clean: downgrade typing syntax and stdlibrary use to python 3.8

Also gitignore env8 directory, where I keep my python3.8 environment

.gitignore

@@ -16,6 +16,7 @@ venv/
 ENV/
 env.bak/
 venv.bak/
+env8
 
 # automatically generated by setuptools-scm
 pysindy/version.py

pysindy/differentiation/finite_difference.py

@@ -1,3 +1,4 @@
+from typing import List
 from typing import Union
 
 import numpy as np
@@ -232,7 +233,7 @@ def _accumulate(self, coeffs, x):
         )
 
     def _differentiate(
-        self, x: NDArray, t: Union[NDArray, float, list[float]]
+        self, x: NDArray, t: Union[NDArray, float, List[float]]
     ) -> NDArray:
         """
         Apply finite difference method.

pysindy/utils/axes.py

@@ -20,6 +20,7 @@
 from enum import Enum
 from typing import Collection
 from typing import Dict
+from typing import get_args
 from typing import List
 from typing import Literal
 from typing import NewType
@@ -36,9 +37,9 @@
 HANDLED_FUNCTIONS = {}
 
 AxesWarning = type("AxesWarning", (SyntaxWarning,), {})
-BasicIndexer = Union[slice, int, type(Ellipsis), type(None), str]
-Indexer = BasicIndexer | NDArray | list
-StandardIndexer = Union[slice, int, type(None), NDArray[np.dtype(int)]]
+BasicIndexer = Union[slice, int, type(Ellipsis), None, str]
+Indexer = Union[BasicIndexer, NDArray, List]
+StandardIndexer = Union[slice, int, None, NDArray[np.dtype(int)]]
 OldIndex = NewType("OldIndex", int)  # Before moving advanced axes adajent
 KeyIndex = NewType("KeyIndex", int)
 NewIndex = NewType("NewIndex", int)
@@ -52,8 +53,8 @@ class Sentinels(Enum):
 class _AxisMapping:
     """Convenience wrapper for a two-way map between axis names and indexes."""
 
-    fwd_map: dict[str, list[int]]
-    reverse_map: dict[int, str]
+    fwd_map: Dict[str, List[int]]
+    reverse_map: Dict[int, str]
 
     def __init__(
         self,
@@ -90,14 +91,14 @@ def coerce_sequence(obj):
             )
 
     @staticmethod
-    def fwd_from_names(names: List[str]) -> dict[str, Sequence[int]]:
-        fwd_map: dict[str, Sequence[int]] = {}
+    def fwd_from_names(names: List[str]) -> Dict[str, Sequence[int]]:
+        fwd_map: Dict[str, Sequence[int]] = {}
         for ax_ind, name in enumerate(names):
             _compat_dict_append(fwd_map, name, [ax_ind])
         return fwd_map
 
     @staticmethod
-    def _compat_axes(in_dict: dict[str, list[int]]) -> dict[str, Union[list[int], int]]:
+    def _compat_axes(in_dict: Dict[str, List[int]]) -> Dict[str, Union[list[int], int]]:
         """Like fwd_map, but unpack single-element axis lists"""
         axes = {}
         for k, v in in_dict.items():
@@ -269,7 +270,7 @@ def __getattr__(self, name):
             return shape
         raise AttributeError(f"'{type(self)}' object has no attribute '{name}'")
 
-    def __getitem__(self, key: Indexer | Sequence[Indexer], /):
+    def __getitem__(self, key: Union[Indexer, Sequence[Indexer]], /):
         if isinstance(key, tuple):
             base_indexer = tuple(None if isinstance(k, str) else k for k in key)
         else:
@@ -542,12 +543,14 @@ def einsum(
 
 def _join_unique_names(l_of_s: List[str]) -> str:
     ordered_uniques = dict.fromkeys(l_of_s).keys()
-    return "_".join(ax_name.removeprefix("ax_") for ax_name in ordered_uniques)
+    return "_".join(
+        ax_name[3:] if ax_name[:3] == "ax_" else ax_name for ax_name in ordered_uniques
+    )
 
