from __future__ import annotations

import contextlib
import math
import operator
import sys
import warnings
from collections.abc import Collection, Mapping, Sequence
from datetime import timedelta
from functools import reduce
from io import BytesIO, StringIO
from pathlib import Path
from typing import (
    TYPE_CHECKING,
    Any,
    Callable,
    ClassVar,
    NoReturn,
    TypeVar,
)

import polars._reexport as pl
from polars import functions as F
from polars._utils.convert import negate_duration_string, parse_as_duration_string
from polars._utils.deprecation import (
    deprecate_function,
    deprecate_renamed_parameter,
    issue_deprecation_warning,
)
from polars._utils.parse import (
    parse_into_expression,
    parse_into_list_of_expressions,
    parse_predicates_constraints_into_expression,
)
from polars._utils.unstable import issue_unstable_warning, unstable
from polars._utils.various import (
    BUILDING_SPHINX_DOCS,
    extend_bool,
    find_stacklevel,
    no_default,
    normalize_filepath,
    sphinx_accessor,
    warn_null_comparison,
)
from polars.datatypes import Int64, is_polars_dtype, parse_into_dtype
from polars.dependencies import _check_for_numpy
from polars.dependencies import numpy as np
from polars.exceptions import CustomUFuncWarning, PolarsInefficientMapWarning
from polars.expr.array import ExprArrayNameSpace
from polars.expr.binary import ExprBinaryNameSpace
from polars.expr.categorical import ExprCatNameSpace
from polars.expr.datetime import ExprDateTimeNameSpace
from polars.expr.list import ExprListNameSpace
from polars.expr.meta import ExprMetaNameSpace
from polars.expr.name import ExprNameNameSpace
from polars.expr.string import ExprStringNameSpace
from polars.expr.struct import ExprStructNameSpace
from polars.meta import thread_pool_size

with contextlib.suppress(ImportError):  # Module not available when building docs
    from polars.polars import arg_where as py_arg_where

with contextlib.suppress(ImportError):  # Module not available when building docs
    from polars.polars import PyExpr

if TYPE_CHECKING:
    from collections.abc import Iterable
    from io import IOBase

    from polars import DataFrame, LazyFrame, Series
    from polars._typing import (
        ClosedInterval,
        FillNullStrategy,
        InterpolationMethod,
        IntoExpr,
        IntoExprColumn,
        MapElementsStrategy,
        NullBehavior,
        NumericLiteral,
        PolarsDataType,
        RankMethod,
        RollingInterpolationMethod,
        SchemaDict,
        SearchSortedSide,
        SerializationFormat,
        TemporalLiteral,
        WindowMappingStrategy,
    )
    from polars._utils.various import (
        NoDefault,
    )

    if sys.version_info >= (3, 11):
        from typing import Concatenate, ParamSpec
    else:
        from typing_extensions import Concatenate, ParamSpec

    T = TypeVar("T")
    P = ParamSpec("P")

elif BUILDING_SPHINX_DOCS:
    # note: we assign this way to work around an autocomplete issue in ipython/jedi
    # (ref: https://github.com/davidhalter/jedi/issues/2057)
    current_module = sys.modules[__name__]
    current_module.property = sphinx_accessor


class Expr:
    """Expressions that can be used in various contexts."""

    _pyexpr: PyExpr = None
    _accessors: ClassVar[set[str]] = {
        "arr",
        "cat",
        "dt",
        "list",
        "meta",
        "name",
        "str",
        "bin",
        "struct",
    }

    @classmethod
    def _from_pyexpr(cls, pyexpr: PyExpr) -> Expr:
        expr = cls.__new__(cls)
        expr._pyexpr = pyexpr
        return expr

    def _repr_html_(self) -> str:
        return self._pyexpr.to_str()

    def __repr__(self) -> str:
        if len(expr_str := self._pyexpr.to_str()) > 30:
            expr_str = f"{expr_str[:30]}…"
        return f"<{self.__class__.__name__} [{expr_str!r}] at 0x{id(self):X}>"

    def __str__(self) -> str:
        return self._pyexpr.to_str()

    def __bool__(self) -> NoReturn:
        msg = (
            "the truth value of an Expr is ambiguous"
            "\n\n"
            "You probably got here by using a Python standard library function instead "
            "of the native expressions API.\n"
            "Here are some things you might want to try:\n"
            "- instead of `pl.col('a') and pl.col('b')`, use `pl.col('a') & pl.col('b')`\n"
            "- instead of `pl.col('a') in [y, z]`, use `pl.col('a').is_in([y, z])`\n"
            "- instead of `max(pl.col('a'), pl.col('b'))`, use `pl.max_horizontal(pl.col('a'), pl.col('b'))`\n"
        )
        raise TypeError(msg)

    def __abs__(self) -> Expr:
        return self.abs()

