Math::Handy - Handy math routines and operators that aren't in CORE Raku.
say 25!; # 15511210043330985984000000
say Γ 1/2; # 1.7724538509055163
say binomial(9, 5); # 126
say Σ (^1e2).grep: &is-prime; # 1060
say Π (^1e2).grep: &is-prime; # 2305567963945518424753102147331756070
say 33 divmod 5; # (6 3)
say 33 divmod 5.1; # (6 3)
say 33 /% 5.1; # (6 2.5)
say adr 16781; # (5 2)
say mdr 16781; # (0 4)
say 180°; # 3.141592653589793
say 200ᵍ; # 3.141592653589793
Math::Handy provides several handy functions and operators.
factorial (Int) - the product of the integers from one to $n. Also available as
Factorial is a discrete operation, only valid at integer values. For a continuous function, you want
gamma (Real $n).
gamma (Real) is a continuous factorial function.
Γ($n) =~= ($n - 1)!. Also available as
Γ (Real $n) (Greek uppercase gamma). Calculated using Lanczos approximation. (Only valid for positive arguments at this point.)
Also related to
binomial(Int $n, Int $p), very commonly appears in combinatorics. Is equivalently expressed as:
n! / (p! × (n - p)!).
Raku has the very convenient
sum function. Traditional mathematics spells it
Σ. This module provides a
Σ (*@list) operator to remedy that.
Another common mathematical operator that Raku left out is
product(). Raku has the
[*] meta reduce operator, but that is difficult to chain with other operations. This module provides both a
product (*@list) routine, and the more traditionally spelled:
Π (*@list) (Greek uppercase pi)
div, Raku has
mod, Raku has
polymod(), but sometimes you may want a plain old
infix:<divmod> (Real, Real) coerces arguments to Int and returns the whole divisions and the remainder.
Also available as
infix:</%> (Real, Real):
Real %/ Real which doesn't coerce.
additive digital root of an Integer in a particular base, is the recursive sum of the digits until only a single digit remains. The
persistance is the number of times the function needs to recurse to reach a single digit.
digital-root (Int $n, :$base = 10). Calculates and returns the additive digital root and the persistance, by default in base 10. Pass in a named base (2 = 36) if a different base is desired. Also available as the abbreviated
adr (Int $n, :$base = 10)
Similar to the additive
digital-root() is the
multiplicative-digital-root (Int $n, :$base = 10) is the recursive product of the digits until only one digit remains. Returns the multiplicative digital root and the persistance. Also available as the abbreviated
mdr (Int $n, :$base = 10)
Raku provides a multitude of trigonometric functions, but they all work with radian angle measurements by default. To make it easy to work with degrees (360° in 2π radians), or gradians (400ᵍ in 2π radians), provides two postfix conversion routines.
postfix:<°> (Real $degrees) converts degree measurments to radians.
postfix:<ᵍ> (Real $gradians) converts gradian measurments to radians.
Most of these were code snippets I or someone else wrote as helper functions for solving RosettaCode tasks.
If there is a routine you think should be added, or if I bungled one of the existing, please let me know.
Stephen Schulze (aka thundergnat email@example.com)
COPYRIGHT AND LICENSE
Copyright 2023 thundergnat
This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.