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```#On the name of ALLAH and may the blessing and peace of Allah
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Date : 06/05/10
#version :2.6

"""
Sphere class represents a geometric sphere and a completing_the_squares
function is used for the purpose, while an utility _checksign function
is used to check the sign of all the coefficients and return an empty string
for a positive number and a minus character for a negative number.
A string representation function for the three different outcome
possibilities is used to print the solution of the sphere equation.
"""

from math import sqrt
class Sphere(object):
"""
class that represents a geometric Sphere
"""
def __init__(self,coef_A = 0,coef_B = 0, coef_C = 0, coef_D= 0, coef_E = 0, coef_F = 0, coef_G = 0):
""" Sphere Construction takes coef_A,coef_B,coef_C,coef_D,coef_E,coef_F,coef_G constants """

self._A = coef_A
self._B = coef_B
self._C = coef_C
self._D = coef_D
self._E = coef_E
self._F = coef_F
self._G = coef_G

self._a = self._checkSign(self._D)
self._b = self._checkSign(self._E)
self._c = self._checkSign(self._F)

self._d = pow((self._D/2.0)/self._A,2)
self._e = pow((self._E/2.0)/self._B,2)
self._f = pow((self._F/2.0)/self._C,2)

self._g = chr(253)

self._h = (-self._G/self._A + self._d + self._e + self._f)

def _checkSign(self,value):
""" Utility method to check the values' sign
and return a sign string"""

if value >= 0:
return "+"
else :
return ""

def completing_the_squares(self):
"""
completing the squares function
"""

c_squares = "(x%s %s%sx + %s) + (y%s %s%sy + %s) + (z%s %s%sz + %s) = %s" % \
(self._g,self._a,self._D/self._A,self._d,
self._g,self._b,self._E/self._B,self._e,
self._g,self._c,self._F/self._C,self._f,self._h)

return c_squares

def __str__(self):
"""
String representation of a sphere
"""
print ("\n(x%s%s)%s + (y%s%s)%s + (z%s%s)%s = %s") % \
(self._a,(self._D/2.0)/self._A,self._g,self._b,(self._E/2.0)/self._B,
self._g,self._c,(self._F/2.0)/self._C,self._g,self._h)
if self._h > 0:
return "\n<The graph of this equation is a sphere with centre (%s,%s,%s) and radius %s\n" % \
(-1*self._D/2.0,-1*self._E/2.0,-1*self._F/2.0,"%2.3f" % (sqrt(self._h)))
elif self._h == 0:
return "\n<this sphere has radius = 0 and the graph is a single point(%s,%s,%s)\n " % \
(-1*self._D/2.0,-1*self._E/2.0,-1*self._F/2.0,float(m.sqrt(self._h)))
else :
return "\n<There is no graph for such equation "

if __name__ == "__main__":

sphere = Sphere(1,1,1,-2,-4,8,17)
print sphere.completing_the_squares()
print sphere
sphere1 = Sphere(1,1,1,10,4,2,-19)
print sphere1.completing_the_squares()
print sphere1
sphere2 = Sphere(2,2,2,-2,-3,5,-2)
print sphere2.completing_the_squares()
print sphere2
####C:\Windows\python "C:\Users\MyComputer\Documents\Pyt\Sphere7.py"

#(x² -2x + 1.0) + (y² -4y + 4.0) + (z² +8z + 16.0) = 4.0

#(x-1.0)² + (y-2.0)² + (z+4.0)² = 4.0

#<The graph of this equation is a sphere with centre (1.0,2.0,-4.0) #and radius 2.000

#(x² +10x + 25.0) + (y² +4y + 4.0) + (z² +2z + 1.0) = 49.0

#(x+5.0)² + (y+2.0)² + (z+1.0)² = 49.0

#<The graph of this equation is a sphere with centre (-5.0,-2.0,-1.0) #and radius 7.000

#(x² -1x + 0.25) + (y² -2y + 0.5625) + (z² +2z + 1.5625) = 3.375

#(x-0.5)² + (y-0.75)² + (z+1.25)² = 3.375

#<The graph of this equation is a sphere with centre (1.0,1.5,-2.5) #and radius 1.837
#################################################################
```

#### Diff to Previous Revision

```--- revision 2 2010-05-06 12:27:14
+++ revision 3 2010-05-06 12:28:12
@@ -7,7 +7,8 @@
"""
Sphere class represents a geometric sphere and a completing_the_squares
function is used for the purpose, while an utility _checksign function
-is used to check the sign of all the coefficients and return an empty string for a positive number and a minus character for a negative number.
+is used to check the sign of all the coefficients and return an empty string
+for a positive number and a minus character for a negative number.
A string representation function for the three different outcome
possibilities is used to print the solution of the sphere equation.
"""
```