Multi-dimensional Polynomials

Peform operations with multivariate polynomials such as replacement and multiplication in rust. With this library one can import polynomial functions into rust in an easy way and perform simple operations end evaluations.

The supported type for the coefficients are:

• f64 (real and complex)
• f128 (real and complex)
• num::BigRational

There is a parser that imports expressions from string into num::BigRational:

extern crate mpolynomial;

use mpolynomial::MPolynomial;
use mpolynomial::parser::parse_expression;
use num::{BigInt, BigRational};

fn main() {
    let var_names = vec![
        String::from("x1"),
        String::from("x2"),
        String::from("x3"),
        String::from("x4"),
    ];

    // Geometric Series
    let mpoly_str = "(1-x1^11)^2";
    let factor_str = "(1-x1)^2";
    let res_str = "(1+x1+x1^2+x1^3+x1^4+x1^5+x1^6+x1^7+x1^8+x1^9+x1^10)^2";

    let mut mpoly = parse_expression(mpoly_str, &var_names);
    let factor = parse_expression(factor_str, &var_names);
    let res = parse_expression(res_str, &var_names);

    mpoly.exact_division(&factor).unwrap();
    assert_eq!(res.to_str(&var_names), mpoly.to_str(&var_names));

    // Multivariate
    let mpoly_str = "(11 x1^32 + 12 x2 + 99 x3 + 21 x1*x4)^10";
    let factor_str = "(11 x1**32 + 12 x2 + 99 x3 + 21 x1*x4)^8";

    let factor = parse_expression(factor_str, &var_names);
    let mut mpoly = parse_expression(mpoly_str, &var_names);

    mpoly.exact_division(&factor).unwrap();
    //println!("{}", mpoly);
    let mut res_str = String::new();
    res_str += "+9801*x3^2+2376*x2^1*x3^1+144*x2^2+4158*x1^1*x3^1*x4^1";
    res_str += "+504*x1^1*x2^1*x4^1+441*x1^2*x4^2+2178*x1^32*x3^1";
    res_str += "+264*x1^32*x2^1+462*x1^33*x4^1+121*x1^64";
    assert_eq!(res_str, format!("{}", mpoly));
}

Here is a list of the function implemented for the structure MPolynomial:

• add: add a monomial to the polynomial
• update: update the coefficient of a monomial
• replace: replace one variable with a linear polynomial (e.g. x1-> c+2x1+3x2)
• mult: multiply the current polynomial by another and overwrite
• exact_division: divide by one of the factors of the polynomial (otherwise fails)
• euclidean_division: returns both the quotient and remainder of the division
• multivariate_gcd: compute the gcd of two polynomial
• ...
• ...