Chapter 4

Make a program that (i) asks the user for a temperature in Fahrenheit degrees and reads the number; (ii) computes the correspodning temperature in Celsius degrees; and (iii) prints out the temperature in the Celsius scale. Name of program file: f2c_qa.py.

Make a program that asks for input from the user, apply eval to this input, and print out the type of the resulting object and its value. Test the program by providing five types of input: an integer, a real number, a complex number, a list, and a tuple. Name of program file: objects_qa.py.

Let a program store the result of applying the eval function to the first command-line argument. Print out the resulting object and its type. Run the program with different input: an integer, a real number, a list, and a tuple. (On Unix systems you need to surround the tuple expressions in quotes on the command line to avoid error message from the Unix shell.) Try the string "this is a string" as a commandline argument. Why does this string cause problems and what is the remedy? Name of program file: objects_cml.py.

Consider the simplest program for evaluting the formula \(y(t)=v_{0} t-\) \(0.5 g t^{2}:\) $$ \begin{aligned} &v 0=3 ; g=9.81 ; t=0.6 \\ &y=v 0 * t-0.5 * g * t * 2 \\ &\text { print } y \end{aligned} $$ Modify this code so that the program asks the user questions \(t=?\) and v0 \(=\) ?, and then gets \(t\) and vo from the user's input through the keyboard. Name of program file: ball_qa.py. \(\diamond\)

A car driver, driving at velocity \(v_{0}\), suddenly puts on the brake. What braking distance \(d\) is needed to stop the car? One can derive, from basic physics, that $$ d=\frac{1}{2} \frac{v_{0}^{2}}{\mu g} $$ Make a program for computing \(d\) in \((4.7)\) when the initial car velocity \(v_{0}\) and the friction coefficient \(\mu\) are given on the command line. Run the program for two cases: \(v_{0}=120\) and \(v_{0}=50 \mathrm{~km} / \mathrm{h}\), both with \(\mu=0.3\) \((\mu\) is dimensionless). (Remember to convert the velocity from \(\mathrm{km} / \mathrm{h}\) to \(\mathrm{m} / \mathrm{s}\) before inserting the value in the formula!) Name of program file: stopping_length.py.

The purpose of this exercise is to make a program which takes a date, consisting of year (4 digits), month (2 digits), and day (1-31) on the command line and prints the corresponding name of the weekday (Monday, Tuesday, etc.). Python has a module calendar, which you must look up in the Python Library Reference (see Chapter 2.6.3), for calculating the weekday of a date. Name of program file: weekday.py. \(\diamond\)

The simplest way of writing a try-except block is to test for any exception, for example, try: C \(=\) float(sys.arg [1]) except: print 'C must be provided as command-line argument' sys.exit(1) Write the above statements in a program and test the program. What is the problem? The fact that a user can forget to supply a command-line argument when running the program was the original reason for using a try block. Find out what kind of exception that is relevant for this error and test for this specific exception and re-run the program. What is the problem now? Correct the program. Name of program file: cml_exception.py. \(\diamond\)

Make six conversion functions between temperatures in Celsius, Kelvin, and Fahrenheit: \(\mathrm{C} 2 \mathrm{~F}, \mathrm{~F} 2 \mathrm{C}, \mathrm{C} 2 \mathrm{~K}, \mathrm{~K} 2 \mathrm{C}, \mathrm{F} 2 \mathrm{~K}\), and \(\mathrm{K} 2 \mathrm{~F}\). Collect these functions in a module convert_temp. Make some sample calls to the functions from an interactive Python shell. Name of program file: convert_temp.py.

Because of round-off errors, it could happen that a mathematical rule like \((a b)^{3}=a^{3} b^{3}\) does not hold (exactly) on a computer. The idea of this exercise is to check such identities for a large number of random numbers. We can make random numbers using the random module in Python: import random \(\mathrm{a}=\) random. uniform \((A, B)\) \(b=\) random. uniform \((A, B)\) Here, a and b will be random numbers which are always larger than or equal to A and smaller than \(B\). Make a program that reads the number of tests to be performed from the command line. Set \(A\) and \(B\) to fixed values (say - 100 and 100\()\). Perform the test in a loop. Inside the loop, draw random numbers a and b and test if the two mathematical expressions (a*b)**3 and a**3*b**3 are equivalent. Count the number of failures of equivalence and write out the percentage of failures at the end of the program. Duplicate the code segment outlined above to also compare the expressions \(a / b\) and \(1 /(b / a)\). Name of program file: math_identities_failures.py.

Consider an uncertain event where there are two outcomes only, typically success or failure. Flipping a coin is an example: The outcome is uncertain and of two types, either head (can be considered as success) or tail (failure). Throwing a die can be another example, if (e.g.) getting a six is considered success and all other outcomes represent failure. Let the probability of success be \(p\) and that of failure \(1-p\). If we perform \(n\) experiments, where the outcome of each experiment does not depend on the outcome of previous experiments, the probability of getting success \(x\) times (and failure \(n-x\) times) is given by $$ B(x, n, p)=\frac{n !}{x !(n-x) !} p^{x}(1-p)^{n-x} $$ This formula (4.8) is called the binomial distribution. The expression \(x !\) is the factorial of \(x\) as defined in Exercise 3.14. Implement (4.8) in a function binomial \((x, n, p)\). Make a module containing this binomial function. Include a test block at the end of the module file. Name of program file: binomial_distribution.py.