fix: streamline usage of PowPolynomial

src/spartan/batched_ppsnark.rs

@@ -903,14 +903,10 @@ impl<E: Engine, EE: EvaluationEngineTrait<E>> BatchedRelaxedR1CSSNARKTrait<E>
         let num_rounds_i = rand_sc.len();
         let num_vars_log = num_vars.log_2();
 
-        let eq_rho = {
-          let rho_coords = PowPolynomial::new(&rho, num_rounds_i).coordinates();
-          EqPolynomial::new(rho_coords).evaluate(rand_sc)
-        };
+        let eq_rho = PowPolynomial::new(&rho, num_rounds_i).evaluate(rand_sc);
 
         let (eq_tau, eq_masked_tau) = {
-          let tau_coords = PowPolynomial::new(&tau, num_rounds_i).coordinates();
-          let eq_tau = EqPolynomial::new(tau_coords);
+          let eq_tau: EqPolynomial<_> = PowPolynomial::new(&tau, num_rounds_i).into();
 
           let eq_tau_at_rand = eq_tau.evaluate(rand_sc);
           let eq_masked_tau = MaskedEqPolynomial::new(&eq_tau, num_vars_log).evaluate(rand_sc);

src/spartan/polys/eq.rs

@@ -37,7 +37,7 @@ impl<Scalar: PrimeField> EqPolynomial<Scalar> {
     assert_eq!(self.r.len(), rx.len());
     (0..rx.len())
       .map(|i| self.r[i] * rx[i] + (Scalar::ONE - self.r[i]) * (Scalar::ONE - rx[i]))
-      .fold(Scalar::ONE, |acc, item| acc * item)
+      .product()
   }
 
   /// Evaluates the `EqPolynomial` at all the `2^|r|` points in its domain.

src/spartan/polys/identity.rs

@@ -24,6 +24,6 @@ impl<Scalar: PrimeField> IdentityPolynomial<Scalar> {
         power_of_two *= 2;
         result
       })
-      .fold(Scalar::ZERO, |acc, item| acc + item)
+      .sum()
   }
 }

src/spartan/polys/power.rs

@@ -61,3 +61,9 @@ impl<Scalar: PrimeField> PowPolynomial<Scalar> {
     self.eq.evals()
   }
 }
+
+impl<Scalar: PrimeField> From<PowPolynomial<Scalar>> for EqPolynomial<Scalar> {
+  fn from(polynomial: PowPolynomial<Scalar>) -> Self {
+    polynomial.eq
+  }
+}

src/spartan/ppsnark.rs

@@ -885,12 +885,8 @@ impl<E: Engine, EE: EvaluationEngineTrait<E>> RelaxedR1CSSNARKTrait<E> for Relax
 
     // verify claim_sc_final
     let claim_sc_final_expected = {
-      let rand_eq_bound_rand_sc = {
-        let poly_eq_coords = PowPolynomial::new(&rho, num_rounds_sc).coordinates();
-        EqPolynomial::new(poly_eq_coords).evaluate(&rand_sc)
-      };
-      let taus_coords = PowPolynomial::new(&tau, num_rounds_sc).coordinates();
-      let eq_tau = EqPolynomial::new(taus_coords);
+      let rand_eq_bound_rand_sc = PowPolynomial::new(&rho, num_rounds_sc).evaluate(&rand_sc);
+      let eq_tau: EqPolynomial<_> = PowPolynomial::new(&tau, num_rounds_sc).into();
 
       let taus_bound_rand_sc = eq_tau.evaluate(&rand_sc);
       let taus_masked_bound_rand_sc =