#On the name of ALLAH and may the blessing and peace of Allah
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Author : Fouad Teniou
#Date : 10/01/09
#version :2.4
"""Solving polynomial equations involve using long and synthetic division.
I applied in my program Cubic.py, however, the synthetic division.
Finding the integers and rational zeros (a) of a polynomial p(x), if any,
shows us that (x - a)s are factors of p(x) and p(x)/(x - a) = q(x)
therefore p(x) can be written p(x) = (x - a)q(x)"""
from Quadratic import *
class Cubic(object):
""" Class that represent a Cubic Polynomial Equation
with a,b,c,d properties"""
def __init__(self,a,b,c,d):
""" Cubic constructor takes a,b,c,d coefficients """
self.__a = a
self.__b = b
self.__c = c
self.__d = d
self.signb = self._checkSign(self.__b)
self.signc = self._checkSign(self.__c)
self.signd = self._checkSign(self.__d)
def __str__(self):
""" String representation of Cubic Polynomial Equation"""
try:
self.c1 = Cubic.syntheticDivision(self)[0]
self.c2 = Cubic.syntheticDivision(self)[1]
if self.c1 == float and self.c2 == float:
self.c3 ="-"
self.c4 ="+"
else :
self.c3 = self._checkSign(float(Cubic.syntheticDivision(self)[0])*-1)
self.c4 = self._checkSign(float(Cubic.syntheticDivision(self)[1])*-1)
if self.__d == 0:
return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx = 0 \n \
\n<The linear factorization : p(x) = %sx(x%s%s)(x%s%s) \n\
" % (self.__a,chr(252),self.signb,self.__b,chr(253),
self.signc,self.__c,self.__a,self.c3,-1*float(self.c1),
self.c4,-1*float(self.c2))
else :
if self.__a == 1:
for i in Cubic.integerZero(self):
if (((self.__a*(i**3)) + (self.__b*(i**2))+ (self.__c*i )+ self.__d == 0)
and float(i) != float(self.c2) and float(i) != float(self.c1)):
return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx %s %s = 0 \
\n\n<The integers zeros are :\n\n%s\n \
\n<The linear factorization : p(x) = (x%s%s)(x%s%s)(x%s%s) \n\
" % (self.__a,chr(252),self.signb,self.__b,chr(253),self.signc,
self.__c,self.signd,self.__d,Cubic.integerZero(self),self.c3,
-1*float(self.c1),self.c4,-1*float(self.c2),(self._checkSign(-1*i)),-1*i)
return "\n<None of the integers zeros %s \n\n checks p(x) = %sx%s %s %sx%s %s %sx %s %s = 0\n\n " \
% (Cubic.integerZero(self),self.__a,chr(252),self.signb,self.__b,chr(253),self.signc,self.__c,
self.signd,self.__d)
else :
for j in Cubic.nonintegersRationalZero(self)[1]:
if ((self.__a*(float(str(j))**3)) + (self.__b*(float(str(j))**2))+
(self.__c*float(str(j)) )+ self.__d == 0.00):
return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx %s %s = 0 \
\n\n<The integers Zeros are :\n\n %s \
\n\n<The nonintegers Rational Zeros are :\n\n %s \
\n<The linear factorization : p(x) = (x%s%s)(x%s%s)(x%s%s) \n\
" % (self.__a,chr(252),self.signb,self.__b,chr(253),self.signc,self.__c,
self.signd,self.__d,Cubic.integerZero(self),nonintegersRationalZero(self)[0],
self.c3,-1*float(self.c1),self.c4,-1*float(self.c2),(self._checkSign(-1*j)),-1*j)
return "\n<None of the non integers zeros %s \n\n checks p(x) = %sx%s %s %sx%s %s %sx %s %s = 0\n\n" \
% (Cubic.nonintegersRationalZero(self)[0],self.__a,chr(252),self.signb,self.__b,
chr(253),self.signc,self.__c,self.signd,self.__d)
except TypeError:
if self.__a == 1:
raise "\n<complex solutions \n\n<The integers zeros are %s " \
% Cubic.integerZero(self)
else :
raise "\n<complex solutions \n\n<The nonintegers zeros are %s " \
% Cubic.nonintegersRationalZero(self)[0]
def get_a(self):
