Add more field_norm() unit tests

galois/_fields/_main.py

@@ -2021,14 +2021,17 @@ def field_norm(self) -> "FieldArray":
  x = GF.Elements(); x
  y = x.field_norm(); y
  """
- if not type(self).is_extension_field:
- raise TypeError(f"The Galois field must be an extension field to compute the field norm, not {type(self)}.")
  field = type(self)
- subfield = field.prime_subfield
- p = field.characteristic
- m = field.degree
- norm = self**((p**m - 1) // (p - 1))
- return subfield(norm)
+ x = self
+
+ if field.is_prime_field:
+ return x.copy()
+ else:
+ subfield = field.prime_subfield
+ p = field.characteristic
+ m = field.degree
+ norm = x**((p**m - 1) // (p - 1))
+ return subfield(norm)
 
  def characteristic_poly(self) -> "Poly":
  r"""

scripts/generate_field_test_vectors.py

@@ -315,6 +315,14 @@ def make_luts(field, sub_folder, seed, sparse=False):
  d = {"X": X, "Z": Z}
  save_pickle(d, folder, "field_trace.pkl")
 
+ set_seed(seed + 17)
+ X, Z = io_1d(0, order, sparse=sparse)
+ for i in range(X.shape[0]):
+ z = F(X[i]).norm()
+ Z[i] = int(z)
+ d = {"X": X, "Z": Z}
+ save_pickle(d, folder, "field_norm.pkl")
+
  ###############################################################################
  # Polynomial arithmetic
  ###############################################################################

tests/fields/conftest.py

@@ -351,3 +351,15 @@ def field_trace(field_folder):
  d["X"] = GF(d["X"])
  d["Z"] = GF.prime_subfield(d["Z"])
  return d
+
+
+@pytest.fixture(scope="session")
+def field_norm(field_folder):
+ GF, folder = field_folder
+ with open(os.path.join(folder, "field_norm.pkl"), "rb") as f:
+ print(f"Loading {f}...")
+ d = pickle.load(f)
+ d["GF"] = GF
+ d["X"] = GF(d["X"])
+ d["Z"] = GF.prime_subfield(d["Z"])
+ return d

tests/fields/test_arithmetic_methods.py

@@ -109,3 +109,12 @@ def test_field_trace(field_trace):
  z = x.field_trace()
  assert np.array_equal(z, Z)
  assert type(z) is GF.prime_subfield
+
+
+def test_field_norm(field_norm):
+ GF, X, Z = field_norm["GF"], field_norm["X"], field_norm["Z"]
+ dtype = random.choice(GF.dtypes)
+ x = X.astype(dtype)
+ z = x.field_norm()
+ assert np.array_equal(z, Z)
+ assert type(z) is GF.prime_subfield