code: import copy
  from datetime import date, datetime, timedelta
  from typing import Any, Callable, List, Optional, Sequence, Tuple, Type, Union
  
  import numpy as np
  
  from polars.utils import _timedelta_to_pl_duration
  
  try:
      from polars.polars import PyExpr
  
      _DOCUMENTING = False
  except ImportError:  # pragma: no cover
      _DOCUMENTING = True
  
  from polars import internals as pli
  from polars.datatypes import (
      DataType,
      Date,
      Datetime,
      Float64,
      Int32,
      Object,
      UInt32,
      py_type_to_dtype,
  )
  
  
  def selection_to_pyexpr_list(
      exprs: Union[str, "Expr", Sequence[Union[str, "Expr", "pli.Series"]], "pli.Series"]
  ) -> List["PyExpr"]:
      if isinstance(exprs, (str, Expr, pli.Series)):
          exprs = [exprs]
  
      return [expr_to_lit_or_expr(e, str_to_lit=False)._pyexpr for e in exprs]
  
  
  def wrap_expr(pyexpr: "PyExpr") -> "Expr":
      return Expr._from_pyexpr(pyexpr)
  
  
  class Expr:
      """
      Expressions that can be used in various contexts.
      """
  
      def __init__(self) -> None:
          self._pyexpr: PyExpr  # pragma: no cover
  
      def __str__(self) -> str:
          return self._pyexpr.to_str()
  
      def _repr_html_(self) -> str:
          return self._pyexpr.to_str()
  
      @staticmethod
      def _from_pyexpr(pyexpr: "PyExpr") -> "Expr":
          self = Expr.__new__(Expr)
          self._pyexpr = pyexpr
          return self
  
      def __to_pyexpr(self, other: Any) -> "PyExpr":
          return self.__to_expr(other)._pyexpr
  
      def __to_expr(self, other: Any) -> "Expr":
          if isinstance(other, Expr):
              return other
          return pli.lit(other)
  
      def __bool__(self) -> "Expr":
          raise ValueError(
              "Since Expr are lazy, the truthiness of an Expr is ambiguous. \
              Hint: use '&' or '|' to chain Expr together, not and/or."
          )
  
      def __invert__(self) -> "Expr":
          return self.is_not()
  
      def __xor__(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr._xor(self.__to_pyexpr(other)))
  
      def __rxor__(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr._xor(self.__to_pyexpr(other)))
  
      def __and__(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr._and(self.__to_pyexpr(other)))
  
      def __rand__(self, other: Any) -> "Expr":
          return wrap_expr(self._pyexpr._and(self.__to_pyexpr(other)))
  
      def __or__(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr._or(self.__to_pyexpr(other)))
  
      def __ror__(self, other: Any) -> "Expr":
          return wrap_expr(self.__to_pyexpr(other)._or(self._pyexpr))
  
      def __add__(self, other: Any) -> "Expr":
          return wrap_expr(self._pyexpr + self.__to_pyexpr(other))
  
      def __radd__(self, other: Any) -> "Expr":
          return wrap_expr(self.__to_pyexpr(other) + self._pyexpr)
  
      def __sub__(self, other: Any) -> "Expr":
          return wrap_expr(self._pyexpr - self.__to_pyexpr(other))
  
      def __rsub__(self, other: Any) -> "Expr":
          return wrap_expr(self.__to_pyexpr(other) - self._pyexpr)
  
      def __mul__(self, other: Any) -> "Expr":
          return wrap_expr(self._pyexpr * self.__to_pyexpr(other))
  
      def __rmul__(self, other: Any) -> "Expr":
          return wrap_expr(self.__to_pyexpr(other) * self._pyexpr)
  
      def __truediv__(self, other: Any) -> "Expr":
          return wrap_expr(self._pyexpr / self.__to_pyexpr(other))
  
      def __rtruediv__(self, other: Any) -> "Expr":
          return wrap_expr(self.__to_pyexpr(other) / self._pyexpr)
  
      def __floordiv__(self, other: Any) -> "Expr":
          return wrap_expr(self._pyexpr // self.__to_pyexpr(other))
  
      def __rfloordiv__(self, other: Any) -> "Expr":
          return wrap_expr(self.__to_pyexpr(other) // self._pyexpr)
  
      def __mod__(self, other: Any) -> "Expr":
          return wrap_expr(self._pyexpr % self.__to_pyexpr(other))
  
      def __rmod__(self, other: Any) -> "Expr":
          return wrap_expr(self.__to_pyexpr(other) % self._pyexpr)
  
      def __pow__(self, power: float, modulo: None = None) -> "Expr":
          return self.pow(power)
  
      def __ge__(self, other: Any) -> "Expr":
          return self.gt_eq(self.__to_expr(other))
  
      def __le__(self, other: Any) -> "Expr":
          return self.lt_eq(self.__to_expr(other))
  
      def __eq__(self, other: Any) -> "Expr":  # type: ignore[override]
          return self.eq(self.__to_expr(other))
  
      def __ne__(self, other: Any) -> "Expr":  # type: ignore[override]
          return self.neq(self.__to_expr(other))
  
      def __lt__(self, other: Any) -> "Expr":
          return self.lt(self.__to_expr(other))
  
      def __gt__(self, other: Any) -> "Expr":
          return self.gt(self.__to_expr(other))
  
      def eq(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr.eq(other._pyexpr))
  
      def neq(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr.neq(other._pyexpr))
  
      def gt(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr.gt(other._pyexpr))
  
      def gt_eq(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr.gt_eq(other._pyexpr))
  
      def lt_eq(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr.lt_eq(other._pyexpr))
  
      def lt(self, other: "Expr") -> "Expr":
          return wrap_expr(self._pyexpr.lt(other._pyexpr))
  
      def __neg__(self) -> "Expr":
          return pli.lit(0) - self
  
      def __array_ufunc__(
          self, ufunc: Callable[..., Any], method: str, *inputs: Any, **kwargs: Any
      ) -> "Expr":
          """
          Numpy universal functions.
          """
          out_type = ufunc(np.array([1])).dtype
          dtype: Optional[Type[DataType]]
          if "float" in str(out_type):
              dtype = Float64
          else:
              dtype = None
  
          args = [inp for inp in inputs if not isinstance(inp, Expr)]
  
          def function(s: "pli.Series") -> "pli.Series":
              return ufunc(s, *args, **kwargs)  # pragma: no cover
  
          if "dtype" in kwargs:
              dtype = kwargs["dtype"]
  
          return self.map(function, return_dtype=dtype)
  
      def to_physical(self) -> "Expr":
          """
          Cast to physical representation of the logical dtype.
  
          Date -> Int32
          Datetime -> Int64
          Time -> Int64
          other -> other
          """
          return wrap_expr(self._pyexpr.to_physical())
  
      def any(self) -> "Expr":
          """
          Check if any boolean value in the column is `True`
  
          Returns
          -------
          Boolean literal
          """
          return wrap_expr(self._pyexpr.any())
  
      def all(self) -> "Expr":
          """
          Check if all boolean values in the column are `True`
  
          Returns
          -------
          Boolean literal
          """
          return wrap_expr(self._pyexpr.all())
  
      def sqrt(self) -> "Expr":
          """
          Compute the square root of the elements
          """
          return self ** 0.5
  
      def log(self) -> "Expr":
          """
          Natural logarithm, element-wise.
  
          The natural logarithm log is the inverse of the exponential function, so that log(exp(x)) = x.
          The natural logarithm is logarithm in base e.
          """
          return np.log(self)  # type: ignore
  
      def log10(self) -> "Expr":
          """
          Return the base 10 logarithm of the input array, element-wise.
          """
          return np.log10(self)  # type: ignore
  
      def exp(self) -> "Expr":
          """
          Return the exponential element-wise
          """
          return np.exp(self)  # type: ignore
  
      def alias(self, name: str) -> "Expr":
          """
          Rename the output of an expression.
  
          Parameters
          ----------
          name
              New name.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "a": [1, 2, 3],
          ...         "b": ["a", "b", None],
          ...     }
          ... )
          >>> df
          shape: (3, 2)
          ┌─────┬──────┐
          │ a   ┆ b    │
          │ --- ┆ ---  │
          │ i64 ┆ str  │
          ╞═════╪══════╡
          │ 1   ┆ a    │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 2   ┆ b    │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 3   ┆ null │
          └─────┴──────┘
          >>> df.select(
          ...     [
          ...         pl.col("a").alias("bar"),
          ...         pl.col("b").alias("foo"),
          ...     ]
          ... )
          shape: (3, 2)
          ┌─────┬──────┐
          │ bar ┆ foo  │
          │ --- ┆ ---  │
          │ i64 ┆ str  │
          ╞═════╪══════╡
          │ 1   ┆ a    │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 2   ┆ b    │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 3   ┆ null │
          └─────┴──────┘
  
          """
          return wrap_expr(self._pyexpr.alias(name))
  
      def exclude(
          self,
          columns: Union[str, List[str], Type[DataType], Sequence[Type[DataType]]],
      ) -> "Expr":
          """
          Exclude certain columns from a wildcard/regex selection.
  
          You may also use regexes in the exclude list. They must start with `^` and end with `$`.
  
          Parameters
          ----------
          columns
              Column(s) to exclude from selection.
              This can be:
              - a column name, or multiple names
              - a regular expression starting with `^` and ending with `$`
              - a dtype or multiple dtypes
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "a": [1, 2, 3],
          ...         "b": ["a", "b", None],
          ...         "c": [None, 2, 1],
          ...     }
          ... )
          >>> df
          shape: (3, 3)
          ┌─────┬──────┬──────┐
          │ a   ┆ b    ┆ c    │
          │ --- ┆ ---  ┆ ---  │
          │ i64 ┆ str  ┆ i64  │
          ╞═════╪══════╪══════╡
          │ 1   ┆ a    ┆ null │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 2   ┆ b    ┆ 2    │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 3   ┆ null ┆ 1    │
          └─────┴──────┴──────┘
          >>> df.select(
          ...     pl.col("*").exclude("b"),
          ... )
          shape: (3, 2)
          ┌─────┬──────┐
          │ a   ┆ c    │
          │ --- ┆ ---  │
          │ i64 ┆ i64  │
          ╞═════╪══════╡
          │ 1   ┆ null │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 2   ┆ 2    │
          ├╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ 3   ┆ 1    │
          └─────┴──────┘
  
          """
          if isinstance(columns, str):
              columns = [columns]
              return wrap_expr(self._pyexpr.exclude(columns))
          elif not isinstance(columns, list) and issubclass(columns, DataType):  # type: ignore
              columns = [columns]  # type: ignore
              return wrap_expr(self._pyexpr.exclude_dtype(columns))
  
          if not all(
              [
                  isinstance(a, str) or issubclass(a, DataType)
                  for a in columns  # type: ignore
              ]
          ):
              raise ValueError("input should be all string or all DataType")
  
          if isinstance(columns[0], str):  # type: ignore
              return wrap_expr(self._pyexpr.exclude(columns))
          else:
              return wrap_expr(self._pyexpr.exclude_dtype(columns))
  
      def keep_name(self) -> "Expr":
          """
          Keep the original root name of the expression.
  
