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 project on PyPI
- See Detailed API documentation on GH-Pages
- See Source code on GitHub
Here are the modules and executables which make up the PyPI grscheller.boring_math package.
- 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
- Function gcd(int, int) -> int
- 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
- Function comb(n: int, m: int) -> int
- 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
andf(1) = f1
- defaults to
0, 1, 1, 2, 3, 5, 8, 13, ...
- Function fibonacci(f0: int=0, f1: int=1) -> Iterator
- Number Theory
- 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
is1
- such that
- Iterator finds all primative pythagorean such that
0 < a_start <= a < b < c <= max
wherea <= a_max
- if
max = 0
find all theoretically possible triples witha <= a_max
- Method Pythag3.triples(a_start: int, a_max: int, max: int) -> Iterator
- Pythagorean Triple Class
- 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
- Function ackermann(m: int, n: int) -> int
- Ackermann's Function
Implemented in an OS and package build tool independent way via the project.scripts section of pyproject.toml.
Ackermann, a student of Hilbert, discovered early examples of totally computable functions that are not primitively recursive.
A fairly standard 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
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 thata**2 + b**2 = c**2
wherea,b,c > 0
andgcd(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
- A Pythagorean triple is a 3-tuple of integers