""" Get method for _a attribute """
return self.__a
def set_a(self,value):
""" Set method for _a attribute """
self.__a = value
def del_a(self):
"""Delete method for _a attribute"""
del self.__a
#Create a property
_a = property(get_a,set_a,del_a,"a coefficient")
def get_b(self):
""" Get method for _b attribute """
return self.__b
def set_b(self,value):
""" Set method for _b attribute """
self.__b = value
def del_b(self):
"""Delete method for D attribute"""
del self.__b
#Create a property
_b = property(get_b,set_b,del_b,"b coefficient")
def get_c(self):
""" Get method for _c attribute """
return self.__c
def set_c(self,value):
""" Set method for _c attribute """
self.__c = value
def del_c(self):
"""Delete method for _c attribute"""
del self.__c
#Create a property
_c = property(get_c,set_c,del_c,"c coefficient")
def get_d(self):
""" Get method for _d attribute """
return self.__d
def set_d(self,value):
""" Set method for _d attribute """
self.__d = value
def del_d(self):
"""Delete method for F attribute"""
del self.__d
#Create a property
_d = property(get_d,set_d,del_d,"d coefficient")
def _checkSign(self,value):
""" Utility method to check the values's sign
and return a sign string"""
if value >= 0:
return "+"
else :
return ""
def integerZero(self):
""" Computes Integers zeros of d coefficient """
res = []
for item in range (1,abs(self.__d)+1):
if self.__d%item == 0:
res.append(item)
res.append(-1*item)
return res
def nonintegersRationalZero(self):
""" Computes noninteger rational zeros """
res1 = []
res2 = []
res3 = []
res4 = []
for b in range(1,abs(self.__a)+1):
if self.__a%b == 0:
res1.append(b)
for i in Cubic.integerZero(self):
if i>0:
for j in res1:
if i%j!=0:
res2.append( "%2.2f" % ((i)/float(j)) ),res2.append( "%2.2f" % ((-i)/float(j)) )
for x in res2:
if res2.count(x)>1:
res2.remove(x)
if x == ("%2.2f" % ((i)/float(j))):
res3.append("%d/%d" % (i,j)),res3.append("%d/%d" % (-i,j))
res4.append("%d/%d" % (i,j)),res4.append("%d/%d" % (-i,j))
for w in res3:
if w in res4:
res4.remove(w)
return (res4,res2)
def syntheticDivision(self):
""" Computes coefficients A,B,C by synthetic division """
assert self.__a != 0,"(a) coefficient should be differtent than zero"
self._A = self.__a
self._B = self.__b
self._C = self.__c
y = Quadratic()
if self.__d != 0 and (self.__b**2 - 4*(self.__a *self.__c))>=0:
for i in Cubic.integerZero(self):
if (self.__a*((i)**3)) + (self.__b*((i)**2) )+(self.__c*(i) )+ self.__d == 0:
self._A = self.__a
self._B = self.__b + self._A*i
self._C = self.__c + self._B*i
y(a=self._A,b=self._B,c=self._C)
return Quadratic.__call__(y)
else:
y(a=self._A,b=self._B,c=self._C)
return Quadratic.__call__(y)
if __name__ == "__main__":
cubic1 = Cubic(1,3,-7,-21)
print cubic1
print
cubic5 = Cubic(1,-3,-13,15)
print cubic5
print
cubic2 = Cubic(1,2,-7,-10)
print cubic2
print
cubic3 = Cubic(5,-1,-2,0)
print cubic3
print
cubic4 = Cubic(2,-6,-13,18)
print cubic4
print
cubic4 = Cubic(2,3,-4,-3)
print cubic4
print
################################################################################################
#c:\hp\bin\Python>python "C:\Documents\Programs\Cubic.py"
#<Cubic Equation: p(x) = 1x³ + 3x² -7x -21 = 0
#<The integers zeros are :
#[1, -1, 3, -3, 7, -7, 21, -21]
#<The linear factorization : p(x) = (x-2.65)(x+2.65)(x+3)
#<Cubic Equation: p(x) = 1x³ -3x² -13x + 15 = 0
#<The integers zeros are :
#[1, -1, 3, -3, 5, -5, 15, -15]
#<The linear factorization : p(x) = (x-1.0)(x+3.0)(x-5)
