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