    # operators
    def __add__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr + other)

    def __radd__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(other + self._pyexpr)

    def __and__(self, other: IntoExprColumn | int | bool) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr.and_(other))

    def __rand__(self, other: IntoExprColumn | int | bool) -> Expr:
        other_expr = parse_into_expression(other)
        return self._from_pyexpr(other_expr.and_(self._pyexpr))

    def __eq__(self, other: IntoExpr) -> Expr:  # type: ignore[override]
        warn_null_comparison(other)
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.eq(other))

    def __floordiv__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr // other)

    def __rfloordiv__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(other // self._pyexpr)

    def __ge__(self, other: IntoExpr) -> Expr:
        warn_null_comparison(other)
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.gt_eq(other))

    def __gt__(self, other: IntoExpr) -> Expr:
        warn_null_comparison(other)
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.gt(other))

    def __invert__(self) -> Expr:
        return self.not_()

    def __le__(self, other: IntoExpr) -> Expr:
        warn_null_comparison(other)
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.lt_eq(other))

    def __lt__(self, other: IntoExpr) -> Expr:
        warn_null_comparison(other)
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.lt(other))

    def __mod__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr % other)

    def __rmod__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(other % self._pyexpr)

    def __mul__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr * other)

    def __rmul__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(other * self._pyexpr)

    def __ne__(self, other: IntoExpr) -> Expr:  # type: ignore[override]
        warn_null_comparison(other)
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.neq(other))

    def __neg__(self) -> Expr:
        return self._from_pyexpr(-self._pyexpr)

    def __or__(self, other: IntoExprColumn | int | bool) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr.or_(other))

    def __ror__(self, other: IntoExprColumn | int | bool) -> Expr:
        other_expr = parse_into_expression(other)
        return self._from_pyexpr(other_expr.or_(self._pyexpr))

    def __pos__(self) -> Expr:
        return self

    def __pow__(self, exponent: IntoExprColumn | int | float) -> Expr:
        exponent = parse_into_expression(exponent)
        return self._from_pyexpr(self._pyexpr.pow(exponent))

    def __rpow__(self, base: IntoExprColumn | int | float) -> Expr:
        base = parse_into_expression(base)
        return self._from_pyexpr(base) ** self

    def __sub__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr - other)

    def __rsub__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(other - self._pyexpr)

    def __truediv__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr / other)

    def __rtruediv__(self, other: IntoExpr) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(other / self._pyexpr)

    def __xor__(self, other: IntoExprColumn | int | bool) -> Expr:
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr.xor_(other))

    def __rxor__(self, other: IntoExprColumn | int | bool) -> Expr:
        other_expr = parse_into_expression(other)
        return self._from_pyexpr(other_expr.xor_(self._pyexpr))

    def __getstate__(self) -> bytes:
        return self._pyexpr.__getstate__()

    def __setstate__(self, state: bytes) -> None:
        self._pyexpr = F.lit(0)._pyexpr  # Initialize with a dummy
        self._pyexpr.__setstate__(state)

    def __array_ufunc__(
        self, ufunc: Callable[..., Any], method: str, *inputs: Any, **kwargs: Any
    ) -> Expr:
        """Numpy universal functions."""
        if method != "__call__":
            msg = f"Only call is implemented not {method}"
            raise NotImplementedError(msg)
        # Numpy/Scipy ufuncs have signature None but numba signatures always exists.
        is_custom_ufunc = getattr(ufunc, "signature") is not None  # noqa: B009
        num_expr = sum(isinstance(inp, Expr) for inp in inputs)
        exprs = [
            (inp, True, i) if isinstance(inp, Expr) else (inp, False, i)
            for i, inp in enumerate(inputs)
        ]

