grscheller.boring-math 0.4.0

Libraries of a mathematical nature with example executables.

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 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.

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, ...

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• Pythagorean Triple Module
  • Pythagorean Triple Class
    • Method Pythag3.triples(a_start: int, a_max: int, max: int) -> Iterator
      • 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 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

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• 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

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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 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

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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

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