 
 def _label_einsum_scripts(
-    lscripts: list[str], operands: tuple[AxesArray]
-) -> list[dict[str, str]]:
+    lscripts: List[str], operands: tuple[AxesArray]
+) -> List[dict[str, str]]:
     """Create a list of what axis name each script refers to in its operand."""
     allscript_names: List[Dict[str, List[str]]] = []
     for lscr, op in zip(lscripts.split(","), operands):
@@ -644,9 +647,9 @@ def standardize_indexer(
     if not any(ax_key is Ellipsis for ax_key in key):
         key = [*key, Ellipsis]
 
-    new_key: list[Indexer] = []
+    new_key: List[Indexer] = []
     for ax_key in key:
-        if not isinstance(ax_key, BasicIndexer):
+        if not isinstance(ax_key, get_args(BasicIndexer)):
             ax_key = np.array(ax_key)
             if ax_key.dtype == np.dtype(np.bool_):
                 new_key += ax_key.nonzero()
@@ -655,15 +658,15 @@ def standardize_indexer(
 
     new_key = _expand_indexer_ellipsis(new_key, arr.ndim)
     # Can't identify position of advanced indexers before expanding ellipses
-    adv_inds: list[KeyIndex] = []
+    adv_inds: List[KeyIndex] = []
     for key_ind, ax_key in enumerate(new_key):
         if isinstance(ax_key, np.ndarray):
             adv_inds.append(KeyIndex(key_ind))
 
     return new_key, tuple(adv_inds)
 
 
-def _expand_indexer_ellipsis(key: list[Indexer], ndim: int) -> list[Indexer]:
+def _expand_indexer_ellipsis(key: List[Indexer], ndim: int) -> List[Indexer]:
     """Replace ellipsis in indexers with the appropriate amount of slice(None)"""
     # [...].index errors if list contains numpy array
     ellind = [ind for ind, val in enumerate(key) if val is ...][0]
@@ -686,9 +689,9 @@ def _determine_adv_broadcasting(
 
 
 def _rename_broadcast_axes(
-    new_axes: list[tuple[int, None | str | Literal[Sentinels.ADV_NAME]]],
-    adv_names: list[str],
-) -> list[tuple[int, str]]:
+    new_axes: List[tuple[int, None | str | Literal[Sentinels.ADV_NAME]]],
+    adv_names: List[str],
+) -> List[tuple[int, str]]:
     """Normalize sentinel and NoneType names"""
 
     def _calc_bcast_name(*names: str) -> str:
@@ -713,7 +716,7 @@ def _calc_bcast_name(*names: str) -> str:
 
 def replace_adv_indexers(
     key: Sequence[StandardIndexer],
-    adv_inds: list[int],
+    adv_inds: List[int],
     bcast_start_ax: int,
     bcast_nd: int,
 ) -> tuple[
@@ -727,9 +730,9 @@ def replace_adv_indexers(
 
 
 def _apply_indexing(
-    key: tuple[StandardIndexer], reverse_map: dict[int, str]
+    key: tuple[StandardIndexer], reverse_map: Dict[int, str]
 ) -> tuple[
-    list[int], list[tuple[int, None | str | Literal[Sentinels.ADV_NAME]]], list[str]
+    List[int], List[tuple[int, None | str | Literal[Sentinels.ADV_NAME]]], List[str]
 ]:
     """Determine where axes should be removed and added
 
@@ -810,8 +813,8 @@ def wrap_axes(axes: dict, obj):
 
 
 T = TypeVar("T", bound=int)  # TODO: Bind to a non-sequence after type-negation PEP
-ItemOrList = Union[T, list[T]]
-CompatDict = dict[str, ItemOrList[T]]
+ItemOrList = Union[T, List[T]]
+CompatDict = Dict[str, ItemOrList[T]]
 
 
 def _compat_dict_append(