# Boring Math Library - Pythagorean triples
Package containing a class to generate Pythagorean triples along
with a CLI executable.
## Repos and Documentation
### Repositories
- [bm.pythagorean-triples][1] project on *PyPI*
- [Source code][2] on *GitHub*
### Detailed documentation
- [Detailed API documentation][3] on *GH-Pages*
## Overview
Geometrically, a *Pythagorean* triangle is a right triangle with
positive integer sides.
This project is part of the [Boring Math][4] **bm.** namespace project.
### Library modules
#### Pythagorean Triple Class
- Pythagorean Triple Class
- Method `Pythag3.triples(a_start: int, a_max: int, max: Optional[int]) -> Iterator[int]`
- Returns an iterator of tuples of primitive *Pythagorean* triples
- A Pythagorean triple is a tuple in positive integers (a, b, c)
- such that `a² + b² = c²`
- `a, b, c` represent integer sides of a right triangle
- a *Pythagorean* triple is primitive if gcd of `a, b, c` is `1`
- Iterator finds all primitive Pythagorean Triples
- where `0 < a_start <= a < b < c <= max` where `a <= a_max`
- if `max` not given, find all theoretically possible triples with `a <= a_max`
______________________________________________________________________
### CLI Applications
- program [pythag3](#cli-program-pythag3)
These programs are implemented in an OS and package
build tool independent way via the `project.scripts` section of
`pyproject.toml`.
#### CLI program pythag3
- Generates primitive Pythagorean triples
- **Usage:** `pythag3 [m [n [max]]`
- 3 args print all triples with `m <= a <= n` and `a < b < c <= max`
- 2 args print all theoretically possible triples with `m <= a <= n`
- 1 arg prints all theoretically possible triples with `a <= m`
- 0 args print all triples with `3 <= a <= 100`
______________________________________________________________________
[1]: https://pypi.org/project/bm.pythagorean-triples/
[2]: https://github.com/grscheller/bm-pythagorean-triples/
[3]: https://grscheller.github.io/boring-math-docs/pythagorean-triples/
[4]: https://github.com/grscheller/boring-math-docs
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