diff --git a/tests/test_circle.py b/tests/test_circle.py
index 1fd66d0..542c32b 100644
--- a/tests/test_circle.py
+++ b/tests/test_circle.py
@@ -6,7 +6,7 @@
 sys.path.append('src')
 sys.path.append('../src')
 
-from circle import CirclePCS, CFFT, F31, FRI, evaluate_at_point, eval_at_point_raw, extract_lambda, twin_cosets, combine, standard_position_cosets, log_2, deep_quotient_reduce, deep_quotient_reduce_raw, g_30, group_mul, group_inv
+from circle import CirclePCS, CFFT, F31, FRI, batch_multiplicative_inverse, batch_multiplicative_inverse_raw, evaluate_at_point, eval_at_point_raw, extract_lambda, twin_cosets, combine, standard_position_cosets, log_2, deep_quotient_reduce, deep_quotient_reduce_raw, g_30, group_mul, group_inv
 from merlin.merlin_transcript import MerlinTranscript
 
 def fold(lde, domain, alpha=3, fold_y=False):
@@ -40,17 +40,16 @@ def test_extrapolate(self):
         evals = [1, 2, 3, 4]
         domain = standard_position_cosets[log_2(len(evals))]
         blowup_factor = 2
-        lde = CFFT.extrapolate(evals, domain, blowup_factor)
+        lde = CFFT.extrapolate(evals, blowup_factor)
 
         assert len(lde) == len(evals) * blowup_factor, f'len(lde) != len(evals) * blowup_factor, {len(lde)}, {len(evals) * blowup_factor}'
         for i, p in enumerate(standard_position_cosets[log_2(len(evals) * blowup_factor)]):
             assert eval_at_point_raw(evals, domain, p) == lde[i], f'evaluate_at_point error, {eval_at_point_raw(evals, domain, p)}, {lde[i]}'
 
     def test_fold(self):
-        evals = [F31(randint(0, 31)) for _ in range(4)]
-        domain = standard_position_cosets[log_2(len(evals))]
+        evals = [F31(randint(0, 30)) for _ in range(4)]
         blowup_factor = 2
-        lde = CFFT.extrapolate(evals, domain, blowup_factor)
+        lde = CFFT.extrapolate(evals, blowup_factor)
 
         domain_lde = standard_position_cosets[log_2(len(evals) * blowup_factor)]
         # print('domain_lde:', domain_lde)
@@ -59,18 +58,42 @@ def test_fold(self):
         assert folded_folded[0] == folded_folded[1], f'folded_folded[0] != folded_folded[1], {folded_folded[0]}, {folded_folded[1]}'
 
     def test_fft(self):
-        evals = [F31(randint(0, 31)) for _ in range(4)]
+        evals = [F31(randint(0, 30)) for _ in range(4)]
         domain = standard_position_cosets[log_2(len(evals))]
         
         coeffs = CFFT.ifft(CFFT.vec_2_poly(evals, domain))
         evals_fft = CFFT.poly_2_vec(CFFT.fft(coeffs, domain), domain)
         assert evals_fft == evals, f'evals_fft != evals, {evals_fft}, {evals}'
 
+    def test_fft_list(self):
+        evals = [F31(randint(0, 30)) for _ in range(4)]
+        coeffs = CFFT.ifft_list(evals)
+        evals_fft = CFFT.fft_list(coeffs)
+        assert evals_fft == evals, f'evals_fft != evals, {evals_fft}, {evals}'
+
+    def test_eval_at_point_raw(self):
+        evals = [F31(randint(0, 30)) for _ in range(4)]
+        domain = standard_position_cosets[log_2(len(evals))]
+        new_domain = standard_position_cosets[log_2(len(evals)) + 1]
+        point = new_domain[randint(0, len(new_domain) - 1)]
+        eval_at_p = eval_at_point_raw(evals, domain, point)
+        coeffs = CFFT.ifft(CFFT.vec_2_poly(evals, domain))
+        new_coeffs = [F31(0) for _ in range(len(coeffs) * 2)]
+        for i in range(len(coeffs) * 2):
+            new_coeffs[i] = coeffs[i // 2] if i % 2 == 0 else F31(0)
+        new_evals = CFFT.fft(new_coeffs, new_domain)
+        assert new_evals[point] == eval_at_p, f'new_evals[point] != eval_at_p, {new_evals[point]}, {eval_at_p}'
+
+    def test_batch_multiplicative_inverse(self):
+        evals = [F31(randint(1, 30)) for _ in range(14)]
+        inv = batch_multiplicative_inverse_raw(evals)
+        assert inv == batch_multiplicative_inverse(evals), f'inv != batch_multiplicative_inverse, {inv}, {batch_multiplicative_inverse(evals)}'
+
     def test_fri_prove(self):
-        evals = [F31(randint(0, 31)) for _ in range(4)]
+        evals = [F31(randint(0, 30)) for _ in range(4)]
         domain = standard_position_cosets[log_2(len(evals))]
         blowup_factor = 2
-        lde = CFFT.extrapolate(evals, domain, blowup_factor)
+        lde = CFFT.extrapolate(evals, blowup_factor)
 
         domain_lde = standard_position_cosets[log_2(len(evals) * blowup_factor)]
         # print('domain_lde:', domain_lde)
@@ -93,14 +116,14 @@ def test_fri_prove(self):
     #     assert p == expected, f'evaluate_at_point error, {p}, {expected}'
 
     def test_deep_quotient_reduce(self):
-        evals = [F31(randint(0, 31)) for _ in range(4)]
+        evals = [F31(randint(0, 30)) for _ in range(4)]
         domain = standard_position_cosets[log_2(len(evals))]
         alpha = 3
         zeta = g_30 ** 3
         p_at_zeta = eval_at_point_raw(evals, domain, zeta)
 
         blowup_factor = 2
-        lde = CFFT.extrapolate(evals, domain, blowup_factor)
+        lde = CFFT.extrapolate(evals, blowup_factor)
         domain_lde = standard_position_cosets[log_2(len(evals) * blowup_factor)]
 
         reduced = deep_quotient_reduce(lde, domain_lde, alpha, zeta, p_at_zeta)
@@ -113,8 +136,8 @@ def test_deep_quotient_reduce(self):
                 assert c == F31(0), f'coeffs[{i}] != 0, coeffs: {coeffs}'
 
     def test_extract_lambda(self):
-        evals = [F31(randint(0, 31)) for _ in range(4)]
-        lde = CFFT.extrapolate(evals, standard_position_cosets[2], 2)
+        evals = [F31(randint(0, 30)) for _ in range(4)]
+        lde = CFFT.extrapolate(evals, 2)
         domain = standard_position_cosets[3]
 
         zeta = g_30 ** 3
@@ -139,7 +162,7 @@ def test_extract_lambda(self):
                 assert c == F31(0), f'coeffs[{i}] != 0, coeffs: {q_interpolated}'
 
     def test_circle_pcs(self):
-        evals = [F31(randint(0, 31)) for _ in range(4)]
+        evals = [F31(randint(0, 30)) for _ in range(4)]
         domain = CirclePCS.natural_domain_for_degree(len(evals))
         log_blowup = 1