In [24]:

    

from numpy import roots
from math import atan, fabs


    

In [34]:

    

def cubic (Qx, Qy, Ux, Uy):
    
    a = Uy
    b = (Ux + 2*Qy)
    c = (2*Qx - Uy)
    d = -Ux
    
    det = -4*b**3*d + b**2*c**2 -4*a*c**3 + 18*a*b*c*d - 27*a**2*d**2
    
    print det
    
    if (det < 0):
        answer = 'c'
        print answer
        
    if (det > 0):
        a = roots([a, b, c, d])
        a = a.real
        print a
        a = atan(a[0])/(fabs(atan(a[0]))) + atan(a[1])/(fabs(atan(a[1]))) + atan(a[2])/(fabs(atan(a[2])))
        
        if (a == 3.0):
            answer = 'b'
        if (a == 1.0):
            answer = 'b'
        if (a == -1.0):
            answer = 'a'
        print answer
        
    #return answer


    

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