# Daddy's boring math library
WARNING: This project was ARCHIVED!
It was becoming a mono-repo and was split up into four namespace
projects:
* bm.integer-math
* bm.probability-distributions
* bm.pythagorean-triples
* bm.recursive-functions
Python package of modules of a mathematical nature. The project
name was suggested by my then 13 year old daughter Mary.
* **Repositories**
* [grscheller.boring-math][1] project on *PyPI*
* [Source code][2] on *GitHub*
* **Detailed documentation**
* [Detailed API documentation][3] on *GH-Pages*
## Overview
Here are the [modules](#library-modules) and
[executables](#cli-applications) which make up the
grscheller.boring-math PyPI project.
## 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: int) -> Iterator[int]
* now using *Wilson's Theorem*
* Function **legendre_symbol**(a: int, p: int) -> int
* where `p > 2` is a prime number
* Function **jacobi_symbol**(a: int, n: int) -> int
* where `n > 0`
* 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
---
### Pythagorean Triple Module
* 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 = 0` find all theoretically possible triples with `a <= a_max`
---
### Recursive Function Module
#### Ackermann's Function
* Function **ackermann_list**(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
#### Fibonacci Sequences
* Function **fibonacci**(f0: int=0, f1: int=1) -> Iterator[int]
* returns a *Fibonacci* sequence iterator where
* `f(0) = f0` and `f(1) = f1`
* `f(n) = f(n-1) + f(n-2)`
* yield defaults to `0, 1, 1, 2, 3, 5, 8, 13, 21, ...`
* Function **rev_fibonacci**(f0: int=0, f1: int=1) -> Iterator[int]
* returns a *Reverse Fibonacci* sequence iterator where
* `rf(0) = f0` and `rf(1) = f1`
* `rf(n) = rf(n-1) - rf(n-2)`
* `rf(0) = fib(-1) = 1`
* `rf(1) = fib(-2) = -1`
* `rf(2) = fib(-3) = 2`
* `rf(3) = fib(-4) = -3`
* `rf(4) = fib(-5) = 5`
* yield defaults to `1, -1, 2, -3, 5, -8, 13, -21, ...`
---
## 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 program **ackermann_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
positive integer sides.
#### CLI program **pythag3**
* Generates primitive Pythagorean triples
* A primitive Pythagorean triple is a 3-tuple of integers `(a, b, c)` such that
* `a³ + b³ = c³` 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 args print all triples with `m <= a <= n` and `a < b < c <= max`
* 2 args print all triples with `m <= a <= n`
* 1 arg prints all triples with `a <= m`
* 0 args print all triples with `3 <= a <= 100`
---
[1]: https://pypi.org/project/grscheller.boring-math/
[2]: https://github.com/grscheller/boring-math/
[3]: https://grscheller.github.io/grscheller-pypi-namespace-docs/boring-math/
[4]: https://mathworld.wolfram.com/AckermannFunction.html
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"description": "# Daddy's boring math library\n\nWARNING: This project was ARCHIVED!\n\nIt was becoming a mono-repo and was split up into four namespace\nprojects:\n\n* bm.integer-math\n* bm.probability-distributions\n* bm.pythagorean-triples\n* bm.recursive-functions\n\nPython package of modules of a mathematical nature. The project\nname was suggested by my then 13 year old daughter Mary.\n\n* **Repositories**\n * [grscheller.boring-math][1] project on *PyPI*\n * [Source code][2] on *GitHub*\n* **Detailed documentation**\n * [Detailed API documentation][3] on *GH-Pages*\n\n## Overview\n\nHere are the [modules](#library-modules) and\n[executables](#cli-applications) which make up the\ngrscheller.boring-math PyPI project.