        if num_expr == 1:
            root_expr = next(expr[0] for expr in exprs if expr[1])
        else:
            # We rename all but the first expression in case someone did e.g.
            # np.divide(pl.col("a"), pl.col("a")); we'll be creating a struct
            # below, and structs can't have duplicate names.
            first_renameable_expr = True
            actual_exprs = []
            for inp, is_actual_expr, index in exprs:
                if is_actual_expr:
                    if first_renameable_expr:
                        first_renameable_expr = False
                    else:
                        inp = inp.alias(f"argument_{index}")
                    actual_exprs.append(inp)
            root_expr = F.struct(actual_exprs)

        def function(s: Series) -> Series:  # pragma: no cover
            args: list[Any] = []
            for i, expr in enumerate(exprs):
                if expr[1] and num_expr > 1:
                    args.append(s.struct[i])
                elif expr[1]:
                    args.append(s)
                else:
                    args.append(expr[0])
            return ufunc(*args, **kwargs)

        if is_custom_ufunc is True:
            msg = (
                "Native numpy ufuncs are dispatched using `map_batches(ufunc, is_elementwise=True)` which "
                "is safe for native Numpy and Scipy ufuncs but custom ufuncs in a group_by "
                "context won't be properly grouped. Custom ufuncs are dispatched with is_elementwise=False. "
                f"If {ufunc.__name__} needs elementwise then please use map_batches directly."
            )
            warnings.warn(
                msg,
                CustomUFuncWarning,
                stacklevel=find_stacklevel(),
            )
            return root_expr.map_batches(function, is_elementwise=False)
        return root_expr.map_batches(function, is_elementwise=True)

    @classmethod
    def deserialize(
        cls,
        source: str | Path | IOBase | bytes,
        *,
        format: SerializationFormat = "binary",
    ) -> Expr:
        """
        Read a serialized expression from a file.

        Parameters
        ----------
        source
            Path to a file or a file-like object (by file-like object, we refer to
            objects that have a `read()` method, such as a file handler (e.g.
            via builtin `open` function) or `BytesIO`).
        format
            The format with which the Expr was serialized. Options:

            - `"binary"`: Deserialize from binary format (bytes). This is the default.
            - `"json"`: Deserialize from JSON format (string).

        Warnings
        --------
        This function uses :mod:`pickle` if the logical plan contains Python UDFs,
        and as such inherits the security implications. Deserializing can execute
        arbitrary code, so it should only be attempted on trusted data.

        See Also
        --------
        Expr.meta.serialize

        Notes
        -----
        Serialization is not stable across Polars versions: a LazyFrame serialized
        in one Polars version may not be deserializable in another Polars version.

        Examples
        --------
        >>> import io
        >>> expr = pl.col("foo").sum().over("bar")
        >>> bytes = expr.meta.serialize()
        >>> pl.Expr.deserialize(io.BytesIO(bytes))  # doctest: +ELLIPSIS
        <Expr ['col("foo").sum().over([col("ba…'] at ...>
        """
        if isinstance(source, StringIO):
            source = BytesIO(source.getvalue().encode())
        elif isinstance(source, (str, Path)):
            source = normalize_filepath(source)
        elif isinstance(source, bytes):
            source = BytesIO(source)

        if format == "binary":
            deserializer = PyExpr.deserialize_binary
        elif format == "json":
            deserializer = PyExpr.deserialize_json
        else:
            msg = f"`format` must be one of {{'binary', 'json'}}, got {format!r}"
            raise ValueError(msg)

        return cls._from_pyexpr(deserializer(source))

    def to_physical(self) -> Expr:
        """
        Cast to physical representation of the logical dtype.

        - :func:`polars.datatypes.Date` -> :func:`polars.datatypes.Int32`
        - :func:`polars.datatypes.Datetime` -> :func:`polars.datatypes.Int64`
        - :func:`polars.datatypes.Time` -> :func:`polars.datatypes.Int64`
        - :func:`polars.datatypes.Duration` -> :func:`polars.datatypes.Int64`
        - :func:`polars.datatypes.Categorical` -> :func:`polars.datatypes.UInt32`
        - `List(inner)` -> `List(physical of inner)`
        - `Array(inner)` -> `Struct(physical of inner)`
        - `Struct(fields)` -> `Array(physical of fields)`

        Other data types will be left unchanged.

