# PyPI grscheller.boring-math Project
Daddy's boring math library.
* Python package of modules of a mathematical nature
* Project name suggested by my then 13 year old daughter Mary
* See [grscheller.boring-math][1] project on PyPI
* See [Detailed API documentation][2] on GH-Pages
* See [Source code][3] on GitHub
Here are the [modules](#library-modules) and
[executables](#cli-applications) which make up the PyPI
grscheller.boring_math package.
## Library Modules
* Integer Math Module
* Number Theory
* Function **gcd**(int, int) -> int
* greatest common divisor of two integers
* always returns a non-negative number greater than 0
* Function **lcm**(int, int) -> int
* least common multiple of two integers
* always returns a non-negative number greater than 0
* Function **coprime**(int, int) -> Tuple(int, int)
* make 2 integers coprime by dividing out gcd
* preserves signs of original numbers
* Function **iSqrt**(int) -> int
* integer square root
* same as math.isqrt
* Function **isSqr**(int) -> bool
* returns true if integer argument is a perfect square
* Function **primes**(start: int, end_before: int) -> Iterator
* uses *Sieve of Eratosthenes* algorithm
* Combinatorics
* Function **comb**(n: int, m: int) -> int
* returns number of combinations of n items taken m at a time
* pure integer implementation of math.comb
* Fibonacci Sequences
* Function **fibonacci**(f0: int=0, f1: int=1) -> Iterator
* returns a *Fibonacci* sequence iterator
* `f(n) = f(n-1) + f(n-2)`
* `f(0) = f0` and `f(1) = f1`
* defaults to `0, 1, 1, 2, 3, 5, 8, 13, ...`
---
* Pythagorean Triple Module
* Pythagorean Triple Class
* Method **Pythag3.triples**(a_start: int, a_max: int, max: int) -> Iterator
* Returns an interator of tuples of primative *Pythagorean* triples
* A *Pythagorean* triple is a tuple in positive integers (a, b, c)
* such that `a**2 + b**2 = c**2`
* `a, b, c` represent integer sides of a right triangle
* a *Pythagorean* triple is primative if gcd of `a, b, c` is `1`
* Iterator finds all primative pythagorean such that
* `0 < a_start <= a < b < c <= max` where `a <= a_max`
* if `max = 0` find all theoretically possible triples with `a <= a_max`
---
* Recursive Function Module
* Ackermann's Function
* Function **ackermann**(m: int, n: int) -> int
* an example of a total computable function that is not primitive recursive
* becomes numerically intractable after m=4
* see CLI section below for mathematical definition
---
## CLI Applications
Implemented in an OS and package build tool independent way via the
project.scripts section of pyproject.toml.
#### Ackermann's function CLI scripts
Ackermann, a student of Hilbert, discovered early examples of totally
computable functions that are not primitively recursive.
A [fairly standard][4] definition of the Ackermann function is
recursively defined for `m,n >= 0` by
```
ackermann(0,n) = n+1
ackermann(m,0) = ackermann(m-1,1)
ackermann(m,n) = ackermann(m-1, ackermann(m, n-1))
```
* CLI script **ackerman_list**
* Given two non-negative integers, evaluates Ackermann's function
* Implements the recursion via a Python array
* Usage: `ackerman_list m n`
---
#### Pythagorean triple CLI script
Geometrically, a *Pythagorean* triangle is a right triangle with
with positive integer sides.
* CLI script **pythag3**
* A Pythagorean triple is a 3-tuple of integers `(a, b, c)` such that
* `a**2 + b**2 = c**2` where `a,b,c > 0` and `gcd(a,b,c) = 1`
* The integers `a, b, c` represent the sides of a right triangle
* Usage: `pythag3 [m [n [max]]`
* 3 arguments print all triples with m <= a <= n and a < b < c <= max
* 2 arguments print all triples with m <= a <= n
* 1 argument prints all triples with a <= m
* 0 arguments print all triples with 3 <= a <= 100
---
[1]: https://pypi.org/project/grscheller.boring-math/
[2]: https://grscheller.github.io/boring-math/API/development/html/grscheller/boring_math/index.html
[3]: https://github.com/grscheller/boring-math
[4]: https://mathworld.wolfram.com/AckermannFunction.html
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