test(mle2): improve and expand unit tests

Enhance existing tests and add new ones for MLEPolynomial class.
Verify correctness of NTT, evaluation, and decomposition methods.

tests/test_mle2.py

@@ -5,9 +5,9 @@
 sys.path.append('../src')
 sys.path.append('src')
 
-from mle2 import MLEPolynomial, pow_2
+from mle2 import MLEPolynomial
+from utils import bits_le_with_width
 
-# Assuming Fp is defined in your original file, if not, you may need to import or define it here
 Fp = GF(2**64 - 2**32 + 1)
 
 class TestMLEPolynomial(unittest.TestCase):
@@ -21,53 +21,54 @@ def test_init(self):
     def test_from_coeffs(self):
         coeffs = [Fp(1), Fp(2), Fp(3), Fp(4)]
         mle = MLEPolynomial.from_coeffs(coeffs, 2)
-        self.assertEqual(len(mle.evals), 4)
+        self.assertEqual(mle.evals, MLEPolynomial.compute_evals_from_coeffs(coeffs))
 
     def test_ntt_core(self):
         vs = [Fp(1), Fp(2), Fp(3), Fp(4)]
         result = MLEPolynomial.ntt_core(vs, Fp(1))
-        self.assertEqual(len(result), 4)
+        self.assertEqual(result, [MLEPolynomial(vs, 2).evaluate(bits_le_with_width(x, 2)) for x in range(4)])
+        self.assertEqual(vs, MLEPolynomial.ntt_core(result, -1))
 
     def test_compute_evals_from_coeffs(self):
         coeffs = [Fp(1), Fp(2), Fp(3), Fp(4)]
         evals = MLEPolynomial.compute_evals_from_coeffs(coeffs)
-        self.assertEqual(len(evals), 4)
+        self.assertEqual(evals, [MLEPolynomial(coeffs, 2).evaluate(bits_le_with_width(x, 2)) for x in range(4)])
 
     def test_compute_coeffs_from_evals(self):
         evals = [Fp(1), Fp(2), Fp(3), Fp(4)]
         coeffs = MLEPolynomial.compute_coeffs_from_evals(evals)
-        self.assertEqual(len(coeffs), 4)
+        self.assertEqual(evals, [MLEPolynomial(coeffs, 2).evaluate(bits_le_with_width(x, 2)) for x in range(4)])
 
     def test_evaluate(self):
         evals = [Fp(1), Fp(2), Fp(3), Fp(4)]
         mle = MLEPolynomial(evals, 2)
         result = mle.evaluate([Fp(1), Fp(2)])
-        # self.assertIsInstance(result, Fp)
+        self.assertEqual(result, MLEPolynomial.evaluate_from_evals(evals, [Fp(1), Fp(2)]))
 
     def test_evaluate_from_coeffs(self):
         coeffs = [Fp(1), Fp(2), Fp(3), Fp(4)]
         result = MLEPolynomial.evaluate_from_coeffs(coeffs, [Fp(1), Fp(2)])
-        # self.assertIsInstance(result, Fp)
-
-    def test_eval_from_coeffs(self):
-        coeffs = [Fp(1), Fp(2), Fp(3), Fp(4)]
-        result = MLEPolynomial.eval_from_coeffs(coeffs, Fp(2))
-        # self.assertIsInstance(result, Fp)
+        self.assertEqual(result, MLEPolynomial.evaluate_from_evals(MLEPolynomial.compute_evals_from_coeffs(coeffs), [Fp(1), Fp(2)]))
 
     def test_decompose_by_div(self):
-        evals = [Fp(i) for i in range(8)]
+        evals = [i for i in range(8)]
         mle = MLEPolynomial(evals, 3)
-        point = [Fp(1), Fp(2), Fp(3)]
+        point = [1, 2, 3]
+        k = len(point)
         quotients, remainder = mle.decompose_by_div(point)
-        self.assertEqual(len(quotients), 3)
-        # self.assertIsInstance(remainder, Fp)
+        remainder = MLEPolynomial([remainder], 0)
+        for i in range(k):
+            remainder = MLEPolynomial.mul_quotients(quotients[i], remainder, point[i])
+        self.assertEqual(remainder.evals, mle.evals)
 
     def test_decompose_by_div_from_coeffs(self):
         coeffs = [Fp(i) for i in range(8)]
         point = [Fp(1), Fp(2), Fp(3)]
-        quotients, remainder = MLEPolynomial.decompose_by_div_from_coeffs(coeffs, point)
-        self.assertEqual(len(quotients), 3)
-        # self.assertIsInstance(remainder, Fp)
+        evals = MLEPolynomial.compute_evals_from_coeffs(coeffs[:])
+        self.assertEqual(evals, [0, 1, 2, 6, 4, 10, 12, 28])
+        quotients, remainder = MLEPolynomial(evals, 3).decompose_by_div(point)
+        quotients = [MLEPolynomial.compute_coeffs_from_evals(q.evals) for q in quotients]
+        self.assertEqual((quotients, remainder), MLEPolynomial.decompose_by_div_from_coeffs(coeffs, point))
 
     def test_eq_poly_vec(self):
         point = [Fp(i) for i in range(4)]