doc: fix a few nits (#160)

* refactor: rename powers -> squares

- Renamed the `powers` method to `squares` in `PowPolynomial` struct within `src/spartan/polys/power.rs` and changed its visibility level.

* fix: comment

* fix: comment of batch

src/spartan/batched.rs

@@ -186,7 +186,7 @@ where
     // Generate tau polynomial corresponding to eq(τ, τ², τ⁴ , …)
     // for a random challenge τ
     let tau = transcript.squeeze(b"t")?;
-    let all_taus = PowPolynomial::powers(&tau, num_rounds_x_max);
+    let all_taus = PowPolynomial::squares(&tau, num_rounds_x_max);
 
     let polys_tau = num_rounds_x
       .iter()

src/spartan/batched_ppsnark.rs

@@ -570,7 +570,7 @@ where
       // Sample new random variable for eq polynomial
       let rho = transcript.squeeze(b"r")?;
       let N_max = N.iter().max().unwrap();
-      let all_rhos = PowPolynomial::powers(&rho, N_max.log_2());
+      let all_rhos = PowPolynomial::squares(&rho, N_max.log_2());
 
       let instances = zip_with!(
         (

src/spartan/mod.rs

@@ -111,7 +111,7 @@ pub struct PolyEvalWitness<E: Engine> {
 }
 
 impl<E: Engine> PolyEvalWitness<E> {
-  /// Given [Pᵢ] and [sᵢ], compute P = ∑ᵢ sᵢ⋅Pᵢ
+  /// Given [Pᵢ] and s, compute P = ∑ᵢ sⁱ⋅Pᵢ
   ///
   /// # Details
   ///
@@ -154,7 +154,13 @@ impl<E: Engine> PolyEvalWitness<E> {
     PolyEvalWitness { p }
   }
 
-  // This method panics unless all vectors in p_vec are of the same length
+  /// Given a set of polynomials \[Pᵢ\] and a scalar `s`, this method computes the weighted sum
+  /// of the polynomials, where each polynomial Pᵢ is scaled by sⁱ. The method handles polynomials
+  /// of different sizes by padding smaller ones with zeroes up to the size of the largest polynomial.
+  ///
+  /// # Panics
+  ///
+  /// This method panics if the polynomials in `p_vec` are not all of the same length.
   fn batch(p_vec: &[&Vec<E::Scalar>], s: &E::Scalar) -> PolyEvalWitness<E> {
     p_vec
       .iter()

src/spartan/polys/power.rs

@@ -18,7 +18,7 @@ impl<Scalar: PrimeField> PowPolynomial<Scalar> {
   /// Creates a new `PowPolynomial` from a Scalars `t`.
   pub fn new(t: &Scalar, ell: usize) -> Self {
     // t_pow = [t^{2^0}, t^{2^1}, ..., t^{2^{ell-1}}]
-    let t_pow = Self::powers(t, ell);
+    let t_pow = Self::squares(t, ell);
 
     PowPolynomial {
       eq: EqPolynomial::new(t_pow),
@@ -27,7 +27,7 @@ impl<Scalar: PrimeField> PowPolynomial<Scalar> {
 
   /// Create powers the following powers of `t`:
   /// [t^{2^0}, t^{2^1}, ..., t^{2^{ell-1}}]
-  pub(crate) fn powers(t: &Scalar, ell: usize) -> Vec<Scalar> {
+  pub(in crate::spartan) fn squares(t: &Scalar, ell: usize) -> Vec<Scalar> {
     successors(Some(*t), |p: &Scalar| Some(p.square()))
       .take(ell)
       .collect::<Vec<_>>()