        Warnings
        --------
        The physical representations are an implementation detail
        and not guaranteed to be stable.

        Examples
        --------
        Replicating the pandas
        `pd.factorize
        <https://pandas.pydata.org/docs/reference/api/pandas.factorize.html>`_
        function.

        >>> pl.DataFrame({"vals": ["a", "x", None, "a"]}).with_columns(
        ...     pl.col("vals").cast(pl.Categorical),
        ...     pl.col("vals")
        ...     .cast(pl.Categorical)
        ...     .to_physical()
        ...     .alias("vals_physical"),
        ... )
        shape: (4, 2)
        ┌──────┬───────────────┐
        │ vals ┆ vals_physical │
        │ ---  ┆ ---           │
        │ cat  ┆ u32           │
        ╞══════╪═══════════════╡
        │ a    ┆ 0             │
        │ x    ┆ 1             │
        │ null ┆ null          │
        │ a    ┆ 0             │
        └──────┴───────────────┘
        """
        return self._from_pyexpr(self._pyexpr.to_physical())

    def any(self, *, ignore_nulls: bool = True) -> Expr:
        """
        Return whether any of the values in the column are `True`.

        Only works on columns of data type :class:`Boolean`.

        Parameters
        ----------
        ignore_nulls
            Ignore null values (default).

            If set to `False`, `Kleene logic`_ is used to deal with nulls:
            if the column contains any null values and no `True` values,
            the output is null.

            .. _Kleene logic: https://en.wikipedia.org/wiki/Three-valued_logic

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [True, False],
        ...         "b": [False, False],
        ...         "c": [None, False],
        ...     }
        ... )
        >>> df.select(pl.col("*").any())
        shape: (1, 3)
        ┌──────┬───────┬───────┐
        │ a    ┆ b     ┆ c     │
        │ ---  ┆ ---   ┆ ---   │
        │ bool ┆ bool  ┆ bool  │
        ╞══════╪═══════╪═══════╡
        │ true ┆ false ┆ false │
        └──────┴───────┴───────┘

        Enable Kleene logic by setting `ignore_nulls=False`.

        >>> df.select(pl.col("*").any(ignore_nulls=False))
        shape: (1, 3)
        ┌──────┬───────┬──────┐
        │ a    ┆ b     ┆ c    │
        │ ---  ┆ ---   ┆ ---  │
        │ bool ┆ bool  ┆ bool │
        ╞══════╪═══════╪══════╡
        │ true ┆ false ┆ null │
        └──────┴───────┴──────┘
        """
        return self._from_pyexpr(self._pyexpr.any(ignore_nulls))

    def all(self, *, ignore_nulls: bool = True) -> Expr:
        """
        Return whether all values in the column are `True`.

        Only works on columns of data type :class:`Boolean`.

        .. note::
            This method is not to be confused with the function :func:`polars.all`,
            which can be used to select all columns.

        Parameters
        ----------
        ignore_nulls
            Ignore null values (default).

            If set to `False`, `Kleene logic`_ is used to deal with nulls:
            if the column contains any null values and no `False` values,
            the output is null.

            .. _Kleene logic: https://en.wikipedia.org/wiki/Three-valued_logic

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [True, True],
        ...         "b": [False, True],
        ...         "c": [None, True],
        ...     }
        ... )
        >>> df.select(pl.col("*").all())
        shape: (1, 3)
        ┌──────┬───────┬──────┐
        │ a    ┆ b     ┆ c    │
        │ ---  ┆ ---   ┆ ---  │
        │ bool ┆ bool  ┆ bool │
        ╞══════╪═══════╪══════╡
        │ true ┆ false ┆ true │
        └──────┴───────┴──────┘

        Enable Kleene logic by setting `ignore_nulls=False`.