          Examples
          --------
  
          A groupby aggregation often changes the name of a column.
          With `keep_name` we can keep the original name of the column
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "a": [1, 2, 3],
          ...         "b": ["a", "b", None],
          ...     }
          ... )
          >>> df.groupby("a").agg(pl.col("b").list()).sort(by="a")
          shape: (3, 2)
          ┌─────┬────────────┐
          │ a   ┆ b_agg_list │
          │ --- ┆ ---        │
          │ i64 ┆ list [str] │
          ╞═════╪════════════╡
          │ 1   ┆ ["a"]      │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 2   ┆ ["b"]      │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 3   ┆ [null]     │
          └─────┴────────────┘
  
          Keep the original column name:
  
          >>> df.groupby("a").agg(pl.col("b").list().keep_name()).sort(by="a")
          shape: (3, 2)
          ┌─────┬────────────┐
          │ a   ┆ b          │
          │ --- ┆ ---        │
          │ i64 ┆ list [str] │
          ╞═════╪════════════╡
          │ 1   ┆ ["a"]      │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 2   ┆ ["b"]      │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 3   ┆ [null]     │
          └─────┴────────────┘
  
          """
  
          return wrap_expr(self._pyexpr.keep_name())
  
      def prefix(self, prefix: str) -> "Expr":
          """
          Add a prefix the to root column name of the expression.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "A": [1, 2, 3, 4, 5],
          ...         "fruits": ["banana", "banana", "apple", "apple", "banana"],
          ...         "B": [5, 4, 3, 2, 1],
          ...         "cars": ["beetle", "audi", "beetle", "beetle", "beetle"],
          ...     }
          ... )
          >>> df
          shape: (5, 4)
          ┌─────┬────────┬─────┬────────┐
          │ A   ┆ fruits ┆ B   ┆ cars   │
          │ --- ┆ ---    ┆ --- ┆ ---    │
          │ i64 ┆ str    ┆ i64 ┆ str    │
          ╞═════╪════════╪═════╪════════╡
          │ 1   ┆ banana ┆ 5   ┆ beetle │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 2   ┆ banana ┆ 4   ┆ audi   │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 3   ┆ apple  ┆ 3   ┆ beetle │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 4   ┆ apple  ┆ 2   ┆ beetle │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 5   ┆ banana ┆ 1   ┆ beetle │
          └─────┴────────┴─────┴────────┘
          >>> df.select(
          ...     [
          ...         pl.all(),
          ...         pl.all().reverse().suffix("_reverse"),
          ...     ]
          ... )
          shape: (5, 8)
          ┌─────┬────────┬─────┬────────┬───────────┬────────────────┬───────────┬──────────────┐
          │ A   ┆ fruits ┆ B   ┆ cars   ┆ A_reverse ┆ fruits_reverse ┆ B_reverse ┆ cars_reverse │
          │ --- ┆ ---    ┆ --- ┆ ---    ┆ ---       ┆ ---            ┆ ---       ┆ ---          │
          │ i64 ┆ str    ┆ i64 ┆ str    ┆ i64       ┆ str            ┆ i64       ┆ str          │
          ╞═════╪════════╪═════╪════════╪═══════════╪════════════════╪═══════════╪══════════════╡
          │ 1   ┆ banana ┆ 5   ┆ beetle ┆ 5         ┆ banana         ┆ 1         ┆ beetle       │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 2   ┆ banana ┆ 4   ┆ audi   ┆ 4         ┆ apple          ┆ 2         ┆ beetle       │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 3   ┆ apple  ┆ 3   ┆ beetle ┆ 3         ┆ apple          ┆ 3         ┆ beetle       │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 4   ┆ apple  ┆ 2   ┆ beetle ┆ 2         ┆ banana         ┆ 4         ┆ audi         │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 5   ┆ banana ┆ 1   ┆ beetle ┆ 1         ┆ banana         ┆ 5         ┆ beetle       │
          └─────┴────────┴─────┴────────┴───────────┴────────────────┴───────────┴──────────────┘
  
          """
          return wrap_expr(self._pyexpr.prefix(prefix))
  
      def suffix(self, suffix: str) -> "Expr":
          """
          Add a suffix the to root column name of the expression.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "A": [1, 2, 3, 4, 5],
          ...         "fruits": ["banana", "banana", "apple", "apple", "banana"],
          ...         "B": [5, 4, 3, 2, 1],
          ...         "cars": ["beetle", "audi", "beetle", "beetle", "beetle"],
          ...     }
          ... )
          >>> df
          shape: (5, 4)
          ┌─────┬────────┬─────┬────────┐
          │ A   ┆ fruits ┆ B   ┆ cars   │
          │ --- ┆ ---    ┆ --- ┆ ---    │
          │ i64 ┆ str    ┆ i64 ┆ str    │
          ╞═════╪════════╪═════╪════════╡
          │ 1   ┆ banana ┆ 5   ┆ beetle │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 2   ┆ banana ┆ 4   ┆ audi   │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 3   ┆ apple  ┆ 3   ┆ beetle │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 4   ┆ apple  ┆ 2   ┆ beetle │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┤
          │ 5   ┆ banana ┆ 1   ┆ beetle │
          └─────┴────────┴─────┴────────┘
          >>> df.select(
          ...     [
          ...         pl.all(),
          ...         pl.all().reverse().prefix("reverse_"),
          ...     ]
          ... )
          shape: (5, 8)
          ┌─────┬────────┬─────┬────────┬───────────┬────────────────┬───────────┬──────────────┐
          │ A   ┆ fruits ┆ B   ┆ cars   ┆ reverse_A ┆ reverse_fruits ┆ reverse_B ┆ reverse_cars │
          │ --- ┆ ---    ┆ --- ┆ ---    ┆ ---       ┆ ---            ┆ ---       ┆ ---          │
          │ i64 ┆ str    ┆ i64 ┆ str    ┆ i64       ┆ str            ┆ i64       ┆ str          │
          ╞═════╪════════╪═════╪════════╪═══════════╪════════════════╪═══════════╪══════════════╡
          │ 1   ┆ banana ┆ 5   ┆ beetle ┆ 5         ┆ banana         ┆ 1         ┆ beetle       │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 2   ┆ banana ┆ 4   ┆ audi   ┆ 4         ┆ apple          ┆ 2         ┆ beetle       │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 3   ┆ apple  ┆ 3   ┆ beetle ┆ 3         ┆ apple          ┆ 3         ┆ beetle       │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 4   ┆ apple  ┆ 2   ┆ beetle ┆ 2         ┆ banana         ┆ 4         ┆ audi         │
          ├╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 5   ┆ banana ┆ 1   ┆ beetle ┆ 1         ┆ banana         ┆ 5         ┆ beetle       │
          └─────┴────────┴─────┴────────┴───────────┴────────────────┴───────────┴──────────────┘
  
          """
          return wrap_expr(self._pyexpr.suffix(suffix))
  
      def is_not(self) -> "Expr":
          """
          Negate a boolean expression.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "a": [True, False, False],
          ...         "b": ["a", "b", None],
          ...     }
          ... )
          >>> df
          shape: (3, 2)
          ┌───────┬──────┐
          │ a     ┆ b    │
          │ ---   ┆ ---  │
          │ bool  ┆ str  │
          ╞═══════╪══════╡
          │ true  ┆ a    │
          ├╌╌╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ false ┆ b    │
          ├╌╌╌╌╌╌╌┼╌╌╌╌╌╌┤
          │ false ┆ null │
          └───────┴──────┘
          >>> df.select(pl.col("a").is_not())
          shape: (3, 1)
          ┌───────┐
          │ a     │
          │ ---   │
          │ bool  │
          ╞═══════╡
          │ false │
          ├╌╌╌╌╌╌╌┤
          │ true  │
          ├╌╌╌╌╌╌╌┤
          │ true  │
          └───────┘
  
          """
          return wrap_expr(self._pyexpr.is_not())
  
      def is_null(self) -> "Expr":
          """
          Create a boolean expression returning `True` where the expression contains null values.
          """
          return wrap_expr(self._pyexpr.is_null())
  
      def is_not_null(self) -> "Expr":
          """
          Create a boolean expression returning `True` where the expression does not contain null values.
          """
          return wrap_expr(self._pyexpr.is_not_null())
  
      def is_finite(self) -> "Expr":
          """
          Create a boolean expression returning `True` where the expression values are finite.
          """
          return wrap_expr(self._pyexpr.is_finite())
  
      def is_infinite(self) -> "Expr":
          """
          Create a boolean expression returning `True` where the expression values are infinite.
          """
          return wrap_expr(self._pyexpr.is_infinite())
  
      def is_nan(self) -> "Expr":
          """
          Create a boolean expression returning `True` where the expression values are NaN (Not A Number).
          """
          return wrap_expr(self._pyexpr.is_nan())
  
      def is_not_nan(self) -> "Expr":
          """
          Create a boolean expression returning `True` where the expression values are not NaN (Not A Number).
          """
          return wrap_expr(self._pyexpr.is_not_nan())
  
      def agg_groups(self) -> "Expr":
          """
          Get the group indexes of the group by operation.
          Should be used in aggregation context only.
          """
          return wrap_expr(self._pyexpr.agg_groups())
  
      def count(self) -> "Expr":
          """Count the number of values in this expression"""
          return wrap_expr(self._pyexpr.count())
  
      def len(self) -> "Expr":
          """
          Alias for count
          Count the number of values in this expression
          """
          return self.count()
  
      def slice(self, offset: int, length: int) -> "Expr":
          """
          Slice the Series.
  
          Parameters
          ----------
          offset
              Start index.
          length
              Length of the slice.
          """
          return wrap_expr(self._pyexpr.slice(offset, length))
  
      def drop_nulls(self) -> "Expr":
          """
          Syntactic sugar for:
  
          >>> pl.col("foo").filter(pl.col("foo").is_not_null())  # doctest: +IGNORE_RESULT
  
          """
          return self.filter(self.is_not_null())
  
      def cumsum(self, reverse: bool = False) -> "Expr":
          """
          Get an array with the cumulative sum computed at every element.
  
          Parameters
          ----------
          reverse
              Reverse the operation.
  
          Notes
          -----
          Dtypes in {Int8, UInt8, Int16, UInt16} are cast to
          Int64 before summing to prevent overflow issues.
          """
          return wrap_expr(self._pyexpr.cumsum(reverse))
  
      def cumprod(self, reverse: bool = False) -> "Expr":
          """
          Get an array with the cumulative product computed at every element.
  
          Parameters
          ----------
          reverse
              Reverse the operation.
  
          Notes
          -----
          Dtypes in {Int8, UInt8, Int16, UInt16} are cast to
          Int64 before summing to prevent overflow issues.
          """
          return wrap_expr(self._pyexpr.cumprod(reverse))
  
      def cummin(self, reverse: bool = False) -> "Expr":
          """
          Get an array with the cumulative min computed at every element.
  
          Parameters
          ----------
          reverse
              Reverse the operation.
          """
          return wrap_expr(self._pyexpr.cummin(reverse))
  
      def cummax(self, reverse: bool = False) -> "Expr":
          """
          Get an array with the cumulative max computed at every element.
  
