# Program to calculate the real roots
# of a cubic equation
# 
# It based on 
# A new approach to solving the cubic Cardan's
# solution revealed
# R.W.D. Nickalls
# The mathematical gazette, 1993, vol 77, pp. 354-359
#
# Fraga  6 Jun, 2010
# Fraga  8 Jun, 2015 program in python! :-)
# Fraga  23 Oct, 2020. In python 3.7
import sys
import math

def cubic_root( v ) : 
	signo = 1
	if v < 0.0 :
		signo = -1
		v = v * -1

	val = signo* math.exp( math.log(v)/3.0 )

	return( val )

n = len( sys.argv )
if n != 5 : 
	print( "Args: a b c d" )
	sys.exit(1)

a = float(sys.argv[1]) 
b = float(sys.argv[2])
c = float(sys.argv[3])
d = float(sys.argv[4])

xN = -b/(3.0*a)

yN = xN*( xN*(a*xN + b) + c ) + d
yN2 = yN*yN

delta2 = (b*b - 3.0*a*c)/(9.0*a*a) 
h2 = 4.0*a*a*delta2*delta2*delta2

print( "yN^2=", yN2, "h^2=", h2 )

if math.fabs(yN2 - h2) < 1e-8 :
	if math.fabs( yN2 ) < 1e-8 :
		print("Tres raices reales iguales en ", xN)

	else :
		print("Dos reales iguales y la tercera distinta")
		val = cubic_root( yN/(2.0*a) )
		r1 = xN + val
		r3 = xN - 2.0*val
		print("Dos raices en ", r1)
		print("Una raiz en ", r3)

elif yN2 > h2 :
	print("Una raiz real")
	v = math.sqrt( yN2 - h2 );
	v1 = cubic_root( (-yN + v)/(2*a) )
	v2 = cubic_root( (-yN - v)/(2*a) )

	r1 = xN + v1 + v2;
	print( "Raiz en ", r1 )
else :
	print( "Tres raices reales distintas" )

	delta = math.sqrt( delta2 )
	c = -yN/(2.0*a*delta2*delta)
	theta = math.acos( c )/3.0
	print( "Theta = ", theta )
	delta *= 2.0;
	r1 = xN + delta*math.cos( theta )
	r2 = xN + delta*math.cos( theta + 2.09439510266 )
	r3 = xN + delta*math.cos( theta + 4.18879020533 )
	print( "Raices: ", r1, r2, r3 )