diff --git a/mvpoly/src/pbt.rs b/mvpoly/src/pbt.rs
index 130c6c9fc4..011258f295 100644
--- a/mvpoly/src/pbt.rs
+++ b/mvpoly/src/pbt.rs
@@ -19,7 +19,7 @@
 use crate::MVPoly;
 use ark_ff::PrimeField;
 use rand::{seq::SliceRandom, Rng};
-use std::ops::Neg;
+use std::{collections::HashMap, ops::Neg};
 
 pub fn test_mul_by_one<F: PrimeField, const N: usize, const D: usize, T: MVPoly<F, N, D>>() {
     let mut rng = o1_utils::tests::make_test_rng(None);
@@ -587,3 +587,137 @@ pub fn test_is_constant<F: PrimeField, const N: usize, const D: usize, T: MVPoly
     let p = unsafe { T::random(&mut rng, None) };
     assert!(!p.is_constant());
 }
+
+pub fn test_compute_combined_cross_terms_expected_nb_of_cross_terms<
+    F: PrimeField,
+    const N: usize,
+    const D: usize,
+    T: MVPoly<F, N, D>,
+>() {
+    let mut rng = o1_utils::tests::make_test_rng(None);
+    // Generate max 40 polynomials
+    let n = rng.gen_range(1..10);
+    let polys = (0..n)
+        .map(|_| unsafe { T::random(&mut rng, None) })
+        .collect::<Vec<_>>();
+    let eval1: [F; N] = std::array::from_fn(|_| F::rand(&mut rng));
+    let eval2: [F; N] = std::array::from_fn(|_| F::rand(&mut rng));
+    let u1 = F::rand(&mut rng);
+    let u2 = F::rand(&mut rng);
+
+    {
+        let alpha1 = F::rand(&mut rng);
+        let alpha2 = F::rand(&mut rng);
+
+        let combined_cross_terms = crate::compute_combined_cross_terms(
+            polys.clone(),
+            alpha1,
+            alpha2,
+            eval1,
+            eval2,
+            u1,
+            u2,
+        );
+        assert_eq!(combined_cross_terms.len(), D);
+    }
+
+    // Check that even if zero is given, we get the right number of cross terms
+    {
+        let alpha1 = F::zero();
+        let alpha2 = F::rand(&mut rng);
+        let combined_cross_terms = crate::compute_combined_cross_terms(
+            polys.clone(),
+            alpha1,
+            alpha2,
+            eval1,
+            eval2,
+            u1,
+            u2,
+        );
+        assert_eq!(combined_cross_terms.len(), D);
+    }
+
+    {
+        let alpha1 = F::rand(&mut rng);
+        let alpha2 = F::zero();
+        let combined_cross_terms = crate::compute_combined_cross_terms(
+            polys.clone(),
+            alpha1,
+            alpha2,
+            eval1,
+            eval2,
+            u1,
+            u2,
+        );
+        assert_eq!(combined_cross_terms.len(), D);
+    }
+
+    {
+        let alpha1 = F::zero();
+        let alpha2 = F::zero();
+        let combined_cross_terms =
+            crate::compute_combined_cross_terms(polys, alpha1, alpha2, eval1, eval2, u1, u2);
+        assert_eq!(combined_cross_terms.len(), D);
+    }
+}
+
+pub fn test_compute_combined_cross_terms_right_alpha_null<
+    F: PrimeField,
+    const N: usize,
+    const D: usize,
+    T: MVPoly<F, N, D>,
+>() {
+    let mut rng = o1_utils::tests::make_test_rng(None);
+    let p = unsafe { T::random(&mut rng, Some(D - 1)) };
+    let eval1: [F; N] = std::array::from_fn(|_| F::rand(&mut rng));
+    let eval2: [F; N] = std::array::from_fn(|_| F::rand(&mut rng));
+    let u1 = F::rand(&mut rng);
+    let u2 = F::rand(&mut rng);
+    let cross_terms = p.compute_cross_terms(&eval1, &eval2, u1, u2);
+
+    let alpha2 = F::zero();
+    {
+        let alpha1 = F::one();
+        let combined_cross_terms = crate::compute_combined_cross_terms(
+            vec![p.clone()],
+            alpha1,
+            alpha2,
+            eval1,
+            eval2,
+            u1,
+            u2,
+        );
+        let mut exp_cross_terms = cross_terms.clone();
+        exp_cross_terms.insert(D, F::zero());
+        assert_eq!(exp_cross_terms, combined_cross_terms);
+    }
+
+    {
+        let alpha1 = F::rand(&mut rng);
+        let combined_cross_terms = crate::compute_combined_cross_terms(
+            vec![p.clone()],
+            alpha1,
+            alpha2,
+            eval1,
+            eval2,
+            u1,
+            u2,
+        );
+        // alpha is never used as there is only one polynomial
+        let mut exp_cross_terms: HashMap<usize, F> = cross_terms.clone();
+        exp_cross_terms.insert(D, F::zero());
+        assert_eq!(exp_cross_terms, combined_cross_terms);
+    }
+
+    // Special case with alpha1 = 0
+    {
+        let alpha1 = F::zero();
+        let combined_cross_terms =
+            crate::compute_combined_cross_terms(vec![p], alpha1, alpha2, eval1, eval2, u1, u2);
+        let mut zeroes: HashMap<usize, F> = HashMap::new();
+        for i in 1..=D {
+            zeroes.insert(i, F::zero());
+        }
+        assert_eq!(combined_cross_terms, zeroes);
+    }
+}
diff --git a/mvpoly/tests/monomials.rs b/mvpoly/tests/monomials.rs
index 902a3fcfbc..ca7d265454 100644
--- a/mvpoly/tests/monomials.rs
+++ b/mvpoly/tests/monomials.rs
@@ -712,3 +712,33 @@ fn test_from_expr_ec_addition() {
         assert_eq!(eval, exp_eval);
     }
 }
+
+#[test]
+fn test_compute_combined_cross_terms_expected_nb_of_cross_terms() {
+    mvpoly::pbt::test_compute_combined_cross_terms_expected_nb_of_cross_terms::<
+        Fp,
+        4,
+        2,
+        Sparse<Fp, 4, 2>,
+    >();
+    mvpoly::pbt::test_compute_combined_cross_terms_expected_nb_of_cross_terms::<
+        Fp,
+        6,
+        3,
+        Sparse<Fp, 6, 3>,
+    >();
+    mvpoly::pbt::test_compute_combined_cross_terms_expected_nb_of_cross_terms::<
+        Fp,
+        4,
+        8,
+        Sparse<Fp, 4, 8>,
+    >();
+}
+
+#[test]
+fn test_compute_combined_cross_terms_right_alpha_null() {
+    mvpoly::pbt::test_compute_combined_cross_terms_right_alpha_null::<Fp, 15, 2, Sparse<Fp, 15, 2>>(
+    );
+    mvpoly::pbt::test_compute_combined_cross_terms_right_alpha_null::<Fp, 6, 3, Sparse<Fp, 6, 3>>();
+    mvpoly::pbt::test_compute_combined_cross_terms_right_alpha_null::<Fp, 4, 8, Sparse<Fp, 4, 8>>();
+}