### Mathematical Libraries
Project description
Daddy's boring math library
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
Overview
Here are the modules and executables 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_before
: int**) -> Iterator[int]**- 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 takenm
at a time - pure integer implementation of math.comb
- returns number of combinations of
- Function 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
andf(1) = f1
- defaults to
0, 1, 1, 2, 3, 5, 8, 13, 21, ...
- Function fibonacci(
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
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
is1
- such that
- Iterator finds all primitive Pythagorean Triples
- where
0 < a_start <= a < b < c <= max
wherea <= a_max
- if
max = 0
find all theoretically possible triples witha <= a_max
- where
- Method Pythag3.triples(
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
- Function ackermann_list(
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 program ackerman_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 thata³ + b³ = c³
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 args print all triples with
m <= a <= n
anda < 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
- 3 args print all triples with
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