diff --git a/core/sonic/src/helped/prover.rs b/core/sonic/src/helped/prover.rs
index b26c3ca9..7a0a0209 100644
--- a/core/sonic/src/helped/prover.rs
+++ b/core/sonic/src/helped/prover.rs
@@ -6,7 +6,7 @@ use crate::cs::{SynthesisDriver, Circuit, Backend, Variable, Coeff};
 use crate::srs::SRS;
 use crate::transcript::ProvingTranscript;
 use crate::polynomials::commitment::{polynomial_commitment};
-use crate::utils::{ChainExt, mul_powers};
+use crate::utils::{ChainExt, coeffs_consecutive_powers};
 
 pub const NUM_BLINDINGS: usize = 4;
 
@@ -106,7 +106,7 @@ impl<E: Engine> Proof<E> {
         let first_power = y_inv.pow(&[(2 * n + NUM_BLINDINGS) as u64]);
 
         // Evaluate the polynomial r(X, Y) at y
-        mul_powers(
+        coeffs_consecutive_powers(
             &mut rxy,
             first_power,
             y,
diff --git a/core/sonic/src/polynomials/mod.rs b/core/sonic/src/polynomials/mod.rs
index 309416ee..7c8c87d7 100644
--- a/core/sonic/src/polynomials/mod.rs
+++ b/core/sonic/src/polynomials/mod.rs
@@ -1,3 +1,6 @@
+use pairing::Engine;
 pub mod commitment;
 pub mod s_eval;
 pub mod operations;
+
+pub struct Polynomial<E: Engine>(Vec<E::Fr>);
diff --git a/core/sonic/src/polynomials/operations.rs b/core/sonic/src/polynomials/operations.rs
index e69de29b..f77b7d42 100644
--- a/core/sonic/src/polynomials/operations.rs
+++ b/core/sonic/src/polynomials/operations.rs
@@ -0,0 +1,18 @@
+use bellman::multicore::Worker;
+use pairing::{Engine, Field};
+
+pub fn add_polynomials<F: Field>(a: &mut [F], b: &[F]) {
+    assert_eq!(a.len(), b.len());
+
+    let worker = Worker::new();
+
+    worker.scope(a.len(), |scope, chunk| {
+        for (a, b) in a.chunks_mut(chunk).zip(b.chunks(chunk)) {
+            scope.spawn(move |_| {
+                for (a, b) in a.iter_mut().zip(b.iter()) {
+                    a.add_assign(b);
+                }
+            });
+        }
+    });
+}
diff --git a/core/sonic/src/polynomials/s_eval.rs b/core/sonic/src/polynomials/s_eval.rs
index df0493d1..060ee2eb 100644
--- a/core/sonic/src/polynomials/s_eval.rs
+++ b/core/sonic/src/polynomials/s_eval.rs
@@ -2,6 +2,7 @@ use pairing::{Engine, Field};
 use bellman::SynthesisError;
 
 /// Defined in Section 5: SYSTEM OF CONSTRAINTS
+/// Evaluation of s(X, Y) at x
 #[derive(Clone)]
 pub struct SxEval<E: Engine> {
     y: E::Fr,
@@ -20,7 +21,8 @@ pub struct SxEval<E: Engine> {
 }
 
 impl<E: Engine> SxEval<E> {
+    ///  Initialize s(X, y) where y is fixed.
     pub fn new(y: E::Fr, n: usize) -> Result<Self, SynthesisError>  {
         unimplemented!();
     }
-}
\ No newline at end of file
+}
diff --git a/core/sonic/src/utils.rs b/core/sonic/src/utils.rs
index 18de0e11..00c60908 100644
--- a/core/sonic/src/utils.rs
+++ b/core/sonic/src/utils.rs
@@ -69,7 +69,7 @@ impl<T, U> DoubleEndedIterator for Chain<T, U>
 /// Multiply each coefficient by some power of the base in a form
 /// `first_power * base^{i}`
 /// This would be sparse, consecutive multiplication based on non-zero coefficients.
-pub fn mul_powers<'a, F: Field> (
+pub fn coeffs_consecutive_powers<'a, F: Field> (
     coeffs: &mut [F],
     first_power: F,
     base: F