          Parameters
          ----------
          reverse
              Reverse the operation.
          """
          return wrap_expr(self._pyexpr.cummax(reverse))
  
      def cumcount(self, reverse: bool = False) -> "Expr":
          """
          Get an array with the cumulative count computed at every element.
          Counting from 0 to len
  
          Parameters
          ----------
          reverse
              Reverse the operation.
          """
          return wrap_expr(self._pyexpr.cumcount(reverse))
  
      def floor(self) -> "Expr":
          """
          Floor underlying floating point array to the lowest integers smaller or equal to the float value.
  
          Only works on floating point Series
          """
          return wrap_expr(self._pyexpr.floor())
  
      def ceil(self) -> "Expr":
          """
          Ceil underlying floating point array to the heighest integers smaller or equal to the float value.
  
          Only works on floating point Series
          """
          return wrap_expr(self._pyexpr.ceil())
  
      def round(self, decimals: int) -> "Expr":
          """
          Round underlying floating point data by `decimals` digits.
  
          Parameters
          ----------
          decimals
              Number of decimals to round by.
          """
          return wrap_expr(self._pyexpr.round(decimals))
  
      def dot(self, other: Union["Expr", str]) -> "Expr":
          """
          Compute the dot/inner product between two Expressions
  
          Parameters
          ----------
          other
              Expression to compute dot product with
          """
          other = expr_to_lit_or_expr(other, str_to_lit=False)
          return wrap_expr(self._pyexpr.dot(other._pyexpr))
  
      def mode(self) -> "Expr":
          """
          Compute the most occurring value(s). Can return multiple Values
          """
          return wrap_expr(self._pyexpr.mode())
  
      def cast(self, dtype: Type[Any], strict: bool = True) -> "Expr":
          """
          Cast between data types.
  
          Parameters
          ----------
          dtype
              DataType to cast to
          strict
              Throw an error if a cast could not be done for instance due to an overflow
          """
          dtype = py_type_to_dtype(dtype)
          return wrap_expr(self._pyexpr.cast(dtype, strict))
  
      def sort(self, reverse: bool = False, nulls_last: bool = False) -> "Expr":
          """
          Sort this column. In projection/ selection context the whole column is sorted.
          If used in a groupby context, the groups are sorted.
  
          Parameters
          ----------
          reverse
              False -> order from small to large.
              True -> order from large to small.
          nulls_last
              If True nulls are considered to be larger than any valid value
          """
          return wrap_expr(self._pyexpr.sort_with(reverse, nulls_last))
  
      def arg_sort(self, reverse: bool = False) -> "Expr":
          """
          Get the index values that would sort this column.
  
          Parameters
          ----------
          reverse
              False -> order from small to large.
              True -> order from large to small.
  
          Returns
          -------
          out
              Series of type UInt32
          """
          return wrap_expr(self._pyexpr.arg_sort(reverse))
  
      def arg_max(self) -> "Expr":
          """
          Get the index of the maximal value.
          """
          return wrap_expr(self._pyexpr.arg_max())
  
      def arg_min(self) -> "Expr":
          """
          Get the index of the minimal value.
          """
          return wrap_expr(self._pyexpr.arg_min())
  
      def sort_by(
          self,
          by: Union["Expr", str, List[Union["Expr", str]]],
          reverse: Union[bool, List[bool]] = False,
      ) -> "Expr":
          """
          Sort this column by the ordering of another column, or multiple other columns.
          In projection/ selection context the whole column is sorted.
          If used in a groupby context, the groups are sorted.
  
          Parameters
          ----------
          by
              The column(s) used for sorting.
          reverse
              False -> order from small to large.
              True -> order from large to small.
          """
          if not isinstance(by, list):
              by = [by]
          if not isinstance(reverse, list):
              reverse = [reverse]
          by = selection_to_pyexpr_list(by)
  
          return wrap_expr(self._pyexpr.sort_by(by, reverse))
  
      def take(self, index: Union[List[int], "Expr", "pli.Series", np.ndarray]) -> "Expr":
          """
          Take values by index.
  
          Parameters
          ----------
          index
              An expression that leads to a UInt32 dtyped Series.
  
          Returns
          -------
          Values taken by index
          """
          if isinstance(index, (list, np.ndarray)):
              index_lit = pli.lit(pli.Series("", index, dtype=UInt32))
          else:
              index_lit = pli.expr_to_lit_or_expr(index, str_to_lit=False)
          return pli.wrap_expr(self._pyexpr.take(index_lit._pyexpr))
  
      def shift(self, periods: int = 1) -> "Expr":
          """
          Shift the values by a given period and fill the parts that will be empty due to this operation
          with `Nones`.
  
          Parameters
          ----------
          periods
              Number of places to shift (may be negative).
          """
          return wrap_expr(self._pyexpr.shift(periods))
  
      def shift_and_fill(
          self, periods: int, fill_value: Union[int, float, bool, str, "Expr"]
      ) -> "Expr":
          """
          Shift the values by a given period and fill the parts that will be empty due to this operation
          with the result of the `fill_value` expression.
  
          Parameters
          ----------
          periods
              Number of places to shift (may be negative).
          fill_value
              Fill None values with the result of this expression.
          """
          fill_value = expr_to_lit_or_expr(fill_value, str_to_lit=True)
          return wrap_expr(self._pyexpr.shift_and_fill(periods, fill_value._pyexpr))
  
      def fill_null(self, fill_value: Union[int, float, bool, str, "Expr"]) -> "Expr":
          """
          Fill null values using a filling strategy, literal, or Expr.
  
          fill_value
              One of:
              - "backward"
              - "forward"
              - "min"
              - "max"
              - "mean"
              - "one"
              - "zero"
              Or an expression.
          """
          # we first must check if it is not an expr, as expr does not implement __bool__
          # and thus leads to a value error in the second comparisson.
          if not isinstance(fill_value, Expr) and fill_value in [
              "backward",
              "forward",
              "min",
              "max",
              "mean",
              "zero",
              "one",
          ]:
              return wrap_expr(self._pyexpr.fill_null_with_strategy(fill_value))
  
          fill_value = expr_to_lit_or_expr(fill_value, str_to_lit=True)
          return wrap_expr(self._pyexpr.fill_null(fill_value._pyexpr))
  
      def fill_nan(self, fill_value: Union[str, int, float, bool, "Expr"]) -> "Expr":
          """
          Fill floating point NaN value with a fill value
          """
          fill_value = expr_to_lit_or_expr(fill_value, str_to_lit=True)
          return wrap_expr(self._pyexpr.fill_nan(fill_value._pyexpr))
  
      def forward_fill(self) -> "Expr":
          """
          Fill missing values with the latest seen values
          """
          return wrap_expr(self._pyexpr.forward_fill())
  
      def backward_fill(self) -> "Expr":
          """
          Fill missing values with the next to be seen values
          """
          return wrap_expr(self._pyexpr.backward_fill())
  
      def reverse(self) -> "Expr":
          """
          Reverse the selection.
          """
          return wrap_expr(self._pyexpr.reverse())
  
      def std(self) -> "Expr":
          """
          Get standard deviation.
          """
          return wrap_expr(self._pyexpr.std())
  
      def var(self) -> "Expr":
          """
          Get variance.
          """
          return wrap_expr(self._pyexpr.var())
  
      def max(self) -> "Expr":
          """
          Get maximum value.
          """
          return wrap_expr(self._pyexpr.max())
  
      def min(self) -> "Expr":
          """
          Get minimum value.
          """
          return wrap_expr(self._pyexpr.min())
  
      def sum(self) -> "Expr":
          """
          Get sum value.
  
          Notes
          -----
          Dtypes in {Int8, UInt8, Int16, UInt16} are cast to
          Int64 before summing to prevent overflow issues.
          """
          return wrap_expr(self._pyexpr.sum())
  
      def mean(self) -> "Expr":
          """
          Get mean value.
          """
          return wrap_expr(self._pyexpr.mean())
  
      def median(self) -> "Expr":
          """
          Get median value using linear interpolation.
          """
          return wrap_expr(self._pyexpr.median())
  
      def product(self) -> "Expr":
          """
          Compute the product of an expression
          """
          return wrap_expr(self._pyexpr.product())
  
      def n_unique(self) -> "Expr":
          """Count unique values."""
          return wrap_expr(self._pyexpr.n_unique())
  
      def arg_unique(self) -> "Expr":
          """Get index of first unique value."""
          return wrap_expr(self._pyexpr.arg_unique())
  
      def unique(self) -> "Expr":
          """Get unique values."""
          return wrap_expr(self._pyexpr.unique())
  
      def first(self) -> "Expr":
          """
          Get the first value.
          """
          return wrap_expr(self._pyexpr.first())
  
      def last(self) -> "Expr":
          """
          Get the last value.
          """
          return wrap_expr(self._pyexpr.last())
  
      def list(self) -> "Expr":
          """
          Aggregate to list.
          """
          return wrap_expr(self._pyexpr.list())
  
      def over(self, expr: Union[str, "Expr", List[Union["Expr", str]]]) -> "Expr":
          """
          Apply window function over a subgroup.
          This is similar to a groupby + aggregation + self join.
          Or similar to [window functions in Postgres](https://www.postgresql.org/docs/9.1/tutorial-window.html)
  
          Parameters
          ----------
          expr
              Column(s) to group by.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "groups": [1, 1, 2, 2, 1, 2, 3, 3, 1],
          ...         "values": [1, 2, 3, 4, 5, 6, 7, 8, 8],
          ...     }
          ... )
          >>> (
          ...     df.lazy()
          ...     .select(
          ...         [
          ...             pl.col("groups").sum().over("groups"),
          ...         ]
          ...     )
          ...     .collect()
          ... )
          shape: (9, 1)
          ┌────────┐
          │ groups │
          │ ---    │
          │ i64    │
          ╞════════╡
          │ 4      │
          ├╌╌╌╌╌╌╌╌┤
          │ 4      │
          ├╌╌╌╌╌╌╌╌┤
          │ 6      │
          ├╌╌╌╌╌╌╌╌┤
          │ 6      │
          ├╌╌╌╌╌╌╌╌┤
          │ ...    │
          ├╌╌╌╌╌╌╌╌┤
          │ 6      │
          ├╌╌╌╌╌╌╌╌┤
          │ 6      │
          ├╌╌╌╌╌╌╌╌┤
          │ 6      │
          ├╌╌╌╌╌╌╌╌┤
          │ 4      │
          └────────┘
  
          """
  
          pyexprs = selection_to_pyexpr_list(expr)
  
          return wrap_expr(self._pyexpr.over(pyexprs))
  
      def is_unique(self) -> "Expr":
          """
          Get mask of unique values.
          """
          return wrap_expr(self._pyexpr.is_unique())
  
      def is_first(self) -> "Expr":
          """
          Get a mask of the first unique value.
  
          Returns
          -------
          Boolean Series
          """
          return wrap_expr(self._pyexpr.is_first())
  
      def is_duplicated(self) -> "Expr":
          """
          Get mask of duplicated values.
          """
          return wrap_expr(self._pyexpr.is_duplicated())
  
      def quantile(self, quantile: float, interpolation: str = "nearest") -> "Expr":
          """
          Get quantile value.
  
  
          Parameters
          ----------
          quantile
              quantile between 0.0 and 1.0
  
          interpolation
              interpolation type, options: ['nearest', 'higher', 'lower', 'midpoint', 'linear']
          """
          return wrap_expr(self._pyexpr.quantile(quantile, interpolation))
  
      def filter(self, predicate: "Expr") -> "Expr":
          """
          Filter a single column.
          Mostly useful in in aggregation context. If you want to filter on a DataFrame level, use `LazyFrame.filter`.
  
