type LDT = FRI_LDT<Fr, DensePolynomial<Fr>, Keccak256Hash<Fr>>;

let deg = 31;
let p = DensePolynomial::<Fr>::rand(deg, &mut ark_std::test_rng());

let proof = LDT::prove(&p);

let v = LDT::verify(proof, deg);
assert!(v);

type PCS = FRI_PCS<Fr, DensePolynomial<Fr>, Keccak256Hash<Fr>>;

let deg = 31;
let mut rng = ark_std::test_rng();
let p = DensePolynomial::<Fr>::rand(deg, &mut rng);

let commitment = PCS::commit(&p);

let r = Fr::rand(&mut rng);

let (proof, claimed_y) = PCS::open(&p, r);

let v = PCS::verify(commitment, proof, r, claimed_y);
assert!(v);