Add scalar multiplication impl for DensePolynomial (#258)

CHANGELOG.md

@@ -5,6 +5,7 @@
 ### Features
 
 - [\#230](https://github.com/arkworks-rs/algebra/pull/230) (ark-ec) Add `wnaf_mul` implementation for `ProjectiveCurve`.
+- [\#258](https://github.com/arkworks-rs/algebra/pull/258) (ark-poly) Add `Mul<F>` implementation for `DensePolynomial`
 
 ### Improvements
 

poly/src/polynomial/univariate/dense.rs

@@ -398,6 +398,23 @@ impl<'a, 'b, F: Field> Div<&'a DensePolynomial<F>> for &'b DensePolynomial<F> {
     }
 }
 
+impl<'a, 'b, F: Field> Mul<F> for &'b DensePolynomial<F> {
+    type Output = DensePolynomial<F>;
+
+    #[inline]
+    fn mul(self, elem: F) -> DensePolynomial<F> {
+        if self.is_zero() || elem.is_zero() {
+            DensePolynomial::zero()
+        } else {
+            let mut result = self.clone();
+            cfg_iter_mut!(result).for_each(|e| {
+                *e *= elem;
+            });
+            result
+        }
+    }
+}
+
 /// Performs O(nlogn) multiplication of polynomials if F is smooth.
 impl<'a, 'b, F: FftField> Mul<&'a DensePolynomial<F>> for &'b DensePolynomial<F> {
     type Output = DensePolynomial<F>;
@@ -566,6 +583,19 @@ mod tests {
         }
     }
 
+    #[test]
+    fn mul_random_element() {
+        let rng = &mut test_rng();
+        for degree in 0..70 {
+            let a = DensePolynomial::<Fr>::rand(degree, rng);
+            let e = Fr::rand(rng);
+            assert_eq!(
+                &a * e,
+                a.naive_mul(&DensePolynomial::from_coefficients_slice(&[e]))
+            )
+        }
+    }
+
     #[test]
     fn mul_polynomials_random() {
         let rng = &mut test_rng();