          Parameters
          ----------
          predicate
              Boolean expression.
          """
          return wrap_expr(self._pyexpr.filter(predicate._pyexpr))
  
      def where(self, predicate: "Expr") -> "Expr":
          """
          Alias for filter
  
          Parameters
          ----------
          predicate
              Boolean expression.
          """
          return self.filter(predicate)
  
      def map(
          self,
          f: Callable[["pli.Series"], "pli.Series"],
          return_dtype: Optional[Type[DataType]] = None,
          agg_list: bool = False,
      ) -> "Expr":
          """
          Apply a custom python function. This function must produce a `Series`. Any other value will be stored as
          null/missing. If you want to apply a function over single values, consider using `apply`.
  
          [read more in the book](https://pola-rs.github.io/polars-book/user-guide/howcani/apply/udfs.html)
  
          Parameters
          ----------
          f
              Lambda/ function to apply.
          return_dtype
              Dtype of the output Series.
          agg_list
  
          """
          if return_dtype is not None:
              return_dtype = py_type_to_dtype(return_dtype)
          return wrap_expr(self._pyexpr.map(f, return_dtype, agg_list))
  
      def apply(
          self,
          f: Union[Callable[["pli.Series"], "pli.Series"], Callable[[Any], Any]],
          return_dtype: Optional[Type[DataType]] = None,
      ) -> "Expr":
          """
          Apply a custom function in a GroupBy or Projection context.
  
          Depending on the context it has the following behavior:
  
          ## Context
  
          * Select/Project
              expected type `f`: Callable[[Any], Any]
              Applies a python function over each individual value in the column.
          * GroupBy
              expected type `f`: Callable[[Series], Series]
              Applies a python function over each group.
  
          Parameters
          ----------
          f
              Lambda/ function to apply.
          return_dtype
              Dtype of the output Series.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "a": [1, 2, 1, 1],
          ...         "b": ["a", "b", "c", "c"],
          ...     }
          ... )
          >>> (
          ...     df.lazy()
          ...     .groupby("b", maintain_order=True)
          ...     .agg(
          ...         [
          ...             pl.col("a").apply(lambda x: x.sum()),
          ...         ]
          ...     )
          ...     .collect()
          ... )
          shape: (3, 2)
          ┌─────┬─────┐
          │ b   ┆ a   │
          │ --- ┆ --- │
          │ str ┆ i64 │
          ╞═════╪═════╡
          │ a   ┆ 1   │
          ├╌╌╌╌╌┼╌╌╌╌╌┤
          │ b   ┆ 2   │
          ├╌╌╌╌╌┼╌╌╌╌╌┤
          │ c   ┆ 2   │
          └─────┴─────┘
  
          """
  
          # input x: Series of type list containing the group values
          def wrap_f(x: "pli.Series") -> "pli.Series":  # pragma: no cover
              return x.apply(f, return_dtype=return_dtype)
  
          return self.map(wrap_f, agg_list=True)
  
      def flatten(self) -> "Expr":
          """
          Alias for explode.
  
          Explode a list or utf8 Series. This means that every item is expanded to a new row.
  
          Returns
          -------
          Exploded Series of same dtype
          """
  
          return wrap_expr(self._pyexpr.explode())
  
      def explode(self) -> "Expr":
          """
          Explode a list or utf8 Series. This means that every item is expanded to a new row.
  
          Returns
          -------
          Exploded Series of same dtype
          """
          return wrap_expr(self._pyexpr.explode())
  
      def take_every(self, n: int) -> "Expr":
          """
          Take every nth value in the Series and return as a new Series.
          """
          return wrap_expr(self._pyexpr.take_every(n))
  
      def head(self, n: Optional[int] = None) -> "Expr":
          """
          Take the first n values.
          """
          return wrap_expr(self._pyexpr.head(n))
  
      def tail(self, n: Optional[int] = None) -> "Expr":
          """
          Take the last n values.
          """
          return wrap_expr(self._pyexpr.tail(n))
  
      def pow(self, exponent: float) -> "Expr":
          """
          Raise expression to the power of exponent.
          """
          return wrap_expr(self._pyexpr.pow(exponent))
  
      def is_in(self, other: Union["Expr", List[Any]]) -> "Expr":
          """
          Check if elements of this Series are in the right Series, or List values of the right Series.
  
          Parameters
          ----------
          other
              Series of primitive type or List type.
  
          Returns
          -------
          Expr that evaluates to a Boolean Series.
  
          Examples
          --------
          >>> df = pl.DataFrame(
          ...     {"sets": [[1, 2, 3], [1, 2], [9, 10]], "optional_members": [1, 2, 3]}
          ... )
          >>> df.select([pl.col("optional_members").is_in("sets").alias("contains")])
          shape: (3, 1)
          ┌──────────┐
          │ contains │
          │ ---      │
          │ bool     │
          ╞══════════╡
          │ true     │
          ├╌╌╌╌╌╌╌╌╌╌┤
          │ true     │
          ├╌╌╌╌╌╌╌╌╌╌┤
          │ false    │
          └──────────┘
  
          """
          if isinstance(other, list):
              other = pli.lit(pli.Series(other))
          else:
              other = expr_to_lit_or_expr(other, str_to_lit=False)
          return wrap_expr(self._pyexpr.is_in(other._pyexpr))
  
      def repeat_by(self, by: Union["Expr", str]) -> "Expr":
          """
          Repeat the elements in this Series `n` times by dictated by the number given by `by`.
          The elements are expanded into a `List`
  
          Parameters
          ----------
          by
              Numeric column that determines how often the values will be repeated.
              The column will be coerced to UInt32. Give this dtype to make the coercion a no-op.
  
          Returns
          -------
          Series of type List
          """
          by = expr_to_lit_or_expr(by, False)
          return wrap_expr(self._pyexpr.repeat_by(by._pyexpr))
  
      def is_between(
          self,
          start: Union["Expr", datetime],
          end: Union["Expr", datetime],
          include_bounds: Union[bool, Sequence[bool]] = False,
      ) -> "Expr":
          """
          Check if this expression is between start and end.
  
          Parameters
          ----------
          start
              Lower bound as primitive type or datetime.
          end
              Upper bound as primitive type or datetime.
          include_bounds
             False:           Exclude both start and end (default).
             True:            Include both start and end.
             [False, False]:  Exclude start and exclude end.
             [True, True]:    Include start and include end.
             [False, True]:   Exclude start and include end.
             [True, False]:   Include start and exclude end.
  
          Returns
          -------
          Expr that evaluates to a Boolean Series.
          """
          cast_to_datetime = False
          if isinstance(start, datetime):
              start = pli.lit(start)
              cast_to_datetime = True
          if isinstance(end, datetime):
              end = pli.lit(end)
              cast_to_datetime = True
          if cast_to_datetime:
              expr = self.cast(Datetime)
          else:
              expr = self
          if include_bounds is False or include_bounds == [False, False]:
              return ((expr > start) & (expr < end)).alias("is_between")
          elif include_bounds is True or include_bounds == [True, True]:
              return ((expr >= start) & (expr <= end)).alias("is_between")
          elif include_bounds == [False, True]:
              return ((expr > start) & (expr <= end)).alias("is_between")
          elif include_bounds == [True, False]:
              return ((expr >= start) & (expr < end)).alias("is_between")
          else:
              raise ValueError(
                  "include_bounds should be a boolean or [boolean, boolean]."
              )
  
      def hash(self, k0: int = 0, k1: int = 1, k2: int = 2, k3: int = 3) -> "Expr":
          """
          Hash the Series.
  
          The hash value is of type `Datetime`
  
          Parameters
          ----------
          k0
              seed parameter
          k1
              seed parameter
          k2
              seed parameter
          k3
              seed parameter
          """
          return wrap_expr(self._pyexpr.hash(k0, k1, k2, k3))
  
      def reinterpret(self, signed: bool) -> "Expr":
          """
          Reinterpret the underlying bits as a signed/unsigned integer.
          This operation is only allowed for 64bit integers. For lower bits integers,
          you can safely use that cast operation.
  
          Parameters
          ----------
          signed
              True -> pl.Int64
              False -> pl.UInt64
          """
          return wrap_expr(self._pyexpr.reinterpret(signed))
  
      def inspect(self, fmt: str = "{}") -> "Expr":
          """
          Prints the value that this expression evaluates to and passes on the value.
  
          >>> df = pl.DataFrame({"foo": [1, 1, 2]})
          >>> df.select(pl.col("foo").cumsum().inspect("value is: {}").alias("bar"))
          value is: shape: (3,)
          Series: 'foo' [i64]
          [
              1
              2
              4
          ]
          shape: (3, 1)
          ┌─────┐
          │ bar │
          │ --- │
          │ i64 │
          ╞═════╡
          │ 1   │
          ├╌╌╌╌╌┤
          │ 2   │
          ├╌╌╌╌╌┤
          │ 4   │
          └─────┘
  
          """
  
          def inspect(s: "pli.Series") -> "pli.Series":  # pragma: no cover
              print(fmt.format(s))
              return s
  
          return self.map(inspect, return_dtype=None, agg_list=True)
  
      def interpolate(self) -> "Expr":
          """
          Interpolate intermediate values. The interpolation method is linear.
          """
          return wrap_expr(self._pyexpr.interpolate())
  
      def rolling_min(
          self,
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          apply a rolling min (moving min) over the values in this array.
          A window of length `window_size` will traverse the array. The values that fill this window
          will (optionally) be multiplied with the weights given by the `weight` vector. The resulting
          values will be aggregated to their sum.
  
          Parameters
          ----------
          window_size
              The length of the window.
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
          """
          if min_periods is None:
              min_periods = window_size
          return wrap_expr(
              self._pyexpr.rolling_min(window_size, weights, min_periods, center)
          )
  
      def rolling_max(
          self,
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Apply a rolling max (moving max) over the values in this array.
          A window of length `window_size` will traverse the array. The values that fill this window
          will (optionally) be multiplied with the weights given by the `weight` vector. The resulting
          values will be aggregated to their sum.
  
          Parameters
          ----------
          window_size
              The length of the window.
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
          """
          if min_periods is None:
              min_periods = window_size
          return wrap_expr(
              self._pyexpr.rolling_max(window_size, weights, min_periods, center)
          )
  
      def rolling_mean(
          self,
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Apply a rolling mean (moving mean) over the values in this array.
          A window of length `window_size` will traverse the array. The values that fill this window
          will (optionally) be multiplied with the weights given by the `weight` vector. The resulting
          values will be aggregated to their sum.
  
