Convert Union[a, b] to a | b

This is allowed with `from __future__ import annotations`

src/galois/_codes/_bch.py

@@ -4,7 +4,7 @@
 from __future__ import annotations
 
 import math
-from typing import Tuple, List, Optional, Union, Type, overload
+from typing import Tuple, List, Optional, Type, overload
 from typing_extensions import Literal
 
 import numba
@@ -420,7 +420,7 @@ def encode(self, message: ArrayLike, parity_only: bool = False) -> GF2:
  codeword = message @ self.G
  return codeword
 
- def detect(self, codeword: ArrayLike) -> Union[np.bool_, np.ndarray]:
+ def detect(self, codeword: ArrayLike) -> np.bool_ | np.ndarray:
  r"""
  Detects if errors are present in the BCH codeword :math:`\mathbf{c}`.
 
@@ -577,7 +577,7 @@ def detect(self, codeword: ArrayLike) -> Union[np.bool_, np.ndarray]:
  def decode(self, codeword: ArrayLike, errors: Literal[False] = False) -> GF2:
  ...
  @overload
- def decode(self, codeword: ArrayLike, errors: Literal[True]) -> Tuple[GF2, Union[np.integer, np.ndarray]]:
+ def decode(self, codeword: ArrayLike, errors: Literal[True]) -> Tuple[GF2, np.integer | np.ndarray]:
  ...
  def decode(self, codeword, errors=False):
  r"""

src/galois/_codes/_reed_solomon.py

@@ -3,7 +3,7 @@
 """
 from __future__ import annotations
 
-from typing import Tuple, Optional, Union, Type, overload
+from typing import Tuple, Optional, Type, overload
 from typing_extensions import Literal
 
 import numba
@@ -307,7 +307,7 @@ def encode(self, message: ArrayLike, parity_only: bool = False) -> FieldArray:
  codeword = message @ self.G
  return codeword
 
- def detect(self, codeword: ArrayLike) -> Union[np.bool_, np.ndarray]:
+ def detect(self, codeword: ArrayLike) -> np.bool_ | np.ndarray:
  r"""
  Detects if errors are present in the Reed-Solomon codeword :math:`\mathbf{c}`.
 
@@ -466,7 +466,7 @@ def detect(self, codeword: ArrayLike) -> Union[np.bool_, np.ndarray]:
  def decode(self, codeword: ArrayLike, errors: Literal[False] = False) -> FieldArray:
  ...
  @overload
- def decode(self, codeword: ArrayLike, errors: Literal[True]) -> Tuple[FieldArray, Union[np.integer, np.ndarray]]:
+ def decode(self, codeword: ArrayLike, errors: Literal[True]) -> Tuple[FieldArray, np.integer | np.ndarray]:
  ...
  def decode(self, codeword, errors=False):
  r"""

src/galois/_domains/_array.py

@@ -6,7 +6,7 @@
 import abc
 import contextlib
 import random
-from typing import Optional, Union, Generator
+from typing import Optional, Generator
 from typing_extensions import Literal
 
 import numpy as np
@@ -34,7 +34,7 @@ class Array(LinalgFunctionMixin, FunctionMixin, UFuncMixin, np.ndarray, metaclas
 
  def __new__(
  cls,
- x: Union[ElementLike, ArrayLike],
+ x: ElementLike | ArrayLike,
  dtype: Optional[DTypeLike] = None,
  copy: bool = True,
  order: Literal["K", "A", "C", "F"] = "K",
@@ -70,7 +70,7 @@ def _get_dtype(cls, dtype: DTypeLike) -> np.dtype:
 
  @classmethod
  @abc.abstractmethod
- def _verify_array_like_types_and_values(cls, x: Union[ElementLike, ArrayLike]) -> Union[ElementLike, ArrayLike]:
+ def _verify_array_like_types_and_values(cls, x: ElementLike | ArrayLike) -> ElementLike | ArrayLike:
  """
  Verify the types of the array-like object. Also verify the values of the array are within the range [0, order).
  """
@@ -237,7 +237,7 @@ def Random(
  shape: ShapeLike = (),
  low: ElementLike = 0,
  high: Optional[ElementLike] = None,
- seed: Optional[Union[int, np.random.Generator]] = None,
+ seed: Optional[int | np.random.Generator] = None,
  dtype: Optional[DTypeLike] = None
  ) -> Array:
  """

src/galois/_fields/_array.py

@@ -3,7 +3,7 @@
 """
 from __future__ import annotations
 
-from typing import Tuple, Optional, Union
+from typing import Tuple, Optional
 from typing_extensions import Literal
 
 import numpy as np
@@ -55,7 +55,7 @@ class FieldArray(Array, metaclass=FieldArrayMeta):
 
