*Max. 9 points*

Download hw_3.tar.gz and extract it. This archive contains a grader which works for all current versions of Python 3 and expects the solution files to be placed in the same directory. It has to be executed from this directory via

```
python hw3_grader.py
```

Add your solutions in the directory contained in the archive. Right after the shebang, each of your files must contain your name using the following template

`"""`

.. moduleauthor:: Your Name <your.name@example.com>

"""

We did not discuss every detail required to solve the following tasks. Use your favorite search engine and some common sense to solve the tasks.

This homework is to be prepared in teams of two students. Ask the lecturer to announce the teams to know who you'll be working with.

**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:

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

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

. 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. Use the formulas$$\text{capital}}\ast (1+{\textstyle \text{rate}}\ast (1-{\textstyle \text{tax}}){)}^{{\textstyle \text{years}}$$

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

that returns the profit (compound interest) of investing money.

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.

A sample execution of this function:

Name the program file:`>>> read_string_list('r101.txt')`

[' 1 35.00 35.00 0.00 0.00 230.00 0.00\n',

' 2 41.00 49.00 10.00 161.00 171.00 10.00\n',

...

'100 20.00 26.00 9.00 83.00 93.00 10.00\n',

'101 18.00 18.00 17.00 185.00 195.00 10.00\n']`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. This main function is a first attempt of testing your code in the other modules. For each of the other tasks, create valid input data and deduce the functions output. Print these values, followed by the actual values the function produces for these inputs. Here's an example line this function could contain:

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:`def main():`

# ...

print('prime_addition.prime_sum_to(9); expected: 17, actual:',

prime_addition.prime_sum_to(9))

# ...`main.py`

All resulting files must be placed in a single directory. The name of the
directory must be `3_firstname_lastname` (in case of team
homeworks, add each member's first and last names). Make sure to also include
the grader. Compress the directory to either
`3_firstname_lastname.tar.gz` or
`3_firstname_lastname.tar.bz2` before sending it to
assignments@senarclens.eu.