          Parameters
          ----------
          window_size
              The length of the window.
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
  
          Examples
          --------
  
          >>> df = pl.DataFrame({"A": [1.0, 8.0, 6.0, 2.0, 16.0, 10.0]})
          >>> df.select(
          ...     [
          ...         pl.col("A").rolling_mean(window_size=2),
          ...     ]
          ... )
          shape: (6, 1)
          ┌──────┐
          │ A    │
          │ ---  │
          │ f64  │
          ╞══════╡
          │ null │
          ├╌╌╌╌╌╌┤
          │ 4.5  │
          ├╌╌╌╌╌╌┤
          │ 7    │
          ├╌╌╌╌╌╌┤
          │ 4    │
          ├╌╌╌╌╌╌┤
          │ 9    │
          ├╌╌╌╌╌╌┤
          │ 13   │
          └──────┘
  
          """
          if min_periods is None:
              min_periods = window_size
          return wrap_expr(
              self._pyexpr.rolling_mean(window_size, weights, min_periods, center)
          )
  
      def rolling_sum(
          self,
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Apply a rolling sum (moving sum) over the values in this array.
          A window of length `window_size` will traverse the array. The values that fill this window
          will (optionally) be multiplied with the weights given by the `weight` vector. The resulting
          values will be aggregated to their sum.
  
          Parameters
          ----------
          window_size
              The length of the window.
          weights
              An optional slice with the same length of the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
          """
          if min_periods is None:
              min_periods = window_size
          return wrap_expr(
              self._pyexpr.rolling_sum(window_size, weights, min_periods, center)
          )
  
      def rolling_std(
          self,
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Compute a rolling std dev
  
          A window of length `window_size` will traverse the array. The values that fill this window
          will (optionally) be multiplied with the weights given by the `weight` vector. The resulting
          values will be aggregated to their sum.
  
          Parameters
          ----------
          window_size
              The length of the window.
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
          """
          if min_periods is None:
              min_periods = window_size
          return wrap_expr(
              self._pyexpr.rolling_std(window_size, weights, min_periods, center)
          )
  
      def rolling_var(
          self,
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Compute a rolling variance.
  
          A window of length `window_size` will traverse the array. The values that fill this window
          will (optionally) be multiplied with the weights given by the `weight` vector. The resulting
          values will be aggregated to their sum.
  
          Parameters
          ----------
          window_size
              The length of the window.
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
          """
          if min_periods is None:
              min_periods = window_size
          return wrap_expr(
              self._pyexpr.rolling_var(window_size, weights, min_periods, center)
          )
  
      def rolling_apply(
          self,
          function: Callable[["pli.Series"], Any],
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Allows a custom rolling window function.
          Prefer the specific rolling window functions over this one, as they are faster.
  
          Prefer:
  
              * rolling_min
              * rolling_max
              * rolling_mean
              * rolling_sum
  
          Parameters
          ----------
          function
              Aggregation function
          window_size
              The length of the window.
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "A": [1.0, 2.0, 9.0, 2.0, 13.0],
          ...     }
          ... )
          >>> df.select(
          ...     [
          ...         pl.col("A").rolling_apply(lambda s: s.std(), window_size=3),
          ...     ]
          ... )
          shape: (5, 1)
          ┌────────────────────┐
          │ A                  │
          │ ---                │
          │ f64                │
          ╞════════════════════╡
          │ null               │
          ├╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ null               │
          ├╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 4.358898943540674  │
          ├╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 4.041451884327381  │
          ├╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
          │ 5.5677643628300215 │
          └────────────────────┘
  
          """
          if min_periods is None:
              min_periods = window_size
          return wrap_expr(
              self._pyexpr.rolling_apply(
                  function, window_size, weights, min_periods, center
              )
          )
  
      def rolling_median(
          self,
          window_size: int,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Compute a rolling median
  
          Parameters
          ----------
          window_size
              Size of the rolling window
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
          """
          return wrap_expr(
              self._pyexpr.rolling_median(window_size, weights, min_periods, center)
          )
  
      def rolling_quantile(
          self,
          quantile: float,
          interpolation: str = "nearest",
          window_size: int = 2,
          weights: Optional[List[float]] = None,
          min_periods: Optional[int] = None,
          center: bool = False,
      ) -> "Expr":
          """
          Compute a rolling quantile
  
          Parameters
          ----------
          quantile
              quantile to compute
          interpolation
              interpolation type, options: ['nearest', 'higher', 'lower', 'midpoint', 'linear']
          window_size
              The length of the window.
          weights
              An optional slice with the same length as the window that will be multiplied
              elementwise with the values in the window.
          min_periods
              The number of values in the window that should be non-null before computing a result.
              If None, it will be set equal to window size.
          center
              Set the labels at the center of the window
          """
          return wrap_expr(
              self._pyexpr.rolling_quantile(
                  quantile, interpolation, window_size, weights, min_periods, center
              )
          )
  
      def rolling_skew(self, window_size: int, bias: bool = True) -> "Expr":
          """
          Compute a rolling skew
  
          Parameters
          ----------
          window_size
              Size of the rolling window
          bias
              If False, then the calculations are corrected for statistical bias.
          """
          return wrap_expr(self._pyexpr.rolling_skew(window_size, bias))
  
      def abs(self) -> "Expr":
          """
          Take absolute values
          """
          return wrap_expr(self._pyexpr.abs())
  
      def argsort(self, reverse: bool = False) -> "Expr":
          """
          Index location of the sorted variant of this Series.
  
          Parameters
          ----------
          reverse
              Reverse the ordering. Default is from low to high.
          """
          return pli.argsort_by([self], [reverse])
  
      def rank(self, method: str = "average", reverse: bool = False) -> "Expr":
          """
          Assign ranks to data, dealing with ties appropriately.
  
          Parameters
          ----------
          method
              {'average', 'min', 'max', 'dense', 'ordinal', 'random'}, optional
              The method used to assign ranks to tied elements.
              The following methods are available (default is 'average'):
              - 'average': The average of the ranks that would have been assigned to
              all the tied values is assigned to each value.
              - 'min': The minimum of the ranks that would have been assigned to all
              the tied values is assigned to each value.  (This is also
              referred to as "competition" ranking.)
              - 'max': The maximum of the ranks that would have been assigned to all
              the tied values is assigned to each value.
              - 'dense': Like 'min', but the rank of the next highest element is
              assigned the rank immediately after those assigned to the tied
              elements.
              - 'ordinal': All values are given a distinct rank, corresponding to
              the order that the values occur in `a`.
              - 'random': Like 'ordinal', but the rank for ties is not dependent
              on the order that the values occur in `a`.
          reverse
              reverse the operation
          """
          return wrap_expr(self._pyexpr.rank(method, reverse))
  
      def diff(self, n: int = 1, null_behavior: str = "ignore") -> "Expr":
          """
          Calculate the n-th discrete difference.
  
          Parameters
          ----------
          n
              number of slots to shift
          null_behavior
              {'ignore', 'drop'}
          """
          return wrap_expr(self._pyexpr.diff(n, null_behavior))
  
      def pct_change(self, n: int = 1) -> "Expr":
          """
          Percentage change (as fraction) between current element and most-recent
          non-null element at least n period(s) before the current element.
  
          Computes the change from the previous row by default.
  
          Parameters
          ----------
          n
              periods to shift for forming percent change.
          """
          return wrap_expr(self._pyexpr.pct_change(n))
  
      def skew(self, bias: bool = True) -> "Expr":
          r"""Compute the sample skewness of a data set.
          For normally distributed data, the skewness should be about zero. For
          unimodal continuous distributions, a skewness value greater than zero means
          that there is more weight in the right tail of the distribution. The
          function `skewtest` can be used to determine if the skewness value
          is close enough to zero, statistically speaking.
  
  
          See scipy.stats for more information.
  
          Parameters
          ----------
          bias : bool, optional
              If False, then the calculations are corrected for statistical bias.
  
          Notes
          -----
          The sample skewness is computed as the Fisher-Pearson coefficient
          of skewness, i.e.
  
          .. math:: g_1=\frac{m_3}{m_2^{3/2}}
  
          where
  
          .. math:: m_i=\frac{1}{N}\sum_{n=1}^N(x[n]-\bar{x})^i
  
          is the biased sample :math:`i\texttt{th}` central moment, and
          :math:`\bar{x}` is
          the sample mean.  If ``bias`` is False, the calculations are
          corrected for bias and the value computed is the adjusted
          Fisher-Pearson standardized moment coefficient, i.e.
  
          .. math:: G_1=\frac{k_3}{k_2^{3/2}}= \frac{\sqrt{N(N-1)}}{N-2}\frac{m_3}{m_2^{3/2}}
  
          """
          return wrap_expr(self._pyexpr.skew(bias))
  
      def kurtosis(self, fisher: bool = True, bias: bool = True) -> "Expr":
          """Compute the kurtosis (Fisher or Pearson) of a dataset.
          Kurtosis is the fourth central moment divided by the square of the
          variance. If Fisher's definition is used, then 3.0 is subtracted from
          the result to give 0.0 for a normal distribution.
          If bias is False then the kurtosis is calculated using k statistics to
          eliminate bias coming from biased moment estimators
  
          See scipy.stats for more information
  
          Parameters
          ----------
          fisher : bool, optional
              If True, Fisher's definition is used (normal ==> 0.0). If False,
              Pearson's definition is used (normal ==> 3.0).
          bias : bool, optional
              If False, then the calculations are corrected for statistical bias.
          """
          return wrap_expr(self._pyexpr.kurtosis(fisher, bias))
  
      def clip(self, min_val: Union[int, float], max_val: Union[int, float]) -> "Expr":
          """
          Clip (limit) the values in an array to any value that fits in 64 floating poitns range.
  
          Only works for the following dtypes: {Int32, Int64, Float32, Float64, UInt32}.
  
          If you want to clip other dtypes, consider writing a when -> then -> otherwise expression
  
          Parameters
          ----------
          min_val
              Minimum value.
          max_val
              Maximum value.
          """
          return wrap_expr(self._pyexpr.clip(min_val, max_val))
  
      def lower_bound(self) -> "Expr":
          """
          Returns a unit Series with the lowest value possible for the dtype of this expression.
          """
          return wrap_expr(self._pyexpr.lower_bound())
  
      def upper_bound(self) -> "Expr":
          """
          Returns a unit Series with the highest value possible for the dtype of this expression.
          """
          return wrap_expr(self._pyexpr.upper_bound())
  
      def sin(self) -> "Expr":
          """
          Compute the element-wise value for Trigonometric sine on an array
  
          Returns
          -------
          Series of dtype Float64
  
          Examples
          --------
  
          >>> df = pl.DataFrame({"a": [0.0]})
          >>> df.select(pl.col("a").sin())
          shape: (1, 1)
          ┌─────┐
          │ a   │
          │ --- │
          │ f64 │
          ╞═════╡
          │ 0.0 │
          └─────┘
  
          """
          return np.sin(self)  # type: ignore
  
      def cos(self) -> "Expr":
          """
          Compute the element-wise value for Trigonometric cosine on an array
  
          Returns
          -------
          Series of dtype Float64
  
          Examples
          --------
  
          >>> df = pl.DataFrame({"a": [0.0]})
          >>> df.select(pl.col("a").cos())
          shape: (1, 1)
          ┌─────┐
          │ a   │
          │ --- │
          │ f64 │
          ╞═════╡
          │ 1   │
          └─────┘
  
          """
          return np.cos(self)  # type: ignore
  
      def tan(self) -> "Expr":
          """
          Compute the element-wise value for Trigonometric tangent on an array
  
          Returns
          -------
          Series of dtype Float64
  
          Examples
          --------
  
          >>> df = pl.DataFrame({"a": [1.0]})
          >>> df.select(pl.col("a").tan().round(2))
          shape: (1, 1)
          ┌──────┐
          │ a    │
          │ ---  │
          │ f64  │
          ╞══════╡
          │ 1.56 │
          └──────┘
  