  def __new__(
  cls,
- x: Union[ElementLike, ArrayLike],
+ x: ElementLike | ArrayLike,
  dtype: Optional[DTypeLike] = None,
  copy: bool = True,
  order: Literal["K", "A", "C", "F"] = "K",
@@ -67,7 +67,7 @@ def __new__(
 
  def __init__(
  self,
- x: Union[ElementLike, ArrayLike],
+ x: ElementLike | ArrayLike,
  dtype: Optional[DTypeLike] = None,
  copy: bool = True,
  order: Literal["K", "A", "C", "F"] = "K",
@@ -99,7 +99,7 @@ def __init__(
  ###############################################################################
 
  @classmethod
- def _verify_array_like_types_and_values(cls, x: Union[ElementLike, ArrayLike]) -> Union[ElementLike, ArrayLike]:
+ def _verify_array_like_types_and_values(cls, x: ElementLike | ArrayLike) -> ElementLike | ArrayLike:
  if isinstance(x, (int, np.integer)):
  cls._verify_scalar_value(x)
  elif isinstance(x, cls):
@@ -278,7 +278,7 @@ def Random(
  shape: ShapeLike = (),
  low: ElementLike = 0,
  high: Optional[ElementLike] = None,
- seed: Optional[Union[int, np.random.Generator]] = None,
+ seed: Optional[int | np.random.Generator] = None,
  dtype: Optional[DTypeLike] = None
  ) -> FieldArray:
  return super().Random(shape=shape, low=low, high=high, seed=seed, dtype=dtype)
@@ -764,7 +764,7 @@ def primitive_roots_of_unity(cls, n: int) -> FieldArray:
  # Instance methods
  ###############################################################################
 
- def additive_order(self) -> Union[np.integer, np.ndarray]:
+ def additive_order(self) -> np.integer | np.ndarray:
  r"""
  Computes the additive order of each element in :math:`x`.
 
@@ -804,7 +804,7 @@ def additive_order(self) -> Union[np.integer, np.ndarray]:
 
  return order
 
- def multiplicative_order(self) -> Union[np.integer, np.ndarray]:
+ def multiplicative_order(self) -> np.integer | np.ndarray:
  r"""
  Computes the multiplicative order :math:`\textrm{ord}(x)` of each element in :math:`x`.
 
@@ -870,7 +870,7 @@ def multiplicative_order(self) -> Union[np.integer, np.ndarray]:
 
  return order
 
- def is_square(self) -> Union[np.bool_, np.ndarray]:
+ def is_square(self) -> np.bool_ | np.ndarray:
  r"""
  Determines if the elements of :math:`x` are squares in the finite field.
 
@@ -1501,7 +1501,7 @@ def minimal_poly(self) -> Poly:
  else:
  raise ValueError(f"The array must be either 0-D to return the minimal polynomial of a single element or 2-D to return the minimal polynomial of a square matrix, not have shape {self.shape}.")
 
- def log(self, base: Optional[Union[ElementLike, ArrayLike]] = None) -> np.ndarray:
+ def log(self, base: Optional[ElementLike | ArrayLike] = None) -> np.ndarray:
  r"""
  Computes the logarithm of the array :math:`x` base :math:`\beta`.
 

src/galois/_fields/_factory.py

@@ -5,7 +5,7 @@
 
 import sys
 import types
-from typing import Union, Optional, Type
+from typing import Optional, Type
 from typing_extensions import Literal
 
 from .._helper import export, verify_isinstance
@@ -24,7 +24,7 @@
 def GF(
  order: int,
  irreducible_poly: Optional[PolyLike] = None,
- primitive_element: Optional[Union[int, PolyLike]] = None, # pylint: disable=redefined-outer-name
+ primitive_element: Optional[int | PolyLike] = None, # pylint: disable=redefined-outer-name
  verify: bool = True,
  compile: Optional[Literal["auto", "jit-lookup", "jit-calculate", "python-calculate"]] = None, # pylint: disable=redefined-builtin
  display: Optional[Literal["int", "poly", "power"]] = None
@@ -223,7 +223,7 @@ def GF(
 def Field(
  order: int,
  irreducible_poly: Optional[PolyLike] = None,
- primitive_element: Optional[Union[int, PolyLike]] = None, # pylint: disable=redefined-outer-name
+ primitive_element: Optional[int | PolyLike] = None, # pylint: disable=redefined-outer-name
  verify: bool = True,
  compile: Optional[Literal["auto", "jit-lookup", "jit-calculate", "python-calculate"]] = None, # pylint: disable=redefined-builtin
  display: Optional[Literal["int", "poly", "power"]] = None