#<None of the integers zeros [1, -1, 2, -2, 5, -5, 10, -10]
# checks p(x) = 1x³ + 2x² -7x -10 = 0
#<Cubic Equation: p(x) = 5x³ -1x² -2x = 0
#<The linear factorization : p(x) = 5x(x-0.74)(x+0.54)
#<None of the non integers zeros ['1/2', '-1/2', '3/2', '-3/2', '9/2', '-9/2']
#checks p(x) = 2x³ -6x² -13x + 18 = 0
#<None of the non integers zeros ['1/2', '-1/2', '3/2', '-3/2']
#checks p(x) = 2x³ + 3x² -4x -3 = 0
#c:\hp\bin\Python
##########################################################################################
#Version : Python 3.2
#from Quadratic5_7 import *
#class Cubic(object):
# """ Class that represent a Cubic Polynomial Equation
# with a,b,c,d properties"""
#
# def __init__(self,a,b,c,d):
# """ Cubic constructor takes a,b,c,d coefficients """
#
# self.__a = a
# self.__b = b
# self.__c = c
# self.__d = d
#
# self.signb = self._checkSign(self.__b)
# self.signc = self._checkSign(self.__c)
# self.signd = self._checkSign(self.__d)
#
# def __str__(self):
# """ String representation of Cubic Polynomial Equation"""
#
# try:
# self.c1 = Cubic.syntheticDivision(self)[0]
# self.c2 = Cubic.syntheticDivision(self)[1]
# if self.c1 == float and self.c2 == float:
# self.c3 ="-"
# self.c4 ="+"
# else :
# self.c3 = self._checkSign(float(Cubic.syntheticDivision(self)[0])*-1)
# self.c4 = self._checkSign(float(Cubic.syntheticDivision(self)[1])*-1)
#
#
# if self.__d == 0:
# return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx = 0 \n \
# \n<The linear factorization : p(x) = %sx(x%s%s)(x%s%s) \n\
# " % (self.__a,chr(179),self.signb,self.__b,chr(178),
# self.signc,self.__c,self.__a,self.c3,-1*float(self.c1),
# self.c4,-1*float(self.c2))
#
# else :
# if self.__a == 1:
# for i in Cubic.integerZero(self):
# if (((self.__a*(i**3)) + (self.__b*(i**2))+ (self.__c*i )+ #self.__d == 0)
# and float(i) != float(self.c2) and float(i) != float(self.c1)):
# return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx %s %#s = 0 \
# \n\n<The integers zeros are :\n\n%s\n \
# \n<The linear factorization : p(x) = (x%s%s)(x%s%s)(x%s%s) \n\
# " % (self.__a,chr(179),self.signb,self.__b,chr(178),self.signc,
# self.__c,self.signd,self.__d,Cubic.integerZero(self),self.c3,
# -1*float(self.c1),self.c4,-1*float(self.c2),(self._checkSign(-1*i)),-1*i)
# return "\n<None of the integers zeros %s \n\n checks p(x) = %sx%s %s #%sx%s %s %sx %s %s = 0\n\n " \
# % (Cubic.integerZero(self),self.__a,chr(179),self.signb,self.__b,chr(178),self.signc,self.__c,
# self.signd,self.__d)
#
# else :
# for j in Cubic.nonintegersRationalZero(self)[1]:
# if ((self.__a*(float(str(j))**3)) + (self.__b*(float(str(j))**2))#+
# (self.__c*float(str(j)) )+ self.__d == 0.00):
# return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx %s %#s = 0 \
# \n\n<The integers Zeros are :\n\n %s \
# \n\n<The nonintegers Rational Zeros are :\n\n %s \
# \n<The linear factorization : p(x) = (x%s%s)(x%s%s)(x%s%#s) \n\
# " % (self.__a,chr(179),self.signb,self.__b,chr(178),self.signc,self.__c,
# self.signd,self.__d,Cubic.integerZero(self),nonintegersRationalZero(self)[0]
# self.c3,-1*float(self.c1),self.c4,-1*float(self.c2),(self._checkSign(-1*j)),-1*j)
# return "\n<None of the non integers zeros %s \n\n checks p(x) = %sx%#s %s %sx%s %s %sx %s %s = 0\n\n" \
# % (Cubic.nonintegersRationalZero(self)[0],self.__a,chr(179),self.signb,self.__b,
# chr(178),self.signc,self.__c,self.signd,self.__d)
# except TypeError:
# if self.