          """
          return np.tan(self)  # type: ignore
  
      def arcsin(self) -> "Expr":
          """
          Compute the element-wise value for Trigonometric sine on an array
  
          Returns
          -------
          Series of dtype Float64
  
          Examples
          --------
          >>> df = pl.DataFrame({"a": [1.0]})
          >>> df.select(pl.col("a").arcsin())
          shape: (1, 1)
          ┌────────────────────┐
          │ a                  │
          │ ---                │
          │ f64                │
          ╞════════════════════╡
          │ 1.5707963267948966 │
          └────────────────────┘
  
          """
          return np.arcsin(self)  # type: ignore
  
      def arccos(self) -> "Expr":
          """
          Compute the element-wise value for Trigonometric cosine on an array
  
          Returns
          -------
          Series of dtype Float64
  
          Examples
          --------
          >>> df = pl.DataFrame({"a": [0.0]})
          >>> df.select(pl.col("a").arccos())
          shape: (1, 1)
          ┌────────────────────┐
          │ a                  │
          │ ---                │
          │ f64                │
          ╞════════════════════╡
          │ 1.5707963267948966 │
          └────────────────────┘
  
          """
          return np.arccos(self)  # type: ignore
  
      def arctan(self) -> "Expr":
          """
          Compute the element-wise value for Trigonometric tangent on an array
  
          Returns
          -------
          Series of dtype Float64
  
          Examples
          --------
          >>> df = pl.DataFrame({"a": [1.0]})
          >>> df.select(pl.col("a").arctan())
          shape: (1, 1)
          ┌────────────────────┐
          │ a                  │
          │ ---                │
          │ f64                │
          ╞════════════════════╡
          │ 0.7853981633974483 │
          └────────────────────┘
  
          """
          return np.arctan(self)  # type: ignore
  
      def reshape(self, dims: Tuple[int, ...]) -> "Expr":
          """
          Reshape this Expr to a flat series, shape: (len,)
          or a List series, shape: (rows, cols)
  
          if a -1 is used in any of the dimensions, that dimension is inferred.
  
          Parameters
          ----------
          dims
              Tuple of the dimension sizes
  
          Returns
          -------
          Expr
          """
          return wrap_expr(self._pyexpr.reshape(dims))
  
      def shuffle(self, seed: Optional[int] = None) -> "Expr":
          """
          Shuffle the contents of this expr.
  
          Parameters
          ----------
          seed
              Seed initialization. If None given numpy is used.
          """
          if seed is None:
              seed = int(np.random.randint(0, 10000))
          return wrap_expr(self._pyexpr.shuffle(seed))
  
      def sample(
          self,
          fraction: float = 1.0,
          with_replacement: bool = True,
          seed: Optional[int] = 0,
      ) -> "Expr":
          """
          Sample a fraction of the `Series`.
  
          Parameters
          ----------
          fraction
              Fraction 0.0 <= value <= 1.0
          with_replacement
              Allow values to be sampled more than once.
          seed
              Seed initialization. If None given numpy is used.
          """
          if seed is None:
              seed = int(np.random.randint(0, 10000))
          return wrap_expr(self._pyexpr.sample_frac(fraction, with_replacement, seed))
  
      def ewm_mean(
          self,
          com: Optional[float] = None,
          span: Optional[float] = None,
          half_life: Optional[float] = None,
          alpha: Optional[float] = None,
          adjust: bool = True,
          min_periods: int = 1,
      ) -> "Expr":
          r"""
          Exponential moving average.
  
          Parameters
          ----------
          com
              Specify decay in terms of center of mass, :math:`alpha = 1/(1 + com) \;for\; com >= 0`.
          span
              Specify decay in terms of span, :math:`alpha = 2/(span + 1) \;for\; span >= 1`
          half_life
              Specify decay in terms of half-life, :math:`alpha = 1 - exp(-ln(2) / halflife) \;for\; halflife > 0`
          alpha
              Specify smoothing factor alpha directly, :math:`0 < alpha < 1`.
          adjust
              Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings
  
                  - When adjust = True the EW function is calculated using weights :math:`w_i = (1 - alpha)^i`
                  - When adjust = False the EW function is calculated recursively.
          min_periods
              Minimum number of observations in window required to have a value (otherwise result is Null).
  
          """
          alpha = _prepare_alpha(com, span, half_life, alpha)
          return wrap_expr(self._pyexpr.ewm_mean(alpha, adjust, min_periods))
  
      def ewm_std(
          self,
          com: Optional[float] = None,
          span: Optional[float] = None,
          half_life: Optional[float] = None,
          alpha: Optional[float] = None,
          adjust: bool = True,
          min_periods: int = 1,
      ) -> "Expr":
          r"""
          Exponential moving standard deviation.
  
          Parameters
          ----------
          com
              Specify decay in terms of center of mass, :math:`alpha = 1/(1 + com) \;for\; com >= 0`.
          span
              Specify decay in terms of span, :math:`alpha = 2/(span + 1) \;for\; span >= 1`
          half_life
              Specify decay in terms of half-life, :math:`alpha = 1 - exp(-ln(2) / halflife) \;for\; halflife > 0`
          alpha
              Specify smoothing factor alpha directly, :math:`0 < alpha < 1`.
          adjust
              Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings
  
                  - When adjust = True the EW function is calculated using weights :math:`w_i = (1 - alpha)^i`
                  - When adjust = False the EW function is calculated recursively.
          min_periods
              Minimum number of observations in window required to have a value (otherwise result is Null).
  
          """
          alpha = _prepare_alpha(com, span, half_life, alpha)
          return wrap_expr(self._pyexpr.ewm_std(alpha, adjust, min_periods))
  
      def ewm_var(
          self,
          com: Optional[float] = None,
          span: Optional[float] = None,
          half_life: Optional[float] = None,
          alpha: Optional[float] = None,
          adjust: bool = True,
          min_periods: int = 1,
      ) -> "Expr":
          r"""
          Exponential moving standard deviation.
  
          Parameters
          ----------
          com
              Specify decay in terms of center of mass, :math:`alpha = 1/(1 + com) \;for\; com >= 0`.
          span
              Specify decay in terms of span, :math:`alpha = 2/(span + 1) \;for\; span >= 1`
          half_life
              Specify decay in terms of half-life, :math:`alpha = 1 - exp(-ln(2) / halflife) \;for\; halflife > 0`
          alpha
              Specify smoothing factor alpha directly, :math:`0 < alpha < 1`.
          adjust
              Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings
  
                  - When adjust = True the EW function is calculated using weights :math:`w_i = (1 - alpha)^i`
                  - When adjust = False the EW function is calculated recursively.
          min_periods
              Minimum number of observations in window required to have a value (otherwise result is Null).
  
          """
          alpha = _prepare_alpha(com, span, half_life, alpha)
          return wrap_expr(self._pyexpr.ewm_var(alpha, adjust, min_periods))
  
      def extend_constant(
          self, value: Optional[Union[int, float, str, bool]], n: int
      ) -> "Expr":
          """
          Extend the Series with given number of values.
  
          Parameters
          ----------
          value
              The value to extend the Series with. This value may be None to fill with nulls.
          n
              The number of values to extend.
          """
          return wrap_expr(self._pyexpr.extend_constant(value, n))
  
      # Below are the namespaces defined. Keep these at the end of the definition of Expr, as to not confuse mypy with
      # the type annotation `str` with the namespace "str"
  
      @property
      def dt(self) -> "ExprDateTimeNameSpace":
          """
          Create an object namespace of all datetime related methods.
          """
          return ExprDateTimeNameSpace(self)
  
      @property
      def str(self) -> "ExprStringNameSpace":
          """
          Create an object namespace of all string related methods.
          """
          return ExprStringNameSpace(self)
  
      @property
      def arr(self) -> "ExprListNameSpace":
          """
          Create an object namespace of all datetime related methods.
          """
          return ExprListNameSpace(self)
  
  
  class ExprListNameSpace:
      """
      Namespace for list related expressions
      """
  
      def __init__(self, expr: Expr):
          self._pyexpr = expr._pyexpr
  
      def lengths(self) -> Expr:
          """
          Get the length of the arrays as UInt32.
          """
          return wrap_expr(self._pyexpr.arr_lengths())
  
      def sum(self) -> "Expr":
          """
          Sum all the arrays in the list
          """
          return wrap_expr(self._pyexpr.lst_sum())
  
      def max(self) -> "Expr":
          """
          Compute the max value of the arrays in the list
          """
          return wrap_expr(self._pyexpr.lst_max())
  
      def min(self) -> "Expr":
          """
          Compute the min value of the arrays in the list
          """
          return wrap_expr(self._pyexpr.lst_min())
  
      def mean(self) -> "Expr":
          """
          Compute the mean value of the arrays in the list
          """
          return wrap_expr(self._pyexpr.lst_mean())
  
      def sort(self, reverse: bool = False) -> "Expr":
          """
          Sort the arrays in the list
          """
          return wrap_expr(self._pyexpr.lst_sort(reverse))
  
      def reverse(self) -> "Expr":
          """
          Reverse the arrays in the list
          """
          return wrap_expr(self._pyexpr.lst_reverse())
  
      def unique(self) -> "Expr":
          """
          Get the unique/distinct values in the list
          """
          return wrap_expr(self._pyexpr.lst_unique())
  
      def concat(
          self, other: Union[List[Union[Expr, str]], Expr, str, "pli.Series", List[Any]]
      ) -> "Expr":
          """
          Concat the arrays in a Series dtype List in linear time.
  
          Parameters
          ----------
          other
              Columns to concat into a List Series
          """
          if isinstance(other, list) and (
              not isinstance(other[0], (Expr, str, pli.Series))
          ):
              return self.concat(pli.Series([other]))
  
          other_list: List[Union[Expr, str, "pli.Series"]]
          if not isinstance(other, list):
              other_list = [other]
          else:
              other_list = copy.copy(other)  # type: ignore
  
          other_list.insert(0, wrap_expr(self._pyexpr))
          return pli.concat_list(other_list)
  
      def get(self, index: int) -> "Expr":
          """
          Get the value by index in the sublists.
          So index `0` would return the first item of every sublist
          and index `-1` would return the last item of every sublist
          if an index is out of bounds, it will return a `None`.
  
          Parameters
          ----------
          index
              Index to return per sublist
          """
          return wrap_expr(self._pyexpr.lst_get(index))
  
      def first(self) -> "Expr":
          """
          Get the first value of the sublists.
          """
          return self.get(0)
  
      def last(self) -> "Expr":
          """
          Get the last value of the sublists.
          """
          return self.get(-1)
  
      def contains(self, item: Union[float, str, bool, int, date, datetime]) -> "Expr":
          """
          Check if sublists contain the given item.
  
          Parameters
          ----------
          item
              Item that will be checked for membership
  
          Returns
          -------
          Boolean mask
          """
          return wrap_expr(self._pyexpr).map(lambda s: s.arr.contains(item))
  
      def join(self, separator: str) -> "Expr":
          """
          Join all string items in a sublist and place a separator between them.
          This errors if inner type of list `!= Utf8`.
  
