert a == c and b >= 0
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+ a, b, c = a, b - 2*a, c - b + a
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+ return a, b, c
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+
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+def lincong(a, b, m):
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+ # 1
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+ g, d, e = xgcd(a, m)
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+ assert g == gcd(a, m)
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+ assert d*a + e*m == g
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+
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+ # 2
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+ q = floor(b/g)
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+ r = b % g
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+
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+ # 3
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+ if r != 0:
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+ return None
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+
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+ # 4
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+ μ = q*d % m
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+ υ = m/g
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+
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+ return μ, υ
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+
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+# Composition algo taken from chia class groups document
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+def compose(f1, f2):
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+ a, b, c = f1
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+ α, β, γ = f2
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+
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+ # 1
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+ g = (b + β)/2
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+ h = -(b - β)/2
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+ w = gcd([a, α, g])
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+
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+ # 2
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+ j = w
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+ s = a/w
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+ t = α/w
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+ u = g/w
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+
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+ # 3
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+ if (vals := lincong(t*u, h*u + s*c, s*t)) is None:
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+ return None
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+ μ, υ = vals
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+
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+ # 4
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+ if (vals := lincong(t*υ, h - t*μ, s)) is None:
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+ return None
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+ λ, _ = vals
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+
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+ # 5
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+ k = μ + υ*λ
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+ l = (k*t - h)/s
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+ m = (t*u*k - h*u - c*s)/(s*t)
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+
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+ # 6
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+ A = s*t
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+ B = j*u - (k*t + l*s)
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+ C = k*l - j*m
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+
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+ # 7
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+ f3 = A, B, C
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+ return reduce(f3)
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+
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+# Class number = 2
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+d = -5
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+D = 4*d
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+
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+e = (1, 0, 5)
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+a = (2, 2, 3)
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+
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+print(compose(e, e))
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+print(compose(e, a))
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+print(compose(a, e))
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+print(compose(a, a))
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+
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