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 project on PyPI
  • Source code on GitHub
• Detailed documentation
  • Detailed API documentation on GH-Pages

Here are the modules and executables which make up the grscheller.boring-math PyPI project.

• 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[int]**
    • 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[int]
    • 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, 21, ...

• 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 a**2 + b**2 = c**2
    • 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

• 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

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 program 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 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