        >>> df.select(pl.col("*").all(ignore_nulls=False))
        shape: (1, 3)
        ┌──────┬───────┬──────┐
        │ a    ┆ b     ┆ c    │
        │ ---  ┆ ---   ┆ ---  │
        │ bool ┆ bool  ┆ bool │
        ╞══════╪═══════╪══════╡
        │ true ┆ false ┆ null │
        └──────┴───────┴──────┘
        """
        return self._from_pyexpr(self._pyexpr.all(ignore_nulls))

    def arg_true(self) -> Expr:
        """
        Return indices where expression evaluates `True`.

        .. warning::
            Modifies number of rows returned, so will fail in combination with other
            expressions. Use as only expression in `select` / `with_columns`.

        See Also
        --------
        Series.arg_true : Return indices where Series is True
        polars.arg_where

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2, 1]})
        >>> df.select((pl.col("a") == 1).arg_true())
        shape: (3, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 0   │
        │ 1   │
        │ 3   │
        └─────┘
        """
        return self._from_pyexpr(py_arg_where(self._pyexpr))

    def sqrt(self) -> Expr:
        """
        Compute the square root of the elements.

        Examples
        --------
        >>> df = pl.DataFrame({"values": [1.0, 2.0, 4.0]})
        >>> df.select(pl.col("values").sqrt())
        shape: (3, 1)
        ┌──────────┐
        │ values   │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.0      │
        │ 1.414214 │
        │ 2.0      │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.sqrt())

    def cbrt(self) -> Expr:
        """
        Compute the cube root of the elements.

        Examples
        --------
        >>> df = pl.DataFrame({"values": [1.0, 2.0, 4.0]})
        >>> df.select(pl.col("values").cbrt())
        shape: (3, 1)
        ┌──────────┐
        │ values   │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.0      │
        │ 1.259921 │
        │ 1.587401 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.cbrt())

    def log10(self) -> Expr:
        """
        Compute the base 10 logarithm of the input array, element-wise.

        Examples
        --------
        >>> df = pl.DataFrame({"values": [1.0, 2.0, 4.0]})
        >>> df.select(pl.col("values").log10())
        shape: (3, 1)
        ┌─────────┐
        │ values  │
        │ ---     │
        │ f64     │
        ╞═════════╡
        │ 0.0     │
        │ 0.30103 │
        │ 0.60206 │
        └─────────┘
        """
        return self.log(10.0)

    def exp(self) -> Expr:
        """
        Compute the exponential, element-wise.

        Examples
        --------
        >>> df = pl.DataFrame({"values": [1.0, 2.0, 4.0]})
        >>> df.select(pl.col("values").exp())
        shape: (3, 1)
        ┌──────────┐
        │ values   │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 2.718282 │
        │ 7.389056 │
        │ 54.59815 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.exp())

    def alias(self, name: str) -> Expr:
        """
        Rename the expression.

        Parameters
        ----------
        name
            The new name.

        See Also
        --------
        name.map
        name.prefix
        name.suffix

        Examples
        --------
        Rename an expression to avoid overwriting an existing column.

        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 3],
        ...         "b": ["x", "y", "z"],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("a") + 10,
        ...     pl.col("b").str.to_uppercase().alias("c"),
        ... )
        shape: (3, 3)
        ┌─────┬─────┬─────┐
        │ a   ┆ b   ┆ c   │
        │ --- ┆ --- ┆ --- │
        │ i64 ┆ str ┆ str │
        ╞═════╪═════╪═════╡
        │ 11  ┆ x   ┆ X   │
        │ 12  ┆ y   ┆ Y   │
        │ 13  ┆ z   ┆ Z   │
        └─────┴─────┴─────┘

        Overwrite the default name of literal columns to prevent errors due to duplicate
        column names.

        >>> df.with_columns(
        ...     pl.lit(True).alias("c"),
        ...     pl.lit(4.0).alias("d"),
        ... )
        shape: (3, 4)
        ┌─────┬─────┬──────┬─────┐
        │ a   ┆ b   ┆ c    ┆ d   │
        │ --- ┆ --- ┆ ---  ┆ --- │
        │ i64 ┆ str ┆ bool ┆ f64 │
        ╞═════╪═════╪══════╪═════╡
        │ 1   ┆ x   ┆ true ┆ 4.0 │
        │ 2   ┆ y   ┆ true ┆ 4.0 │
        │ 3   ┆ z   ┆ true ┆ 4.0 │
        └─────┴─────┴──────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.alias(name))

    def exclude(
        self,
        columns: str | PolarsDataType | Collection[str] | Collection[PolarsDataType],
        *more_columns: str | PolarsDataType,
    ) -> Expr:
        """
        Exclude columns from a multi-column expression.

