Activity 07: Modules and Classes

Solve the following problems.

See https://asu-compmethodsphysics-phy494.github.io/ASU-PHY494/2021/02/09/04_Python_4/ for help.

(Note that the last activity on class inheritance is optional — you don't need the final 10 points to get 100% on this activity even though GitHub autograding will still show the tests as failing. Don't worry about that: if you have 47 points you have 100%)

Modules

constants module

1. Create a module constants.py with values for the mathematical constant π (named pi, see also OEIS A000796) and the physical constants c for the speed of light in vaccuum (in ms/s) and Planck's constant h (in J s).

2. In a file problem1.py, import your constants module and compute the reduced Planck's constant ħ = h/2π and store it in variable hbar. Print it to all 9 significant figures in scientific notation with

   print("hbar = {hbar:.9e}".format(hbar))

myfuncs module

Use your myfuncs module from the last lesson in a file problem2.py and

1. Compute Heaviside(n) for the integers -10 ≤ n ≤ 10, assign the list to a variable y, and print it with

   print(f"Heaviside: {y}")

   (this print uses an f-string, available since Python 3.6 as an improvement over format representations; both use the Format Specification Mini-Language)

2. Compute the temperature of the boiling point of water under standard conditions in degrees Celsius from the value in Kelvin, T_boil = 373.15 K. Assign it to a variable t_boil and print it with

   print(f"Water boils at {t_boil:.2f} C")

Standard library

Import the math module and the os module from the Python Standard Library in a file problem3.py. Look in these modules for functions and attributes to solve the following problems:

1. Compute y_full_circle = sin(tau). (Optionally, you can also print the value.)

2. Define the cumulative distribution function of the normal distribution with mean µ and standard deviation σ

    Phi(x, µ, σ) = 1/2 [1 + erf( (x-µ)/(σ sqrt(2)) )]
   

   as a Python function Phi(x, mu=0., sigma=1.0).

   For a random variable X that is normally distributed with mean µ=88.6 and standard deviation σ=6.3 compute the probability P(X>95) to observe a value of X > 95, using

    P(X > x) = 1 - Phi(x, µ, σ)
   

   Assign your result to a variable P_aplus and print it with

   print(f"P(X > 95) = {100 * P_aplus:.1f}%")

3. Get the current working directory as a string and assign to the variable cwd and print it with

   print(f"cwd = '{cwd}'")

Objects and Classes

String methods

Given the sentence sentence = "MAY THE FORCE BE WITH YOU!" in file problem4.py

1. test if it is lower case (assign the boolean value to a variable all_lower)
2. make it lower case (store in l_sentence)

Creating your own classes

Sphere class definition

Create a file bodies.py that contains the class Sphere.

• A Sphere instance is initialized with its position (Cartesian coordinates a list or tuple with three floating point numbers) and optionally its radius; the default for radius is 1.0.
• Store the position in an attribute pos and the radius in attribute radius.
• The class has a method volume() that returns the volume of the sphere.
• The class has a method translate(t), that changes the position of the sphere by adding the translation vector t (tuple with three floats) to the current position.

Instantiation: A ball is a sphere

Create a file balls.py in which you

1. create an object representing a ball by instantiating a Sphere at position (0, 0, 10) with radius 2 and assigning it to variable ball
2. change the position of the ball to (-5, 0, 0),
3. assign the volume of the ball to a variable volume and print it to 3 decimals,
4. translate the ball by (5, 0, 0)

After each step, print the position of the ball.

Independence: A balloon is not a ball

Create a file ball_oons.py in which you

1. create a ball (as a Sphere) at position (0, 0, 10) with radius 2 (variable ball),
2. create a balloon (as a Sphere) at position (0, 0, 10) with radius 6 (variable balloon),
3. change the ball's position to (-1, -1, 0)
4. compare the balloon's and the ball's position by printing

   print(f"ball at {ball.pos} != balloon at {balloon.pos}")

Inheritance: Earth is a Sphere (OPTIONAL)

In file astronomy.py, define a class Planet that is derived from Sphere and is instantiated as Planet(name, pos, mass, radius).

Planet must have a method Planet.density() that returns the density of the planet, mass/volume.

Use your class to represent Earth (quantities from http://www.wolframalpha.com)

# lengths in m and mass in kg
earth = Planet("Earth", (1.4959802296e11 , 0, 0), 5.9721986e24, 6371e3)
print(earth.density())

and print the density.