ogdoad 1.0.7

Clifford and Weyl algebras, quadratic forms, and games over exact, finite, local, and transfinite scalar backends.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28

//! Sparse PBW Weyl algebra and its rank-one polynomial action. Run with:
//!   cargo run --example weyl

use ogdoad::scalar::{Poly, Rational, Scalar};
use ogdoad::weyl::WeylAlgebra;

fn r(value: i128) -> Rational {
    Rational::from_int(value)
}

fn main() {
    let algebra = WeylAlgebra::<Rational>::standard(1);
    let x = algebra.x(0);
    let d = algebra.d(0);

    println!("[d,x] = {}", algebra.commutator(&d, &x));
    println!(
        "dā†‘2 xā†‘3 = {}",
        algebra.mul(&algebra.pow(&d, 2), &algebra.pow(&x, 3))
    );

    let polynomial = Poly::new(vec![r(1), r(2), r(3)]); // 1 + 2t + 3t^2
    let operator = algebra.mul(&d, &x);
    println!(
        "(d x) ā‹… ({polynomial}) = {}",
        algebra.act_on_poly(&operator, &polynomial).unwrap()
    );
}