grscheller.boring-math 0.1.2

Mathematics libraries with example executables

PyPI grscheller.boring-math

Daddy's boring math library.

• Functions of a mathematical nature
• Project name suggested by my then 13 year old daughter Mary
• Example of a Python package with both libraries and executables
• For detailed API documentation click here.

Overview

Here are the modules which make up the grscheller.boring_math package.

• Integer Math Module

  • Combinatorics
  • Fibonacci Sequences
  • Number Theory
  • Pythagorean Triples
  • Recursive Functions

• Integer Math CLI Module

  • Ackermann's Function
  • Pythagorean Triples

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Integer Math Module

Combinatorics

• Function comb(n: int, m: int) -> int
  • returns C(n,m) - the number of n items taken m at a time
  • contains two additional default parameters that can be adjusted
    • factorsNumerator = 66
    • factorsDenonator = 4
  • actually comb(n, m, 1, 1) runs faster for reasonably small n and m
    • better choice for inner loops and printable results
    • about 3 times slower than C based math.comb(n, m)
    • these default paramenters are better for larger results
  • goal is for it to work reasonably well after math.comb bogs down
  • suspect it will really shine for pypy when it supports Python 3.11

Fibonacci Sequences

• Function fibonacci(f0: int=0, f1: int=1) -> Iterator
  • return an iterator for a Fibonacci sequence
  • defaults to 0, 1, 1, 2, 3, 5, 8, ...

Number theory

• Function gcd(fst: int, snd: int) -> int

  • takes two integers, returns greatest common divisor (gcd)
  • where gcd >= 0
  • gcd(0,0) returns 0 but in this case the gcd does not exist

• Function lcm(fst: int, snd: int) -> int

  • takes two integers, returns least common multiple (lcm)

• Function primes(start: int=2, end_before: int=100) -> Iterator

  • takes two integers, returns least common multiple (lcm)

Pythagorean Triples

The values a, b, c > 0 represent integer sides of a right triangle.

• Function pythag3(a_max: int=3, all_max: int|None=None) -> Iterator
  • Return an interator of tuples of Pythagorean Tiples
  • Side a <= a_max and sides a, b, c <= all_max
  • Iterator finds all primative pythagorean triples up to a given a_max

Recursive Functions

• Function ackermann(m: int, n: int) -> int
  • Ackermann's function is a doublely recursively defined function
  • An example of a computable but not primitive recursive function
  • Becomes numerically intractable after m=4

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Integer Math CLI Module

Ackermann's Function

• Function ackerman_cli(fst: int, snd: int) -> None
  • entry point for program ackermann
  • Ackermann's function is defined recursively by
    • ackermann(0,n) = n+1
    • ackermann(m,0) = ackermann(m-1,1)
    • ackermann(m,n) = ackermann(m-1,ackermann(m, n-1)) for n,m > 0
  • Usage: ackerman m n

Pythagorean Triple Function

• entry point for program pythag3
• A Pythagorean triple is a 3-tuple of integers (a, b, c) such that
  • a*a + b*b = c*c 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]
  • one argument outputs all triples with a <= n
  • two arguments outputs all triples with a <= n and a, b, c <= m

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