WIP: idea of compute_combined_cross_terms

mvpoly/src/lib.rs

@@ -131,3 +131,30 @@ pub trait MVPoly<F: PrimeField, const N: usize, const D: usize>:
     /// variable in each monomial is of maximum degree 1.
     fn is_multilinear(&self) -> bool;
 }
+
+/// Compute the cross terms of a list of polynomials. The polynomials are
+/// linearly combined using the power of a combiner, often called `α`.
+/// The combiner is considered as a variable of the multi-variate polynomial,
+/// therefore increasing the overall degree by one.
+///
+/// All polynomials are supposed to be given as multivariate polynomials of the
+/// same degree and the same number of variables, even if they do not have the
+/// same number of variables nor the same degree.
+/// Therefore, `N` is the maximum number of variables of the polynomials and `D`
+/// is the maximum degree of the polynomials.
+fn _compute_combined_cross_terms<
+    F: PrimeField,
+    const N: usize,
+    const D: usize,
+    T: MVPoly<F, N, D>,
+>(
+    _polys: Vec<T>,
+    _combiner1: F,
+    _combiner2: F,
+    _eval1: [F; N],
+    _eval2: [F; N],
+    _u1: [F; N],
+    _u2: [F; N],
+) -> HashMap<usize, F> {
+    unimplemented!("TODO")
+}