Implements arithmetic congruence monoids (ACM) in Rust.
In a nutshell, an ACM is an arithmetic progression which possesses a multiplicative structure, and specifically is the monoid:
With 
and 
we get a Hilbert monoid:
Over an ACM, we can factor integers into elements of the ACM. This is similar to simple prime factorization except that each factor must be an element of the ACM. We call elements which cannot be expressed as the product of smaller ACM elements atoms.
Finally, the purpose of this library is to study the atomic density of different ACMs, that is, the distance between atoms. In certain ACMs the atomic density is provably constant throughout, but in others it is unknown; not dissimilar to the density, or lack thereof, of prime integers in the set of all integers.
This project started as a C++ port of acm-sage, but my interest in Rust led me to rewrite the project.
Provided is an example CLI program acm-cli with subcommands to test the main ACM module and the
divisors/factorize submodules.
> cargo r --example acm-cli factor 225
(3,2),(5,2)
> cargo r --example acm-cli acm 3 6 factor 225
[15,15],[3, 75]
For usages use the -h flag.
> cargo r --example acm-cli -h
USAGE:
acm-cli <SUBCOMMAND>
FLAGS:
-h, --help Prints help information
-V, --version Prints version information
SUBCOMMANDS:
acm ArithmeticCongruenceMonoid subcommand
divisors Integer divisors subcommand
factorize Integer factorization subcommand
help Prints this message or the help of the given subcommand(s)
> cargo r --example acm-cli acm factor -h
ACM atom factorizations of an integer
USAGE:
acm-cli acm <a> <b> factor <n>
FLAGS:
-h, --help Prints help information
-V, --version Prints version information
ARGS:
<n> Integer to factor
Build all documentation locall and open in your browser:
RUSTDOCFLAGS="--html-in-header katex-header.html" cargo doc --no-deps --open
To run all tests, including documentation tests:
cargo t