# poset

A simple implementation of posets.

[Rust](https://www.rust-lang.org/) already provides some tools to analyse
posets; we can define partial order on a type `T` by implementing `PartialOrd`.
Doing so affords us the ability to use operators as we naturally would, writing
things like `a >= b`.

But implementing `PartialOrd` is not ideal when we wish to consider multiple
partial orders on a type. For example, what if we wanted to consider the
natural numbers (i.e. `u32`) with the divisbility relation: `a >= b` if and
only if `a % b == 0`.

The purpose of this crate is to provide both an ergonomic way to work with
various partial orders, and also helpful tools to study those associated posets
(by generating things like [Hasse
diagrams](https://en.wikipedia.org/wiki/Hasse_diagram)). It is within the
future scope of this crate to provide such things for more general relations,
too.

If you want the crate to be finished quicker, then you could consider
contributing. :)

# Example

```rust
use poset::{Poset, PartialOrder, PartialOrderBehaviour};
use std::error::Error;

fn main() -> Result<(), Box<dyn Error>> {
    // `a >= b` if and only if `b` divides `a`
    let divis = PartialOrder::new(|a: &i32, b: &i32| a % b == 0);

    // 3 is *comparable* with 6
    assert!(divis.cp(&3, &6));
    // 4 is *incomparable* with 6
    assert!(divis.ip(&4, &6));
    // 3 divides 15
    assert!(divis.lt(&3, &15));

    let pos = Poset::with_elements(1..16, divis);
    let chain_decomp = pos.chain_decomposition()?;

    let antichains = pos.antichains(chain_decomp);

    // c.f. [OEIS A051026](https://oeis.org/A051026)
    assert_eq!(antichains.count(), 1133);

    // if you want to generate Hasse diagrams
    #[cfg(feature = "graff")]
    {
        use graff::{Graph, GraphBehaviour};

        let g = pos.hasse()?;
        assert_eq!(g.edge_count(), 19);
    }

    Ok(())
}
```

## License

This project is released under [The Unlicense](https://unlicense.org/),
dedicated to the public domain.

## Contributing

Contributions welcome! :)

By submitting a pull request or otherwise contributing to this project, you
agree to dedicate your contribution to the public domain under the terms of
[The Unlicense](https://unlicense.org/), and you certify that you have the
right to do so.