Poly-rust

This is a multivariate polynomial library over generic types for Rust, as I was unable to find a suitable one that already exists.

Well actually, this is a combination of two projects: A polynomial library for Rust, and an implementation of a polynomial grammar I made to parse multivaraite polynomial expressions. One day I'll push this as a crate.

The goal is to extend this to infinite series over arbitrary fields, create an interpreter using the parser, and then write programs to mess around with infinite series.

Example

extern crate poly;
pub use poly::Polynomial64; 

let polynomial = Polynomial64::from("(x^2 + y^2 + z^2)^2").unwrap();
println!("{}", polynomial); 
// x^4 + 2x^2y^2 + 2x^2z^2 + y^4 + 2y^2z^2 + z^4

let other = Polynomial64::from("x^4 + y^4 + z^4").unwrap();
let sub = polynomial - other;
println!("{}", sub); 
// 2x^2y^2 + 2x^2z^2 + 2y^2z^2

println!("{}", sub.pow(2)); 
// 4x^4y^4 + 8x^4y^2z^2 + 4x^4z^4 + 8x^2y^4z^2 + 8x^2y^2z^4 + 4y^4z^4

Type Generics

Polynomials are generally elements over a commutative ring K[x_1, ... x_n] whose coefficients are elements over a field K. Practically speaking you really only need the coefficients to be elements over a commutative ring. Hence, this library enforces that the types T for polynomial coefficients of the Polynomial struct (and hence monomial coefficients of the Monomial struct) must satisfy the trait CRing defined as follows.

pub trait CRing<Rhs = Self, Output = Self>:
    Zero
    + One
    + Add<Rhs, Output = Output>
    + Sub<Rhs, Output = Output>
    + Mul<Rhs, Output = Output>
{}

Grammar

The following grammar is used to create the set of acceptable polynomial expressions.

polyexpr -> polyexpr + term
            | polyexpr - term
            | term

term -> term * factor 
        | factor

factor -> (polyexpr)
        | -(polyexpr)
        | polynomial
        | (polyexpr)^n

polynomial -> polynomial + monomial
            | polynomial - monomial
            | monomial

monomial -> x^Int
            | Float x^Int 
            | Float x 
            | x 
            | Float