[poly] Reduce interpolated polynomial

So it doesn't start with zero points.

secp256kfun/src/poly.rs

@@ -210,6 +210,12 @@ pub mod point {
             self::add_in_place(&mut interpolating_polynomial, point_scaled_basis_poly);
         }
 
+        while interpolating_polynomial.len() > 1
+            && interpolating_polynomial.last().unwrap().is_zero()
+        {
+            interpolating_polynomial.pop();
+        }
+
         interpolating_polynomial
     }
 

secp256kfun/tests/poly.rs

@@ -1,5 +1,5 @@
 #![cfg(feature = "alloc")]
-use secp256kfun::{g, marker::*, poly, s, Point, G};
+use secp256kfun::{poly, prelude::*};
 
 #[test]
 fn test_lagrange_lambda() {
@@ -90,28 +90,26 @@ fn test_recover_overdetermined_poly() {
     let points = indicies
         .clone()
         .into_iter()
-        .map(|index| {
-            (
-                index,
-                poly::point::eval(&poly, index.public())
-                    .normalize()
-                    .non_zero()
-                    .unwrap(),
-            )
-        })
+        .map(|index| (index, poly::point::eval(&poly, index.public()).normalize()))
         .collect::<Vec<_>>();
 
     let interpolation = poly::point::interpolate(&points);
 
-    let (interpolated_coeffs, zero_coeffs) = interpolation.split_at(poly.len());
-    let n_extra_points = indicies.len() - poly.len();
+    assert_eq!(interpolation, poly);
+}
+
+#[test]
+fn test_recover_zero_poly() {
+    let interpolation = poly::point::interpolate(&[
+        (s!(1).public(), Point::<Normal, Public, _>::zero()),
+        (s!(2).public(), Point::<Normal, Public, _>::zero()),
+    ]);
+
     assert_eq!(
-        (0..n_extra_points)
-            .map(|_| Point::<Normal, Public, Zero>::zero().public().normalize())
-            .collect::<Vec<_>>(),
-        zero_coeffs.to_vec()
+        interpolation,
+        vec![Point::<NonNormal, Public, _>::zero()],
+        "should not be empty vector"
     );
-    assert_eq!(interpolated_coeffs, poly);
 }
 
 #[test]