ark_poly/polynomial/
mod.rs

1//! Modules for working with univariate or multivariate polynomials.
2use ark_ff::{Field, Zero};
3use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
4use ark_std::{
5    fmt::Debug,
6    hash::Hash,
7    ops::{Add, AddAssign, Neg, SubAssign},
8    rand::Rng,
9    vec::*,
10};
11
12pub mod multivariate;
13pub mod univariate;
14
15/// Describes the common interface for univariate and multivariate polynomials
16pub trait Polynomial<F: Field>:
17    Sized
18    + Clone
19    + Debug
20    + Hash
21    + PartialEq
22    + Eq
23    + Add
24    + Neg
25    + Zero
26    + CanonicalSerialize
27    + CanonicalDeserialize
28    + for<'a> AddAssign<&'a Self>
29    + for<'a> AddAssign<(F, &'a Self)>
30    + for<'a> SubAssign<&'a Self>
31{
32    /// The type of evaluation points for this polynomial.
33    type Point: Sized + Clone + Ord + Debug + Sync + Hash;
34
35    /// Returns the total degree of the polynomial
36    fn degree(&self) -> usize;
37
38    /// Evaluates `self` at the given `point` in `Self::Point`.
39    fn evaluate(&self, point: &Self::Point) -> F;
40}
41
42/// Describes the interface for univariate polynomials
43pub trait DenseUVPolynomial<F: Field>: Polynomial<F, Point = F> {
44    /// Constructs a new polynomial from a list of coefficients.
45    fn from_coefficients_slice(coeffs: &[F]) -> Self;
46
47    /// Constructs a new polynomial from a list of coefficients.
48    fn from_coefficients_vec(coeffs: Vec<F>) -> Self;
49
50    /// Returns the coefficients of `self`
51    fn coeffs(&self) -> &[F];
52
53    /// Returns a univariate polynomial of degree `d` where each
54    /// coefficient is sampled uniformly at random.
55    fn rand<R: Rng>(d: usize, rng: &mut R) -> Self;
56}
57
58/// Describes the interface for multivariate polynomials
59pub trait DenseMVPolynomial<F: Field>: Polynomial<F> {
60    /// The type of the terms of `self`
61    type Term: multivariate::Term;
62
63    /// Constructs a new polynomial from a list of tuples of the form `(coeff, Self::Term)`
64    fn from_coefficients_slice(num_vars: usize, terms: &[(F, Self::Term)]) -> Self {
65        Self::from_coefficients_vec(num_vars, terms.to_vec())
66    }
67
68    /// Constructs a new polynomial from a list of tuples of the form `(coeff, Self::Term)`
69    fn from_coefficients_vec(num_vars: usize, terms: Vec<(F, Self::Term)>) -> Self;
70
71    /// Returns the terms of a `self` as a list of tuples of the form `(coeff, Self::Term)`
72    fn terms(&self) -> &[(F, Self::Term)];
73
74    /// Returns the number of variables in `self`
75    fn num_vars(&self) -> usize;
76
77    /// Outputs an `l`-variate polynomial which is the sum of `l` `d`-degree univariate
78    /// polynomials where each coefficient is sampled uniformly at random.
79    fn rand<R: Rng>(d: usize, num_vars: usize, rng: &mut R) -> Self;
80}
ark_poly/polynomial/mod.rs

ark_poly/polynomial/
mod.rs
