MVPoly: implement compute_cross_terms

mvpoly/src/prime.rs

@@ -369,6 +369,40 @@ impl<F: PrimeField, const N: usize, const D: usize> Dense<F, N, D> {
                 }
             })
     }
+
+    /// Compute the cross-terms as described in [Behind Nova: cross-terms
+    /// computation for high degree
+    /// gates](https://hackmd.io/@dannywillems/Syo5MBq90)
+    ///
+    /// The polynomial must not necessarily be homogeneous. For this reason, the
+    /// values `u1` and `u2` represents the extra variable that is used to make
+    /// the polynomial homogeneous.
+    ///
+    /// The homogeneous degree is supposed to be the one defined by the type of
+    /// the polynomial, i.e. `D`.
+    ///
+    /// A randomizer, coined, `r`, is used to compute the cross-terms.
+    ///
+    /// The output is a list of `D - 1` values that represents the cross-terms
+    /// for each power of `r`.
+    /// The output type is a vector because it is not possible for now to
+    /// perform computation on `const usize`
+    // IMPROVEME: Dummy implementation, a cache can be used to save the
+    // previously computed multiplications and powers.
+    pub fn compute_cross_terms(
+        &self,
+        _eval1: [F; N],
+        _eval2: [F; N],
+        _r: F,
+        _u1: F,
+        _u2: F,
+    ) -> Vec<F> {
+        assert!(
+            D >= 2,
+            "The degree of the polynomial must be greater than 2"
+        );
+        unimplemented!()
+    }
 }
 
 impl<F: PrimeField, const N: usize, const D: usize> Default for Dense<F, N, D> {