use std::cell::RefCell;
use std::rc::Rc;
use circuit_cas::circuit::dag::CircuitExt;
use circuit_cas::circuit::quotient::QuotientCircuit;
use circuit_cas::circuit::traits::Circuit;
use circuit_cas::poly::ideal::{Generators, Ideal};
use circuit_cas::var;

fn main() {
    let x = var!("x");
    let nx = var!("x\u{0304}");

    let idem: Ideal<_, Generators> = vec![
        1 * (&x ^ 2) - 1 * (&x ^ 1),
        1 * (&nx ^ 2) - 1 * (&nx ^ 1),
        1 * ((&x ^ 1) * (&nx ^ 1)) - 1 * (&x ^ 1),
    ].into();

    let quotient: Rc<RefCell<QuotientCircuit>> = idem.into();

    // Build x * x̄ + x in the DAG
    let xn   = quotient.var("x");
    let nxn  = quotient.var("x\u{0304}");
    let prod = xn * nxn;
    let xn2  = quotient.var("x");
    let expr = prod + xn2;

    println!("dag size: {}", quotient.borrow().len());
    println!("expr node id: {:?}", expr.id);
}