gauss reduction algorithm and cycles

gaussreduction.py

def S((a,b,c), k=1):
    return (a, -2*a*k+b, a*k**2-b*k+c)


def T((a,b,c)):
    return (c,b,a)

x = (1,33,-21)
x = (7, 33, -8)
x = (13,13,-22)

# never changes in this process.  eveluate it once
D = x[1]**2 - 4*x[0]*x[2]

O = [x]
x = (x[2], -1*x[1], x[0])
c = 0

while True:
    while x[1] < 0 or 2*abs(x[2]) < np.sqrt(D) - x[1] or 2*abs(x[2]) > np.sqrt(D) + x[1]:
        x = S(x, -1*x[0]/abs(x[0])) 
        
    if x == O[0]:
        break  
    else:
        O += [x]
        x = (x[2], -1*x[1], x[0])
        
O

out.txt

[(13, 13, -22),
 (-22, 31, 4),
 (4, 33, -14),
 (-14, 23, 14),
 (14, 33, -4),
 (-4, 31, 22),
 (22, 13, -13),
 (-13, 13, 22),
 (22, 31, -4),
 (-4, 33, 14),
 (14, 23, -14),
 (-14, 33, 4),
 (4, 31, -22),
 (-22, 13, 13)]