Download hw_3.tar.gz and extract it. Then add
your homework solutions to the files contained in the directory. Rename the
directory
according to the rules in the syllabus before submitting it as compressed
archive. Starting from this homework, the grader uses so-called unit
tests, but can be executed as any other Python 3 program.

This homework is the first homework to be solved in teams of two
using pair programming. Find your partner for this homework on
moodle.uni-graz.at. Each team has to
submit only one archive containing all team members' names.

**Equation solver**

Write a function`quadratic(a, b, c)`

that solves quadratic equations. If you have trouble solving this task, have a look at the Python functions video tutorial on youtube. In addition to what is shown in the video, the function must be able to deal with input leading to complex numbers as results.

Name the program file:`equations.py`**Sum**

Write a function`sum_to(num)`

that takes an integer`num >= 0`

as sole argument. The function should return the sum of all positive integers`<= num`

. In the function, assert that the input is ≥ 0 by using`assert`

.

Name the program file:`addition.py`**Conversion between Celsius and Fahrenheit**

Based on the formulas and your code of the second homework, write a function`celsius2fahrenheit(.)`

that converts from Celsius to Fahrenheit and`fahrenheit2celsius(.)`

for the other way around.

Name the program file:`conversion.py`**Geometry functions**

Implement the following functions calculating the perimeters, areas, surfaces or volumes of common gemoetric shapes:

`perimeter_right_triangle(c1, c2)`

`area_right_triangle(c1, c2)`

`perimeter_circle(r)`

`area_circle(r)`

`surface_sphere(r)`

`volume_sphere(r)`

`surface_cylinder(r, h)`

`volume_cylinder(r, h)`

`surface_cone(r, h)`

`volume_cone(r, h)`

Name the program file:`geometry.py`**Business functions**

Implement a function`interest(capital, rate, years=1, tax=0)`

that returns the profit (compound interest) of investing money. If a positive tax value is entered, every year's interest is to be reduced by the tax. The`rate`

and`tax`

parameters must be between 0 (0%) and 1 (100%). The number of years is integral.

Using the above function, implement a second function that returns the terminal value of investing money:`terminal_value(capital, rate, years=1, tax=0)`

.

Name the program file:`business.py`**ROT13**

Building on your solution to the ROT13 task in the last homework, write a function`encode(.)`

that takes a string and returns the given string rotated by 13 places. For symmetry, also provide a corresponding`decode(.)`

function. Convert the input to upper case before performing the rotation.

- Arire gehfg n cebtenz lbh qba'g unir fbheprf sbe.

`rot13.py`**VRPTW instances**

Write a function`read_string_list(.)`

that opens a VRPTW data file given as filename argument. The argument must be optional and default to "r101"). If the argument doesn't contain a filename extension (".txt"), this extension must be added before opening the file. Your function should return a list of strings - one for each entry. The headers should not be included in that list.

Name the program file:`vrptw_reader.py`**More on VRPTW instances**

Expand the file of the last task to include more functions. The second function`get_demand(.)`

takes two arguments. The first argument should be a list of strings (one for each entry) and the second should be a customer number (CUST_NO.). The function has to return that customer's demand as floating point number. The last function,`calc_distance(.)`

, should take three parameters – a list of strings and two customer numbers. It should return the euclidean distance between the two customers.

Name the program file:`vrptw_reader.py`**Main function**

Write a single module that imports all the other modules you wrote for this homework. In the module implement a main function that uses all the functions you created. The main function must be called itself using the ifmain pattern. If all went well, the main function must return 0 to inform the calling process of the successful termination. Name the program file:`main.py`