          Parameters
          ----------
          separator
              string to separate the items with
  
          Returns
          -------
          Series of dtype Utf8
          """
  
          return wrap_expr(self._pyexpr.lst_join(separator))
  
  
  class ExprStringNameSpace:
      """
      Namespace for string related expressions
      """
  
      def __init__(self, expr: Expr):
          self._pyexpr = expr._pyexpr
  
      def strptime(
          self,
          datatype: Union[Type[Date], Type[Datetime]],
          fmt: Optional[str] = None,
          strict: bool = True,
          exact: bool = True,
      ) -> Expr:
          """
          Parse utf8 expression as a Date/Datetimetype.
  
          Parameters
          ----------
          datatype
              Date | Datetime.
          fmt
              format to use, see the following link for examples:
              https://docs.rs/chrono/latest/chrono/format/strftime/index.html
  
              example: "%y-%m-%d".
          strict
              raise an error if any conversion fails
          exact
              - If True, require an exact format match.
              - If False, allow the format to match anywhere in the target string.
          """
          if not issubclass(datatype, DataType):
              raise ValueError(
                  f"expected: {DataType} got: {datatype}"
              )  # pragma: no cover
          if datatype == Date:
              return wrap_expr(self._pyexpr.str_parse_date(fmt, strict, exact))
          elif datatype == Datetime:
              return wrap_expr(self._pyexpr.str_parse_datetime(fmt, strict, exact))
          else:
              raise ValueError(
                  "dtype should be of type {Date, Datetime}"
              )  # pragma: no cover
  
      def lengths(self) -> Expr:
          """
          Get the length of the Strings as UInt32.
          """
          return wrap_expr(self._pyexpr.str_lengths())
  
      def concat(self, delimiter: str = "-") -> "Expr":
          """
          Vertically concat the values in the Series to a single string value.
  
          Returns
          -------
          Series of dtype Utf8
  
          Examples
          --------
  
          >>> df = pl.DataFrame({"foo": [1, None, 2]})
          >>> df = df.select(pl.col("foo").str.concat("-"))
          >>> df
          shape: (1, 1)
          ┌──────────┐
          │ foo      │
          │ ---      │
          │ str      │
          ╞══════════╡
          │ 1-null-2 │
          └──────────┘
  
          """
          return wrap_expr(self._pyexpr.str_concat(delimiter))
  
      def to_uppercase(self) -> Expr:
          """
          Transform to uppercase variant.
          """
          return wrap_expr(self._pyexpr.str_to_uppercase())
  
      def to_lowercase(self) -> Expr:
          """
          Transform to lowercase variant.
          """
          return wrap_expr(self._pyexpr.str_to_lowercase())
  
      def strip(self) -> Expr:
          """
          Remove leading and trailing whitespace.
          """
          return wrap_expr(self._pyexpr.str_strip())
  
      def lstrip(self) -> Expr:
          """
          Remove leading whitespace.
          """
          return wrap_expr(self._pyexpr.str_lstrip())
  
      def rstrip(self) -> Expr:
          """
          Remove trailing whitespace.
          """
          return wrap_expr(self._pyexpr.str_rstrip())
  
      def contains(self, pattern: str) -> Expr:
          """
          Check if string contains regex.
  
          Parameters
          ----------
          pattern
              Regex pattern.
          """
          return wrap_expr(self._pyexpr.str_contains(pattern))
  
      def json_path_match(self, json_path: str) -> Expr:
          """
          Extract the first match of json string with provided JSONPath expression.
          Throw errors if encounter invalid json strings.
          All return value will be casted to Utf8 regardless of the original value.
          Documentation on JSONPath standard: https://goessner.net/articles/JsonPath/
  
          Parameters
          ----------
          json_path
              A valid JSON path query string
  
          Returns
          -------
          Utf8 array. Contain null if original value is null or the json_path return nothing.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {"json_val": ['{"a":"1"}', None, '{"a":2}', '{"a":2.1}', '{"a":true}']}
          ... )
          >>> df.select(pl.col("json_val").str.json_path_match("$.a"))
          shape: (5, 1)
          ┌──────────┐
          │ json_val │
          │ ---      │
          │ str      │
          ╞══════════╡
          │ 1        │
          ├╌╌╌╌╌╌╌╌╌╌┤
          │ null     │
          ├╌╌╌╌╌╌╌╌╌╌┤
          │ 2        │
          ├╌╌╌╌╌╌╌╌╌╌┤
          │ 2.1      │
          ├╌╌╌╌╌╌╌╌╌╌┤
          │ true     │
          └──────────┘
  
          """
          return wrap_expr(self._pyexpr.str_json_path_match(json_path))
  
      def decode(self, encoding: str, strict: bool = False) -> Expr:
          """
          Decodes a value using the provided encoding
  
          Parameters
          ----------
          encoding
              'hex' or 'base64'
          strict
              how to handle invalid inputs
              - True: method will throw error if unable to decode a value
              - False: unhandled values will be replaced with `None`
  
          Examples
          --------
          >>> df = pl.DataFrame({"encoded": ["666f6f", "626172", None]})
          >>> df.select(pl.col("encoded").str.decode("hex"))
          shape: (3, 1)
          ┌─────────┐
          │ encoded │
          │ ---     │
          │ str     │
          ╞═════════╡
          │ foo     │
          ├╌╌╌╌╌╌╌╌╌┤
          │ bar     │
          ├╌╌╌╌╌╌╌╌╌┤
          │ null    │
          └─────────┘
          """
          if encoding == "hex":
              return wrap_expr(self._pyexpr.str_hex_decode(strict))
          elif encoding == "base64":
              return wrap_expr(self._pyexpr.str_base64_decode(strict))
          else:
              raise ValueError("supported encodings are 'hex' and 'base64'")
  
      def encode(self, encoding: str) -> Expr:
          """
          Encodes a value using the provided encoding
  
          Parameters
          ----------
          encoding
              'hex' or 'base64'
  
          Returns
          -------
          Utf8 array with values encoded using provided encoding
  
          Examples
          --------
          >>> df = pl.DataFrame({"strings": ["foo", "bar", None]})
          >>> df.select(pl.col("strings").str.encode("hex"))
          shape: (3, 1)
          ┌─────────┐
          │ strings │
          │ ---     │
          │ str     │
          ╞═════════╡
          │ 666f6f  │
          ├╌╌╌╌╌╌╌╌╌┤
          │ 626172  │
          ├╌╌╌╌╌╌╌╌╌┤
          │ null    │
          └─────────┘
          """
          if encoding == "hex":
              return wrap_expr(self._pyexpr.str_hex_encode())
          elif encoding == "base64":
              return wrap_expr(self._pyexpr.str_base64_encode())
          else:
              raise ValueError("supported encodings are 'hex' and 'base64'")
  
      def extract(self, pattern: str, group_index: int = 1) -> Expr:
          r"""
          Extract the target capture group from provided patterns.
  
          Parameters
          ----------
          pattern
              A valid regex pattern
          group_index
              Index of the targeted capture group.
              Group 0 mean the whole pattern, first group begin at index 1
              Default to the first capture group
  
          Returns
          -------
          Utf8 array. Contain null if original value is null or regex capture nothing.
  
          Examples
          --------
  
          >>> df = pl.DataFrame(
          ...     {
          ...         "a": [
          ...             "http://vote.com/ballon_dor?candidate=messi&ref=polars",
          ...             "http://vote.com/ballon_dor?candidat=jorginho&ref=polars",
          ...             "http://vote.com/ballon_dor?candidate=ronaldo&ref=polars",
          ...         ]
          ...     }
          ... )
          >>> df.select(
          ...     [
          ...         pl.col("a").str.extract(r"candidate=(\w+)", 1),
          ...     ]
          ... )
          shape: (3, 1)
          ┌─────────┐
          │ a       │
          │ ---     │
          │ str     │
          ╞═════════╡
          │ messi   │
          ├╌╌╌╌╌╌╌╌╌┤
          │ null    │
          ├╌╌╌╌╌╌╌╌╌┤
          │ ronaldo │
          └─────────┘
  
          """
          return wrap_expr(self._pyexpr.str_extract(pattern, group_index))
  
      def split(self, by: str, inclusive: bool = False) -> Expr:
          """
          Split the string by a substring.
          The return type will by of type List<Utf8>
  
          Parameters
          ----------
          by
              substring
          inclusive
              Include the split character/string in the results
          """
          if inclusive:
              return wrap_expr(self._pyexpr.str_split_inclusive(by))
          return wrap_expr(self._pyexpr.str_split(by))
  
      def replace(self, pattern: str, value: str) -> Expr:
          """
          Replace first regex match with a string value.
  
          Parameters
          ----------
          pattern
              Regex pattern.
          value
              Replacement string.
          """
          return wrap_expr(self._pyexpr.str_replace(pattern, value))
  
      def replace_all(self, pattern: str, value: str) -> Expr:
          """
          Replace substring on all regex pattern matches.
  
          Parameters
          ----------
          pattern
              Regex pattern.
          value
              Replacement string.
          """
          return wrap_expr(self._pyexpr.str_replace_all(pattern, value))
  
      def slice(self, start: int, length: Optional[int] = None) -> Expr:
          """
          Create subslices of the string values of a Utf8 Series.
  
          Parameters
          ----------
          start
              Start of the slice (negative indexing may be used).
          length
              Optional length of the slice.
  
          Returns
          -------
          Series of Utf8 type
          """
          return wrap_expr(self._pyexpr.str_slice(start, length))
  
  
  class ExprDateTimeNameSpace:
      """
      Namespace for datetime related expressions.
      """
  
      def __init__(self, expr: Expr):
          self._pyexpr = expr._pyexpr
  
      def truncate(
          self,
          every: Union[str, timedelta],
          offset: Optional[Union[str, timedelta]] = None,
      ) -> Expr:
          """
          .. warning::
              This API is experimental and may change without it being considered a breaking change.
  
          Divide the date/ datetime range into buckets.
          Data must be sorted, if not the output does not make sense.
  