\n\n## Library Modules\n\n### Integer Math Module\n\n* Number Theory\n * Function **gcd**(int, int) -> int\n * greatest common divisor of two integers\n * always returns a non-negative number greater than 0\n * Function **lcm**(int, int) -> int\n * least common multiple of two integers\n * always returns a non-negative number greater than 0\n * Function **coprime**(int, int) -> tuple(int, int)\n * make 2 integers coprime by dividing out gcd\n * preserves signs of original numbers\n * Function **iSqrt**(int) -> int\n * integer square root\n * same as math.isqrt\n * Function **isSqr**(int) -> bool\n * returns true if integer argument is a perfect square\n * Function **primes**(start: int, end: int) -> Iterator[int]\n * now using *Wilson's Theorem*\n * Function **legendre_symbol**(a: int, p: int) -> int\n * where `p > 2` is a prime number\n * Function **jacobi_symbol**(a: int, n: int) -> int\n * where `n > 0`\n* Combinatorics\n * Function **comb**(n: int, m: int) -> int\n * returns number of combinations of n items taken m at a time\n * pure integer implementation of math.comb\n\n---\n\n### Pythagorean Triple Module\n\n* Pythagorean Triple Class\n * Method **Pythag3.triples**(a_start: int, a_max: int, max: Optional[int]) -> Iterator[int]\n * Returns an iterator of tuples of primitive *Pythagorean* triples\n * A Pythagorean triple is a tuple in positive integers (a, b, c)\n * such that `a\u00b2 + b\u00b2 = c\u00b2`\n * `a, b, c` represent integer sides of a right triangle\n * a *Pythagorean* triple is primitive if gcd of `a, b, c` is `1`\n * Iterator finds all primitive Pythagorean Triples\n * where `0 < a_start <= a < b < c <= max` where `a <= a_max`\n * if `max = 0` find all theoretically possible triples with `a <= a_max`\n\n---\n\n### Recursive Function Module\n\n#### Ackermann's Function\n\n* Function **ackermann_list**(m: int, n: int) -> int\n * an example of a total computable function that is not primitive recursive\n * becomes numerically intractable after `m=4`\n * see CLI section below for mathematical definition\n\n#### Fibonacci Sequences\n\n* Function **fibonacci**(f0: int=0, f1: int=1) -> Iterator[int]\n * returns a *Fibonacci* sequence iterator where\n * `f(0) = f0` and `f(1) = f1`\n * `f(n) = f(n-1) + f(n-2)`\n * yield defaults to `0, 1, 1, 2, 3, 5, 8, 13, 21, ...`\n\n* Function **rev_fibonacci**(f0: int=0, f1: int=1) -> Iterator[int]\n * returns a *Reverse Fibonacci* sequence iterator where\n * `rf(0) = f0` and `rf(1) = f1`\n * `rf(n) = rf(n-1) - rf(n-2)`\n * `rf(0) = fib(-1) = 1`\n * `rf(1) = fib(-2) = -1`\n * `rf(2) = fib(-3) = 2`\n * `rf(3) = fib(-4) = -3`\n * `rf(4) = fib(-5) = 5`\n * yield defaults to `1, -1, 2, -3, 5, -8, 13, -21, ...`\n\n---\n\n## CLI Applications\n\nImplemented in an OS and package build tool independent way via the\nproject.scripts section of pyproject.toml.\n\n### Ackermann's function CLI scripts\n\nAckermann, a student of Hilbert, discovered early examples of totally\ncomputable functions that are not primitively recursive.\n\nA [fairly standard][4] definition of the Ackermann function is\nrecursively defined for `m,n >= 0` by\n\n```\n ackermann(0,n) = n+1\n ackermann(m,0) = ackermann(m-1,1)\n ackermann(m,n) = ackermann(m-1, ackermann(m, n-1))\n```\n\n#### CLI program **ackermann_list**\n\n* Given two non-negative integers, evaluates Ackermann's function\n* Implements the recursion via a Python array\n* **Usage:** `ackerman_list m n`\n\n---\n\n### Pythagorean triple CLI script\n\nGeometrically, a *Pythagorean* triangle is a right triangle with\npositive integer sides.\n\n#### CLI program **pythag3**\n\n* Generates primitive Pythagorean triples\n * A primitive Pythagorean triple is a 3-tuple of integers `(a, b, c)` such that\n * `a\u00b3 + b\u00b3 = c\u00b3` where `a,b,c > 0` and `gcd(a,b,c) = 1`\n * The integers `a, b, c` represent the sides of a right triangle\n* **Usage:** `pythag3 [m [n [max]]`\n * 3 args print all triples with `m <= a <= n` and `a < b < c <= max`\n * 2 args print all triples with `m <= a <= n`\n * 1 arg prints all triples with `a <= m`\n * 0 args print all triples with `3 <= a <= 100`\n\n---\n\n[1]: https://pypi.org/project/grscheller.boring-math/\n[2]: https://github.com/grscheller/boring-math/\n[3]: https://grscheller.github.io/grscheller-pypi-namespace-docs/boring-math/\n[4]: https://mathworld.wolfram.com/AckermannFunction.html\n",
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