[mgkvibez]

Implements Zeckendorf's theorem: every positive integer can be written uniquely as the sum of one or more distinct, non-consecutive Fibonacci numbers.

maths/zeckendorf.py provides two functions:

• _fibonacci_numbers_up_to(limit) builds the sequence starting at 1, 2 (rather than 1, 1) so that the value 1 is used at most once and the representation stays unique.
• zeckendorf(number) recovers the representation with a greedy pass over those Fibonacci numbers from largest to smallest, which is always optimal for this problem.

>>> zeckendorf(100)
[89, 8, 3]
>>> sum(zeckendorf(100)) == 100
True

Doctests cover 0, 1, 2, 4, 10, 100, 1000, plus TypeError for non-integer input and ValueError for negative input.

Describe your change

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Checklist

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues, then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

Local verification before opening: ruff check and ruff format --check clean under the repo's pyproject.toml, pytest maths/zeckendorf.py --doctest-modules 2 passed, 12 doctests passed. README.md and DIRECTORY.md left untouched for the automation to regenerate.