__a == 1:
# raise "\n<complex solutions \n\n<The integers zeros are %s " \
# % Cubic.integerZero(self)
# else :
# raise "\n<complex solutions \n\n<The nonintegers zeros are %s " \
# % Cubic.nonintegersRationalZero(self)[0]
#
# def get_a(self):
# """ Get method for _a attribute """
#
# return self.__a
#
# def set_a(self,value):
# """ Set method for _a attribute """
#
# self.__a = value
#
# def del_a(self):
# """Delete method for _a attribute"""
#
# del self.__a
# #Create a property
# _a = property(get_a,set_a,del_a,"a coefficient")
# def get_b(self):
# """ Get method for _b attribute """
#
# return self.__b
#
# def set_b(self,value):
# """ Set method for _b attribute """
#
# self.__b = value
#
# def del_b(self):
# """Delete method for D attribute"""
#
# del self.__b
#
# #Create a property
# _b = property(get_b,set_b,del_b,"b coefficient")
#
# def get_c(self):
# """ Get method for _c attribute """
#
# return self.__c
#
# def set_c(self,value):
# """ Set method for _c attribute """
#
# self.__c = value
#
# def del_c(self):
# """Delete method for _c attribute"""
del self.__c
# #Create a property
# _c = property(get_c,set_c,del_c,"c coefficient")
#
# def get_d(self):
# """ Get method for _d attribute """
# return self.__d
# def set_d(self,value):
# """ Set method for _d attribute """
#
# self.__d = value
#
# def del_d(self):
# """Delete method for F attribute"""
#
# del self.__d
#
# #Create a property
# _d = property(get_d,set_d,del_d,"d coefficient")
#
# def _checkSign(self,value):
# """ Utility method to check the values's sign
# and return a sign string"""
#
# if value >= 0:
# return "+"
# else :
# return ""
#
# def integerZero(self):
# """ Computes Integers zeros of d coefficient """
#
# res = []
# for item in range (1,abs(self.__d)+1):
# if self.__d%item == 0:
# res.append(item)
# res.append(-1*item)
# return res
#
# def nonintegersRationalZero(self):
# """ Computes noninteger rational zeros """
#
# res1 = []
# res2 = []
# res3 = []
# res4 = []
#
# for b in range(1,abs(self.__a)+1):
# if self.__a%b == 0:
# res1.append(b)
# for i in Cubic.integerZero(self):
# if i>0:
# for j in res1:
# if i%j!=0:
# res2.append( "%2.2f" % ((i)/float(j)) ),res2.append( "%2.2f" % ((-i)/float(j)) )
# for x in res2:
# if res2.count(x)>1:
# res2.remove(x)
# if x == ("%2.2f" % ((i)/float(j))):
# res3.append("%d/%d" % (i,j)),res3.append("%d/%d" % (-i,j))
# res4.append("%d/%d" % (i,j)),res4.append("%d/%d" % (-i,j))
# for w in res3:
# if w in res4:
# res4.remove(w)
# return (res4,res2)
#
# def syntheticDivision(self):
# """ Computes coefficients A,B,C by synthetic division """
#
# assert self.__a != 0,"(a) coefficient should be differtent than zero"
#
# self._A = self.__a
# self._B = self.__b
# self._C = self.__c
#
# y = Quadratic()
# if self.__d != 0 and (self.__b**2 - 4*(self.__a *self.__c))>=0:
# for i in Cubic.integerZero(self):
# if (self.__a*((i)**3)) + (self.__b*((i)**2) )+(self.__c*(i) )+ self.__d #== 0:
# self._A = self.__a
# self._B = self.__b + self._A*i
# self._C = self.__c + self._B*i
# y(a=self._A,b=self._B,c=self._C)
# return Quadratic.__call__(y)
#
# else:
#
# y(a=self._A,b=self._B,c=self._C)
# return Quadratic.__call__(y)
#
#
#
#if __name__ == "__main__":
# cubic1 = Cubic(1,3,-7,-21)
# print(cubic1)
# print()
# cubic5 = Cubic(1,-3,-13,15)
# print(cubic5)
# print()
# cubic2 = Cubic(1,2,-7,-10)
# print(cubic2)
# print()
# cubic3 = Cubic(5,-1,-2,0)
# print(cubic3)
# print()
# cubic4 = Cubic(2,-6,-13,18)
# print(cubic4)
# print()
# cubic4 = Cubic(2,3,-4,-3)
# print(cubic4)
# print()
#
Diff to Previous Revision
