Mathematical Series

The Fibonacci Series is a numeric series starting with the integers 0 and 1. In this series, the next integer is determined by summing the previous two. This gives us:

0, 1, 1, 2, 3, 5, 8, 13, ...

The Lucas Numbers are a related series of integers that start with the values 2 and 1 rather than 0 and 1. The resulting series looks like this:

2, 1, 3, 4, 7, 11, 18, 29, ...

Tasks

Along with your partner for the week, create a github repository called math-series. In this new repository, create a module series.py. In this same math-series repository, create a virtualenv. Install pytest and pytest-xdist. Use a .gitignore file to ensure that the artifacts of your virtual environment do not end up in GitHub.

Add a file test_series.py to your repository. As you work on the tasks below, use TDD practices. Write tests first, then implement code. Make small changes with many cycles of Red-Green-Refactor

This is not an overly long assignment, so take the time to do the testing right.

Create a function called fibonacci. The function should have one parameter n. The function should return the nth value in the fibonacci series. You may implement the function using recursion or iteration. If you are feeling particularly frisky, do both as separate functions.

Ensure that your function(s) has a well-formed docstring

In your series.py module, add a new function lucas that returns the nth value in the lucas numbers Again, you may use recursion or iteration, or both. Again, ensure that your function has a well-formed docstring.

Both the fibonacci series and the lucas numbers are based on an identical formula. Add a third function called sum_series with one required parameter and two optional parameters. The required parameter will determine which element in the series to print. The two optional parameters will have default values of 0 and 1 and will determine the first two values for the series to be produced.

Calling this function with no optional parameters will produce numbers from the fibonacci series. Calling it with the optional arguments 2 and 1 will produce values from the lucas numbers. Other values for the optional parameters will produce other series. Again, you may use recursion or iteration, or both. Again, ensure that your function has a well-formed docstring.

Add an if __name__ == "__main__": block to the end of your series.py module.

In this block, write code that demonstrates the use of the functions defined in the module. If I run the module from the command line I should see output like this:

$ python series.py

This module defines functions that implement mathematical series.
...

fibonacci(n):

    Returns the nth value in the fibonacci series

>>> fibonacci(2)
1

and so on.

Add your series.py and test_series.py modules to your git clone and commit frequently while working on your implementation. Include good commit messages that explain concisely both what you are doing and why.

Submitting Your Work

When you are finished and all your tests are passing, push your changes to your github repository. Submit a link to your repository for the assignment submission in Canvas.

Use the comment feature in canvas to submit the following:

• At least one well-formed question about the work you did for this assignment
• At least one comment on what went well
• At least one comment on what was particularly difficult or challenging