4.5.2 multi op polynomials

scripts/zk/4.5.2-multi-operation-polynomials.py

@@ -0,0 +1,65 @@
+from bls_py import bls12381
+from finite_fields.modp import IntegersModP
+from finite_fields.polynomial import polynomialsOver
+
+n = bls12381.n
+
+mod_field = IntegersModP(n)
+poly = polynomialsOver(mod_field).factory
+
+def lagrange(points):
+    result = poly([0])
+    for i, (x_i, y_i) in enumerate(points):
+        p = poly([y_i])
+        for j, (x_j, y_j) in enumerate(points):
+            if i == j:
+                continue
+            p *= poly([-x_j, 1]) / (x_i - x_j)
+        #print(poly)
+        #print(poly(1), poly(2), poly(3))
+        result += p
+    return result
+
+def poly_call(poly, x):
+    result = mod_field(0)
+    for degree, coeff in enumerate(poly):
+        result += coeff * (x**degree)
+    return result.n
+
+left_points = [
+    (1, 2), (2, 2), (3, 6)
+]
+left_poly = lagrange(left_points)
+#l = poly([2]) * poly([1, -1])
+print("Left:")
+print(left_poly)
+for x, y in left_points:
+    assert poly_call(left_poly, x) == y
+
+right_points = [
+    (1, 1), (2, 3), (3, 2)
+]
+right_poly = lagrange(right_points)
+print("Right:")
+print(right_poly)
+for x, y in right_points:
+    assert poly_call(right_poly, x) == y
+
+out_points = [
+    (1, 2), (2, 6), (3, 12)
+]
+out_poly = lagrange(out_points)
+print("Out:")
+print(out_poly)
+for x, y in out_points:
+    assert poly_call(out_poly, x) == y
+
+target_poly = poly([-1, 1]) * poly([-2, 1]) * poly([-3, 1])
+assert poly_call(target_poly, 1) == 0
+assert poly_call(target_poly, 2) == 0
+assert poly_call(target_poly, 3) == 0
+
+main_poly = left_poly * right_poly - out_poly
+cofactor_poly = main_poly / target_poly
+
+assert left_poly * right_poly - out_poly == target_poly * cofactor_poly