--- revision 5 2011-01-28 12:32:54
+++ revision 6 2011-01-28 12:43:16
@@ -301,3 +301,249 @@
#c:\hp\bin\Python
+##########################################################################################
+
+#Version : Python 3.2
+
+#from Quadratic5_7 import *
+
+#class Cubic(object):
+# """ Class that represent a Cubic Polynomial Equation
+# with a,b,c,d properties"""
+#
+# def __init__(self,a,b,c,d):
+# """ Cubic constructor takes a,b,c,d coefficients """
+#
+# self.__a = a
+# self.__b = b
+# self.__c = c
+# self.__d = d
+#
+# self.signb = self._checkSign(self.__b)
+# self.signc = self._checkSign(self.__c)
+# self.signd = self._checkSign(self.__d)
+#
+# def __str__(self):
+# """ String representation of Cubic Polynomial Equation"""
+#
+# try:
+# self.c1 = Cubic.syntheticDivision(self)[0]
+# self.c2 = Cubic.syntheticDivision(self)[1]
+# if self.c1 == float and self.c2 == float:
+# self.c3 ="-"
+# self.c4 ="+"
+# else :
+# self.c3 = self._checkSign(float(Cubic.syntheticDivision(self)[0])*-1)
+# self.c4 = self._checkSign(float(Cubic.syntheticDivision(self)[1])*-1)
+#
+#
+# if self.__d == 0:
+# return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx = 0 \n \
+# \n<The linear factorization : p(x) = %sx(x%s%s)(x%s%s) \n\
+# " % (self.__a,chr(179),self.signb,self.__b,chr(178),
+# self.signc,self.__c,self.__a,self.c3,-1*float(self.c1),
+# self.c4,-1*float(self.c2))
+#
+# else :
+# if self.__a == 1:
+# for i in Cubic.integerZero(self):
+# if (((self.__a*(i**3)) + (self.__b*(i**2))+ (self.__c*i )+ #self.__d == 0)
+# and float(i) != float(self.c2) and float(i) != float(self.c1)):
+# return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx %s %#s = 0 \
+# \n\n<The integers zeros are :\n\n%s\n \
+# \n<The linear factorization : p(x) = (x%s%s)(x%s%s)(x%s%s) \n\
+# " % (self.__a,chr(179),self.signb,self.__b,chr(178),self.signc,
+# self.__c,self.signd,self.__d,Cubic.integerZero(self),self.c3,
+# -1*float(self.c1),self.c4,-1*float(self.c2),(self._checkSign(-1*i)),-1*i)
+
+# return "\n<None of the integers zeros %s \n\n checks p(x) = %sx%s %s #%sx%s %s %sx %s %s = 0\n\n " \
+# % (Cubic.integerZero(self),self.__a,chr(179),self.signb,self.__b,chr(178),self.signc,self.__c,
+# self.signd,self.__d)
+#
+# else :
+# for j in Cubic.nonintegersRationalZero(self)[1]:
+# if ((self.__a*(float(str(j))**3)) + (self.__b*(float(str(j))**2))#+
+# (self.__c*float(str(j)) )+ self.__d == 0.00):
+# return "\n<Cubic Equation: p(x) = %sx%s %s %sx%s %s %sx %s %#s = 0 \
+# \n\n<The integers Zeros are :\n\n %s \
+# \n\n<The nonintegers Rational Zeros are :\n\n %s \
+# \n<The linear factorization : p(x) = (x%s%s)(x%s%s)(x%s%#s) \n\
+# " % (self.__a,chr(179),self.signb,self.__b,chr(178),self.signc,self.__c,
+# self.signd,self.__d,Cubic.integerZero(self),nonintegersRationalZero(self)[0]
+# self.c3,-1*float(self.c1),self.c4,-1*float(self.c2),(self._checkSign(-1*j)),-1*j)
+
+# return "\n<None of the non integers zeros %s \n\n checks p(x) = %sx%#s %s %sx%s %s %sx %s %s = 0\n\n" \
+# % (Cubic.nonintegersRationalZero(self)[0],self.__a,chr(179),self.signb,self.__b,
+# chr(178),self.signc,self.__c,self.signd,self.__d)
+# except TypeError:
+# if self.__a == 1:
+# raise "\n<complex solutions \n\n<The integers zeros are %s " \
+# % Cubic.integerZero(self)
+# else :
+# raise "\n<complex solutions \n\n<The nonintegers zeros are %s " \
+# % Cubic.nonintegersRationalZero(self)[0]
+#
+# def get_a(self):
