remove ark-poly for most crates

arithmetic/Cargo.toml

@@ -2,6 +2,10 @@
 name = "arithmetic"
 version = "0.1.0"
 edition = "2021"
+authors = [ 
+    "Zhenfei Zhang<zhenfei.zhang@hotmail.com>", 
+    "Binyi Chen" 
+    ]
 
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
@@ -10,7 +14,7 @@ edition = "2021"
 ark-ff = { version = "^0.3.0", default-features = false }
 ark-std = { version = "^0.3.0", default-features = false }
 ark-poly = { version = "^0.3.0", default-features = false }
-ark-serialize =  { version = "^0.3.0", default-features = false }
+ark-serialize =  { version = "^0.3.0", default-features = false, features = [ "derive" ] }
 ark-bls12-381 = { version = "0.3.0", default-features = false, features = [ "curve" ] }
 
 rand_chacha = { version = "0.3.0", default-features = false }
@@ -27,7 +31,6 @@ parallel = [
     "rayon",
     "ark-std/parallel", 
     "ark-ff/parallel",  
-    "ark-poly/parallel" 
     ]
 print-trace = [ 
     "ark-std/print-trace" 

arithmetic/src/lib.rs

@@ -1,7 +1,69 @@
 mod errors;
 mod multilinear_polynomial;
+mod util;
 mod virtual_polynomial;
 
-pub use errors::ArithErrors;
-pub use multilinear_polynomial::{random_zero_mle_list, DenseMultilinearExtension};
-pub use virtual_polynomial::{build_eq_x_r, VPAuxInfo, VirtualPolynomial};
+pub mod prelude;
+
+use ark_ff::{Field, Zero};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
+use ark_std::{
+    fmt::Debug,
+    hash::Hash,
+    ops::{Add, AddAssign, Index, Neg, SubAssign},
+    rand::Rng,
+    vec::Vec,
+};
+
+/// This trait describes an interface for the multilinear extension
+/// of an array.
+/// The latter is a multilinear polynomial represented in terms of its
+/// evaluations over the domain {0,1}^`num_vars` (i.e. the Boolean hypercube).
+///
+/// Index represents a point, which is a vector in {0,1}^`num_vars` in little
+/// endian form. For example, `0b1011` represents `P(1,1,0,1)`
+pub trait MultilinearExtension<F: Field>:
+    Sized
+    + Clone
+    + Debug
+    + Hash
+    + PartialEq
+    + Eq
+    + Add
+    + Neg
+    + Zero
+    + CanonicalSerialize
+    + CanonicalDeserialize
+    + for<'a> AddAssign<&'a Self>
+    + for<'a> AddAssign<(F, &'a Self)>
+    + for<'a> SubAssign<&'a Self>
+    + Index<usize>
+{
+    /// Returns the number of variables in `self`
+    fn num_vars(&self) -> usize;
+
+    /// Evaluates `self` at the given the vector `point` in slice.
+    /// If the number of variables does not match, return `None`.
+    fn evaluate(&self, point: &[F]) -> Option<F>;
+
+    /// Outputs an `l`-variate multilinear extension where value of evaluations
+    /// are sampled uniformly at random.
+    fn rand<R: Rng>(num_vars: usize, rng: &mut R) -> Self;
+
+    /// Relabel the point by swapping `k` scalars from positions `a..a+k` to
+    /// positions `b..b+k`, and from position `b..b+k` to position `a..a+k`
+    /// in vector.
+    ///
+    /// This function turns `P(x_1,...,x_a,...,x_{a+k - 1},...,x_b,...,x_{b+k -
+    /// 1},...,x_n)` to `P(x_1,...,x_b,...,x_{b+k - 1},...,x_a,...,x_{a+k -
+    /// 1},...,x_n)`
+    fn relabel(&self, a: usize, b: usize, k: usize) -> Self;
+
+    /// Reduce the number of variables of `self` by fixing the
+    /// `partial_point.len()` variables at `partial_point`.
+    fn fix_variables(&self, partial_point: &[F]) -> Self;
+
+    /// Returns a list of evaluations over the domain, which is the boolean
+    /// hypercube.
+    fn to_evaluations(&self) -> Vec<F>;
+}