        Only works after a wildcard or regex column selection, and you cannot provide
        both string column names *and* dtypes (you may prefer to use selectors instead).

        Parameters
        ----------
        columns
            The name or datatype of the column(s) to exclude. Accepts regular expression
            input. Regular expressions should start with `^` and end with `$`.
        *more_columns
            Additional names or datatypes of columns to exclude, specified as positional
            arguments.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "aa": [1, 2, 3],
        ...         "ba": ["a", "b", None],
        ...         "cc": [None, 2.5, 1.5],
        ...     }
        ... )
        >>> df
        shape: (3, 3)
        ┌─────┬──────┬──────┐
        │ aa  ┆ ba   ┆ cc   │
        │ --- ┆ ---  ┆ ---  │
        │ i64 ┆ str  ┆ f64  │
        ╞═════╪══════╪══════╡
        │ 1   ┆ a    ┆ null │
        │ 2   ┆ b    ┆ 2.5  │
        │ 3   ┆ null ┆ 1.5  │
        └─────┴──────┴──────┘

        Exclude by column name(s):

        >>> df.select(pl.all().exclude("ba"))
        shape: (3, 2)
        ┌─────┬──────┐
        │ aa  ┆ cc   │
        │ --- ┆ ---  │
        │ i64 ┆ f64  │
        ╞═════╪══════╡
        │ 1   ┆ null │
        │ 2   ┆ 2.5  │
        │ 3   ┆ 1.5  │
        └─────┴──────┘

        Exclude by regex, e.g. removing all columns whose names end with the letter "a":

        >>> df.select(pl.all().exclude("^.*a$"))
        shape: (3, 1)
        ┌──────┐
        │ cc   │
        │ ---  │
        │ f64  │
        ╞══════╡
        │ null │
        │ 2.5  │
        │ 1.5  │
        └──────┘

        Exclude by dtype(s), e.g. removing all columns of type Int64 or Float64:

        >>> df.select(pl.all().exclude([pl.Int64, pl.Float64]))
        shape: (3, 1)
        ┌──────┐
        │ ba   │
        │ ---  │
        │ str  │
        ╞══════╡
        │ a    │
        │ b    │
        │ null │
        └──────┘
        """
        exclude_cols: list[str] = []
        exclude_dtypes: list[PolarsDataType] = []
        for item in (
            *(
                columns
                if isinstance(columns, Collection) and not isinstance(columns, str)
                else [columns]
            ),
            *more_columns,
        ):
            if isinstance(item, str):
                exclude_cols.append(item)
            elif is_polars_dtype(item):
                exclude_dtypes.append(item)
            else:
                msg = (
                    "invalid input for `exclude`"
                    f"\n\nExpected one or more `str` or `DataType`; found {item!r} instead."
                )
                raise TypeError(msg)

        if exclude_cols and exclude_dtypes:
            msg = "cannot exclude by both column name and dtype; use a selector instead"
            raise TypeError(msg)
        elif exclude_dtypes:
            return self._from_pyexpr(self._pyexpr.exclude_dtype(exclude_dtypes))
        else:
            return self._from_pyexpr(self._pyexpr.exclude(exclude_cols))

    def pipe(
        self,
        function: Callable[Concatenate[Expr, P], T],
        *args: P.args,
        **kwargs: P.kwargs,
    ) -> T:
        r'''
        Offers a structured way to apply a sequence of user-defined functions (UDFs).

        Parameters
        ----------
        function
            Callable; will receive the expression as the first parameter,
            followed by any given args/kwargs.
        *args
            Arguments to pass to the UDF.
        **kwargs
            Keyword arguments to pass to the UDF.

