README-work.md

Math::NumberTheory

Raku package with Number theory functions.

The function names and features follow the Number theory functions of Wolfram Language.

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Installation

From Zef ecosystem:

zef install Math::NumberTheory

From GitHub:

zef install https://github.com/antononcube/Raku-Math-NumberTheory

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Usage examples

Factor integers

Gives a list of the prime factors of an integer argument, together with their exponents:

use Math::NumberTheory;
factor-integer(factorial(20))

Remark: By default factor-integer uses Pollard's Rho algorithm -- specified with method => 'rho' -- as implemented at RosettaCode, [RC1], with similar implementations provided by "Prime::Factor", [SSp1], and "Math::Sequences", [RCp1].

Do partial factorization, pulling out at most k distinct factors:

factor-integer(factorial(20), 3, method => 'trial')

Chinese reminders

Data:

my @data = 931074546, 117172357, 482333642, 199386034, 394354985;

Keys:

#my @keys = random-prime(10**9 .. 10**12, @data.elems);
my @keys = 274199185649, 786765306443, 970592805341, 293623796783, 238475031661;

Remark: Using these larger keys is also a performance check.

Encrypted data:

my $encrypted = chinese-reminder(@data, @keys);

Decrypted:

my @decrypted = @keys.map($encrypted mod *);

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References

[RC1] Rosetta Code, Prime decomposition, Section "Pure Raku".

[RCp1] Raku Community, Math::Sequences Raku package, (2016-2024), GitHub/raku-community-modules.

[SSp1] Stephen Schulze, Prime::Factor Raku package, (2016-2023), GitHub/thundergnat.