write two python classes, programming homework help

a-

1. Write a class that defines a two-dimensional Cartesian coordinate. Write the class such that the following Python program executes correctly.

   #/usr/bin/env python3.2
   #
   # Your header here
   #
   
   # Two-dimensional Cartesian coordinate
   #  class definition here
   class Cartesian2D:
     def __init__(self):
       # etc.
   
   def main( ):
     a = Cartesian2D(2.3, 3.4)
     b = Cartesian2D(4.5, 1.8)
     c = Cartesian2D(8.1, 0.3)
     print("The distance from a to b is {}".format(a.distanceTo(b)))
     print("The distance from b to c is {}".format(b.distanceTo(c)))
     d = a + b
     print("a + b = ({},{})".format(d.x, d.y))
     d = c - b
     print("c - b = ({}, {})".format(d.x, d.y))
     print("The length of a is {}".format(a.length()))
     print("The length of b is {}".format(b.length()))
     print("The length of c is {}".format(c.length()))
     unita = a.normalize()
     unitb = b.normalize()
     unitc = c.normalize()
     print("The length of unit a is {}".format(unita.length()))
     print("The length of unit b is {}".format(unitb.length()))
     print("The length of unit c is {}".format(unitc.length()))
     s = 4
     d = unita * s
     print(d)
     print("The length of d is {}".format(d.length()))
     e = unitb * s
     f = dot(a, b)
     g = dot(unita, unitb)
     h = dot(d, e)
     print("dot(a, b) = {}".format(f))
     print("dot(unita, unitb = {}".format(g))
     print("dot(d, e) = {}".format(h))
   if __name__ == "__main__":
     main( )

   The two-dimensional Cartesian coordinate and main function must all be in the same file and named cartesian_demo.py.

b-

1. Write a class that defines a quaternion object. Quaternions are a hypercomplex numbers that are not commutative, but they are associative. A definition of what a quaternion is and an explanation of the operations performed on a quaternion are given at Wolfram Research’s MathWorld. Write the class such that the following Python program executes correctly.

   #/usr/bin/env python3.2
   #
   # Your header here
   #
   
   # Quaternions class definition here
   clas Quaternion:
     def __init__(self):
       # etc.
   
   def main( ):
     # Quaternion a & b are defined by four constants, which
     # define a + b i + c j + d k where a...d are parameter 1...4 of
     # the constructor
     a = Quaternion(.3, 3.2, 6.5, 1.1)
     b = Quaternion(.5, 4.7, 7.6, 2.2)
     c = a + b
     print(c)
     c = a - b
     print(c)
     print(a.conjugate())
     print(b.conjugate())
     print(c.conjugate())
     print(a*b)
     print(b*a)
     print(a*c)
     print(c*a)
     print("a's angle {} and axis {}".format(a.angle(), a.axis()))
     print("b's angle {} and axis {}".format(b.angle(), b.axis()))
     print("c's angle {} and axis {}".format(c.angle(), c.axis()))
     a.norm()
     b.norm()
     c.norm()
     print("a's angle {} and axis {}".format(a.angle(), a.axis()))
     print("b's angle {} and axis {}".format(b.angle(), b.axis()))
     print("c's angle {} and axis {}".format(c.angle(), c.axis()))
   
   if __name__ == "__main__":
     main( )

   The quaternion class and main function must all be in the same file and named quaternion_demo.py.