Impl sub, mul and div for actual objects (#843)

* Impl sub, mul and div for actual objects

* Add non-reference scalar multiplication

Co-authored-by: Antonio Mejías Gil <anmegi.95@gmail.com>

* Implement arithmetic operators with a macro

Co-authored-by: Antonio Mejías Gil <anmegi.95@gmail.com>

* Undonde smaller breaking change

Co-authored-by: Antonio Mejías Gil <anmegi.95@gmail.com>

* Add non-reference scalar multiplication

Co-authored-by: Antonio Mejías Gil <anmegi.95@gmail.com>

---------

Co-authored-by: Antonio Mejías Gil <anmegi.95@gmail.com>

Author: Cesar199999

poly/src/polynomial/univariate/dense.rs

@@ -285,14 +285,6 @@ impl<F: Field> DerefMut for DensePolynomial<F> {
     }
 }
 
-impl<F: Field> Add for DensePolynomial<F> {
-    type Output = DensePolynomial<F>;
-
-    fn add(self, other: DensePolynomial<F>) -> Self {
-        &self + &other
-    }
-}
-
 impl<'a, 'b, F: Field> Add<&'a DensePolynomial<F>> for &'b DensePolynomial<F> {
     type Output = DensePolynomial<F>;
 
@@ -601,6 +593,15 @@ impl<'b, F: Field> Mul<F> for &'b DensePolynomial<F> {
     }
 }
 
+impl<F: Field> Mul<F> for DensePolynomial<F> {
+    type Output = DensePolynomial<F>;
+
+    #[inline]
+    fn mul(self, elem: F) -> DensePolynomial<F> {
+        &self * elem
+    }
+}
+
 /// 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>;
@@ -620,6 +621,37 @@ impl<'a, 'b, F: FftField> Mul<&'a DensePolynomial<F>> for &'b DensePolynomial<F>
     }
 }
 
+macro_rules! impl_op {
+    ($trait:ident, $method:ident, $field_bound:ident) => {
+        impl<F: $field_bound> $trait<DensePolynomial<F>> for DensePolynomial<F> {
+            type Output = DensePolynomial<F>;
+
+            #[inline]
+            fn $method(self, other: DensePolynomial<F>) -> DensePolynomial<F> {
+                (&self).$method(&other)
+            }
+        }
+
+        impl<'a, F: $field_bound> $trait<&'a DensePolynomial<F>> for DensePolynomial<F> {
+            type Output = DensePolynomial<F>;
+
+            #[inline]
+            fn $method(self, other: &'a DensePolynomial<F>) -> DensePolynomial<F> {
+                (&self).$method(other)
+            }
+        }
+
+        impl<'a, F: $field_bound> $trait<DensePolynomial<F>> for &'a DensePolynomial<F> {
+            type Output = DensePolynomial<F>;
+
+            #[inline]
+            fn $method(self, other: DensePolynomial<F>) -> DensePolynomial<F> {
+                self.$method(&other)
+            }
+        }
+    };
+}
+
 impl<F: Field> Zero for DensePolynomial<F> {
     /// Returns the zero polynomial.
     fn zero() -> Self {
@@ -632,6 +664,11 @@ impl<F: Field> Zero for DensePolynomial<F> {
     }
 }
 
+impl_op!(Add, add, Field);
+impl_op!(Sub, sub, Field);
+impl_op!(Mul, mul, FftField);
+impl_op!(Div, div, Field);
+
 #[cfg(test)]
 mod tests {
     use crate::{polynomial::univariate::*, GeneralEvaluationDomain};