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.
First build:
cargo b
Provided is a CLI program acm-cli with subcommands to test the main ACM
module and the divisors/factorize submodules.
```
./target/debug/acm-cli acm 3 6 factorize 225 [[15, 15], [3, 75]]
./target/debug/acm-cli acm 1 4 atomic_density 100 16-| ● | | 12-| ● ● ● ● ● ● ● ● ● ● ● ● | | 8-| ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ●● ● | | 4-|● ● ●●● ●●● ●● ●●● ● ● ●● ● ●● ● ● ●● ●●● ● ● ● ●●● ● ● ●● ● ●●● ● ●● ● ● ● ● ● ● ● ●● ●● ● ● | | 0+--------------------------------------------------------------------------------------------------------------------- | | | | 20 40 60 80 ```
For full usage lists, try it, and any subcommand, with the -h flag:
```
./target/debug/acm-cli -h acm-cli 0.1 nilsso nilso@enosis.net
USAGE:
acm-cli
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) ```
Build all documentation locall and open in your browser:
RUSTDOCFLAGS="--html-in-header katex-header.html" cargo doc --no-deps --open
cargo t