18.783 Problem Set 10 Problem 3f.sagews

def extend_table(T,g):
    n = len(T)
    h = g.reduced_form()
    d = {T[i]:i for i in range(0,n)}
    r = 1
    while not h in d:
        for i in range(0,n):
            T.append((h*T[i]).reduced_form())
        h = (g*h).reduced_form(); r = r+1
    return r,d[h]

D = -5291
T = [BinaryQF([1,1,1323])]
a = [BinaryQF([3,1,441]),BinaryQF([5,3,265]),BinaryQF([7,1,189])]
r = [0,0,0]
s = [0,0,0]
for i in range(len(a)):
    r[i],s[i]=extend_table(T,a[i])
assert len(T) == QuadraticField(D).class_number()
print "a =",a
print "r =",r
print "s =",s

a = [3*x^2 + x*y + 441*y^2, 5*x^2 + 3*x*y + 265*y^2, 7*x^2 + x*y + 189*y^2] r = [9, 2, 2] s = [0, 4, 6]