+# """ Get method for _a attribute """
+#
+# return self.__a
+#
+# def set_a(self,value):
+# """ Set method for _a attribute """
+#
+# self.__a = value
+#
+# def del_a(self):
+# """Delete method for _a attribute"""
+#
+# del self.__a
+# #Create a property
+# _a = property(get_a,set_a,del_a,"a coefficient")
+
+# def get_b(self):
+# """ Get method for _b attribute """
+#
+# return self.__b
+#
+# def set_b(self,value):
+# """ Set method for _b attribute """
+#
+# self.__b = value
+#
+# def del_b(self):
+# """Delete method for D attribute"""
+#
+# del self.__b
+#
+# #Create a property
+# _b = property(get_b,set_b,del_b,"b coefficient")
+#
+# def get_c(self):
+# """ Get method for _c attribute """
+#
+# return self.__c
+#
+# def set_c(self,value):
+# """ Set method for _c attribute """
+#
+# self.__c = value
+#
+# def del_c(self):
+# """Delete method for _c attribute"""
+ del self.__c
+
+# #Create a property
+# _c = property(get_c,set_c,del_c,"c coefficient")
+#
+# def get_d(self):
+# """ Get method for _d attribute """
+
+# return self.__d
+# def set_d(self,value):
+# """ Set method for _d attribute """
+#
+# self.__d = value
+#
+# def del_d(self):
+# """Delete method for F attribute"""
+#
+# del self.__d
+#
+# #Create a property
+# _d = property(get_d,set_d,del_d,"d coefficient")
+#
+# def _checkSign(self,value):
+# """ Utility method to check the values's sign
+# and return a sign string"""
+#
+# if value >= 0:
+# return "+"
+# else :
+# return ""
+#
+# def integerZero(self):
+# """ Computes Integers zeros of d coefficient """
+#
+# res = []
+# for item in range (1,abs(self.__d)+1):
+# if self.__d%item == 0:
+# res.append(item)
+# res.append(-1*item)
+# return res
+#
+# def nonintegersRationalZero(self):
+# """ Computes noninteger rational zeros """
+#
+# res1 = []
+# res2 = []
+# res3 = []
+# res4 = []
+#
+# for b in range(1,abs(self.__a)+1):
+# if self.__a%b == 0:
+# res1.append(b)
+# for i in Cubic.integerZero(self):
+# if i>0:
+# for j in res1:
+# if i%j!=0:
+# res2.append( "%2.2f" % ((i)/float(j)) ),res2.append( "%2.2f" % ((-i)/float(j)) )
+# for x in res2:
+# if res2.count(x)>1:
+# res2.remove(x)
+# if x == ("%2.2f" % ((i)/float(j))):
+# res3.append("%d/%d" % (i,j)),res3.append("%d/%d" % (-i,j))
+# res4.append("%d/%d" % (i,j)),res4.append("%d/%d" % (-i,j))
+# for w in res3:
+# if w in res4:
+# res4.remove(w)
+# return (res4,res2)
+#
+# def syntheticDivision(self):
+# """ Computes coefficients A,B,C by synthetic division """
+#
+# assert self.__a != 0,"(a) coefficient should be differtent than zero"
+#
+# self._A = self.__a
+# self._B = self.__b
+# self._C = self.__c
+#
+# y = Quadratic()
+# if self.__d != 0 and (self.__b**2 - 4*(self.__a *self.__c))>=0:
+# for i in Cubic.integerZero(self):
+# if (self.__a*((i)**3)) + (self.__b*((i)**2) )+(self.__c*(i) )+ self.__d #== 0:
+# self._A = self.__a
+# self._B = self.__b + self._A*i
+# self._C = self.__c + self._B*i
+# y(a=self._A,b=self._B,c=self._C)
+# return Quadratic.__call__(y)
+#
+# else:
+#
+# y(a=self._A,b=self._B,c=self._C)
+# return Quadratic.__call__(y)
+#
+#
+#
+
+
+
+#if __name__ == "__main__":
+# cubic1 = Cubic(1,3,-7,-21)
+# print(cubic1)
+# print()
+# cubic5 = Cubic(1,-3,-13,15)
+# print(cubic5)
+# print()
+# cubic2 = Cubic(1,2,-7,-10)
+# print(cubic2)
+# print()
+# cubic3 = Cubic(5,-1,-2,0)
+# print(cubic3)
+# print()
+# cubic4 = Cubic(2,-6,-13,18)
+# print(cubic4)
+# print()
+# cubic4 = Cubic(2,3,-4,-3)
+# print(cubic4)
+# print()
+#