          The `every` and `offset` arguments are created with
          the following string language:
  
          1ns # 1 nanosecond
          1us # 1 microsecond
          1ms # 1 millisecond
          1s  # 1 second
          1m  # 1 minute
          1h  # 1 hour
          1d  # 1 day
          1w  # 1 week
          1mo # 1 calendar month
          1y  # 1 calendar year
  
          3d12h4m25s # 3 days, 12 hours, 4 minutes, and 25 seconds
  
          Parameters
          ----------
          every
              Every interval start and period length
          offset
              Offset the window
  
          Returns
          -------
          Date/Datetime series
  
          Examples
          --------
  
          >>> from datetime import timedelta, datetime
          >>> start = datetime(2001, 1, 1)
          >>> stop = datetime(2001, 1, 2)
          >>> s = pl.date_range(start, stop, timedelta(minutes=30), name="dates")
          >>> s
          shape: (49,)
          Series: 'dates' [datetime[ns]]
          [
              2001-01-01 00:00:00
              2001-01-01 00:30:00
              2001-01-01 01:00:00
              2001-01-01 01:30:00
              2001-01-01 02:00:00
              2001-01-01 02:30:00
              2001-01-01 03:00:00
              2001-01-01 03:30:00
              2001-01-01 04:00:00
              2001-01-01 04:30:00
              2001-01-01 05:00:00
              2001-01-01 05:30:00
              ...
              2001-01-01 18:30:00
              2001-01-01 19:00:00
              2001-01-01 19:30:00
              2001-01-01 20:00:00
              2001-01-01 20:30:00
              2001-01-01 21:00:00
              2001-01-01 21:30:00
              2001-01-01 22:00:00
              2001-01-01 22:30:00
              2001-01-01 23:00:00
              2001-01-01 23:30:00
              2001-01-02 00:00:00
          ]
          >>> s.dt.truncate("1h")
          shape: (49,)
          Series: 'dates' [datetime[ns]]
          [
              2001-01-01 00:00:00
              2001-01-01 00:00:00
              2001-01-01 01:00:00
              2001-01-01 01:00:00
              2001-01-01 02:00:00
              2001-01-01 02:00:00
              2001-01-01 03:00:00
              2001-01-01 03:00:00
              2001-01-01 04:00:00
              2001-01-01 04:00:00
              2001-01-01 05:00:00
              2001-01-01 05:00:00
              ...
              2001-01-01 18:00:00
              2001-01-01 19:00:00
              2001-01-01 19:00:00
              2001-01-01 20:00:00
              2001-01-01 20:00:00
              2001-01-01 21:00:00
              2001-01-01 21:00:00
              2001-01-01 22:00:00
              2001-01-01 22:00:00
              2001-01-01 23:00:00
              2001-01-01 23:00:00
              2001-01-02 00:00:00
          ]
          >>> assert s.dt.truncate("1h") == s.dt.truncate(timedelta(hours=1))
  
          """
          if offset is None:
              offset = "0ns"
          if isinstance(every, timedelta):
              every = _timedelta_to_pl_duration(every)
          if isinstance(offset, timedelta):
              offset = _timedelta_to_pl_duration(offset)
          return wrap_expr(self._pyexpr.date_truncate(every, offset))
  
      def strftime(self, fmt: str) -> Expr:
          """
          Format Date/datetime with a formatting rule: See [chrono strftime/strptime](https://docs.rs/chrono/0.4.19/chrono/format/strftime/index.html).
          """
          return wrap_expr(self._pyexpr.strftime(fmt))
  
      def year(self) -> Expr:
          """
          Extract year from underlying Date representation.
          Can be performed on Date and Datetime.
  
          Returns the year number in the calendar date.
  
          Returns
          -------
          Year as Int32
          """
          return wrap_expr(self._pyexpr.year())
  
      def month(self) -> Expr:
          """
          Extract month from underlying Date representation.
          Can be performed on Date and Datetime.
  
          Returns the month number starting from 1.
          The return value ranges from 1 to 12.
  
          Returns
          -------
          Month as UInt32
          """
          return wrap_expr(self._pyexpr.month())
  
      def week(self) -> Expr:
          """
          Extract the week from the underlying Date representation.
          Can be performed on Date and Datetime
  
          Returns the ISO week number starting from 1.
          The return value ranges from 1 to 53. (The last week of year differs by years.)
  
          Returns
          -------
          Week number as UInt32
          """
          return wrap_expr(self._pyexpr.week())
  
      def weekday(self) -> Expr:
          """
          Extract the week day from the underlying Date representation.
          Can be performed on Date and Datetime.
  
          Returns the weekday number where monday = 0 and sunday = 6
  
          Returns
          -------
          Week day as UInt32
          """
          return wrap_expr(self._pyexpr.weekday())
  
      def day(self) -> Expr:
          """
          Extract day from underlying Date representation.
          Can be performed on Date and Datetime.
  
          Returns the day of month starting from 1.
          The return value ranges from 1 to 31. (The last day of month differs by months.)
  
          Returns
          -------
          Day as UInt32
          """
          return wrap_expr(self._pyexpr.day())
  
      def ordinal_day(self) -> Expr:
          """
          Extract ordinal day from underlying Date representation.
          Can be performed on Date and Datetime.
  
          Returns the day of year starting from 1.
          The return value ranges from 1 to 366. (The last day of year differs by years.)
  
          Returns
          -------
          Day as UInt32
          """
          return wrap_expr(self._pyexpr.ordinal_day())
  
      def hour(self) -> Expr:
          """
          Extract hour from underlying DateTime representation.
          Can be performed on Datetime.
  
          Returns the hour number from 0 to 23.
  
          Returns
          -------
          Hour as UInt32
          """
          return wrap_expr(self._pyexpr.hour())
  
      def minute(self) -> Expr:
          """
          Extract minutes from underlying DateTime representation.
          Can be performed on Datetime.
  
          Returns the minute number from 0 to 59.
  
          Returns
          -------
          Minute as UInt32
          """
          return wrap_expr(self._pyexpr.minute())
  
      def second(self) -> Expr:
          """
          Extract seconds from underlying DateTime representation.
          Can be performed on Datetime.
  
          Returns the second number from 0 to 59.
  
          Returns
          -------
          Second as UInt32
          """
          return wrap_expr(self._pyexpr.second())
  
      def nanosecond(self) -> Expr:
          """
          Extract seconds from underlying DateTime representation.
          Can be performed on Datetime.
  
          Returns the number of nanoseconds since the whole non-leap second.
          The range from 1,000,000,000 to 1,999,999,999 represents the leap second.
  
          Returns
          -------
          Nanosecond as UInt32
          """
          return wrap_expr(self._pyexpr.nanosecond())
  
      def to_python_datetime(self) -> Expr:
          """
          Go from Date/Datetime to python DateTime objects
          """
          return wrap_expr(self._pyexpr).map(
              lambda s: s.dt.to_python_datetime(), return_dtype=Object
          )
  
      def epoch_days(self) -> Expr:
          """
          Get the number of days since the unix EPOCH.
          If the date is before the unix EPOCH, the number of days will be negative.
  
          Returns
          -------
          Days as Int32
          """
          return wrap_expr(self._pyexpr).cast(Date).cast(Int32)
  
      def epoch_milliseconds(self) -> Expr:
          """
          Get the number of milliseconds since the unix EPOCH
          If the date is before the unix EPOCH, the number of milliseconds will be negative.
  
          Returns
          -------
          Milliseconds as Int64
          """
          return self.timestamp()
  
      def epoch_seconds(self) -> Expr:
          """
          Get the number of seconds since the unix EPOCH
          If the date is before the unix EPOCH, the number of seconds will be negative.
  
          Returns
          -------
          Milliseconds as Int64
          """
          return wrap_expr(self._pyexpr.dt_epoch_seconds())
  
      def timestamp(self) -> Expr:
          """Return timestamp in milliseconds as Int64 type."""
          return wrap_expr(self._pyexpr.timestamp())
  
      def with_time_unit(self, tu: str) -> Expr:
          """
          Set time unit a Series of dtype Datetime or Duration. This does not modify underlying data,
          and should be used to fix an incorrect time unit.
  
          Parameters
          ----------
          tu
              Time unit for the `Datetime` Series: any of {"ns", "us", "ms"}
          """
          return wrap_expr(self._pyexpr.dt_with_time_unit(tu))
  
      def cast_time_unit(self, tu: str) -> Expr:
          """
          Cast the underlying data to another time unit. This may lose precision.
  
          Parameters
          ----------
          tu
              Time unit for the `Datetime` Series: any of {"ns", "us", "ms"}
          """
          return wrap_expr(self._pyexpr.dt_cast_time_unit(tu))
  
      def and_time_unit(self, tu: str, dtype: Type[DataType] = Datetime) -> Expr:
          """
          Set time unit a Series of type Datetime. This does not modify underlying data,
          and should be used to fix an incorrect time unit.
  
          ..deprecated::
              Use `with_time_unit`
  
  
          Parameters
          ----------
          tu
              Time unit for the `Datetime` Series: any of {"ns", "us", "ms"}
          dtype
              Output data type.
          """
          return self.with_time_unit(tu)
  
      def and_time_zone(self, tz: Optional[str]) -> Expr:
          """
          Set time zone for a Series of type Datetime.
  
          ..deprecated::
              Use `with_time_zone`
  
          Parameters
          ----------
          tz
              Time zone for the `Datetime` Series
  
          """
          return wrap_expr(self._pyexpr).map(
              lambda s: s.dt.with_time_zone(tz), return_dtype=Datetime
          )
  
      def with_time_zone(self, tz: Optional[str]) -> Expr:
          """
          Set time zone for a Series of type Datetime.
  
          Parameters
          ----------
          tz
              Time zone for the `Datetime` Series
  
          """
          return wrap_expr(self._pyexpr).map(
              lambda s: s.dt.with_time_zone(tz), return_dtype=Datetime
          )
  
      def days(self) -> Expr:
          """
          Extract the days from a Duration type.
  
          Returns
          -------
          A series of dtype Int64
          """
          return wrap_expr(self._pyexpr.duration_days())
  
      def hours(self) -> Expr:
          """
          Extract the hours from a Duration type.
  
          Returns
          -------
          A series of dtype Int64
          """
          return wrap_expr(self._pyexpr.duration_hours())
  
      def seconds(self) -> Expr:
          """
          Extract the seconds from a Duration type.
  
          Returns
          -------
          A series of dtype Int64
          """
          return wrap_expr(self._pyexpr.duration_seconds())
  
      def milliseconds(self) -> Expr:
          """
          Extract the milliseconds from a Duration type.
  
          Returns
          -------
          A series of dtype Int64
          """
          return wrap_expr(self._pyexpr.duration_milliseconds())
  
      def nanoseconds(self) -> Expr:
          """
          Extract the nanoseconds from a Duration type.
  
          Returns
          -------
          A series of dtype Int64
          """
          return wrap_expr(self._pyexpr.duration_nanoseconds())
  
  
  def expr_to_lit_or_expr(
      expr: Union[Expr, bool, int, float, str, "pli.Series"],
      str_to_lit: bool = True,
  ) -> Expr:
      """
      Helper function that converts args to expressions.
  
      Parameters
      ----------
      expr
          Any argument.
      str_to_lit
          If True string argument `"foo"` will be converted to `lit("foo")`,
          If False it will be converted to `col("foo")`
  
      Returns
      -------
  
      """
      if isinstance(expr, str) and not str_to_lit:
          return pli.col(expr)
      elif (
          isinstance(expr, (int, float, str, pli.Series, datetime, date)) or expr is None
      ):
          return pli.lit(expr)
      elif isinstance(expr, Expr):
          return expr
      else:
          raise ValueError(
              f"did not expect value {expr} of type {type(expr)}, maybe disambiguate with pl.lit or pl.col"
          )
  
  
  def _prepare_alpha(
      com: Optional[float] = None,
      span: Optional[float] = None,
      half_life: Optional[float] = None,
      alpha: Optional[float] = None,
  ) -> float:
      if com is not None and alpha is None:
          assert com >= 0.0
          alpha = 1.0 / (1.0 + com)
      if span is not None and alpha is None:
          assert span >= 1.0
          alpha = 2.0 / (span + 1.0)
      if half_life is not None and alpha is None:
          assert half_life > 0.0
          alpha = 1.0 - np.exp(-np.log(2.0) / half_life)
      if alpha is None:
          raise ValueError("at least one of {com, span, half_life, alpha} should be set")
      return alpha
  
apis: numpy.arcsin numpy.arctan numpy.arccos numpy.cos numpy.exp numpy.log numpy.log10 numpy.tan numpy.array numpy.sin numpy.random.randint