        Examples
        --------
        >>> def extract_number(expr: pl.Expr) -> pl.Expr:
        ...     """Extract the digits from a string."""
        ...     return expr.str.extract(r"\d+", 0).cast(pl.Int64)
        >>>
        >>> def scale_negative_even(expr: pl.Expr, *, n: int = 1) -> pl.Expr:
        ...     """Set even numbers negative, and scale by a user-supplied value."""
        ...     expr = pl.when(expr % 2 == 0).then(-expr).otherwise(expr)
        ...     return expr * n
        >>>
        >>> df = pl.DataFrame({"val": ["a: 1", "b: 2", "c: 3", "d: 4"]})
        >>> df.with_columns(
        ...     udfs=(
        ...         pl.col("val").pipe(extract_number).pipe(scale_negative_even, n=5)
        ...     ),
        ... )
        shape: (4, 2)
        ┌──────┬──────┐
        │ val  ┆ udfs │
        │ ---  ┆ ---  │
        │ str  ┆ i64  │
        ╞══════╪══════╡
        │ a: 1 ┆ 5    │
        │ b: 2 ┆ -10  │
        │ c: 3 ┆ 15   │
        │ d: 4 ┆ -20  │
        └──────┴──────┘

        '''
        return function(self, *args, **kwargs)

    def 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").not_())
        shape: (3, 1)
        ┌───────┐
        │ a     │
        │ ---   │
        │ bool  │
        ╞═══════╡
        │ false │
        │ true  │
        │ true  │
        └───────┘
        """
        return self._from_pyexpr(self._pyexpr.not_())

    def is_null(self) -> Expr:
        """
        Returns a boolean Series indicating which values are null.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, None, 1, 5],
        ...         "b": [1.0, 2.0, float("nan"), 1.0, 5.0],
        ...     }
        ... )
        >>> df.with_columns(pl.all().is_null().name.suffix("_isnull"))  # nan != null
        shape: (5, 4)
        ┌──────┬─────┬──────────┬──────────┐
        │ a    ┆ b   ┆ a_isnull ┆ b_isnull │
        │ ---  ┆ --- ┆ ---      ┆ ---      │
        │ i64  ┆ f64 ┆ bool     ┆ bool     │
        ╞══════╪═════╪══════════╪══════════╡
        │ 1    ┆ 1.0 ┆ false    ┆ false    │
        │ 2    ┆ 2.0 ┆ false    ┆ false    │
        │ null ┆ NaN ┆ true     ┆ false    │
        │ 1    ┆ 1.0 ┆ false    ┆ false    │
        │ 5    ┆ 5.0 ┆ false    ┆ false    │
        └──────┴─────┴──────────┴──────────┘
        """
        return self._from_pyexpr(self._pyexpr.is_null())

    def is_not_null(self) -> Expr:
        """
        Returns a boolean Series indicating which values are not null.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, None, 1, 5],
        ...         "b": [1.0, 2.0, float("nan"), 1.0, 5.0],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.all().is_not_null().name.suffix("_not_null")  # nan != null
        ... )
        shape: (5, 4)
        ┌──────┬─────┬────────────┬────────────┐
        │ a    ┆ b   ┆ a_not_null ┆ b_not_null │
        │ ---  ┆ --- ┆ ---        ┆ ---        │
        │ i64  ┆ f64 ┆ bool       ┆ bool       │
        ╞══════╪═════╪════════════╪════════════╡
        │ 1    ┆ 1.0 ┆ true       ┆ true       │
        │ 2    ┆ 2.0 ┆ true       ┆ true       │
        │ null ┆ NaN ┆ false      ┆ true       │
        │ 1    ┆ 1.0 ┆ true       ┆ true       │
        │ 5    ┆ 5.0 ┆ true       ┆ true       │
        └──────┴─────┴────────────┴────────────┘
        """
        return self._from_pyexpr(self._pyexpr.is_not_null())

    def is_finite(self) -> Expr:
        """
        Returns a boolean Series indicating which values are finite.

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "A": [1.0, 2],
        ...         "B": [3.0, float("inf")],
        ...     }
        ... )
        >>> df.select(pl.all().is_finite())
        shape: (2, 2)
        ┌──────┬───────┐
        │ A    ┆ B     │
        │ ---  ┆ ---   │
        │ bool ┆ bool  │
        ╞══════╪═══════╡
        │ true ┆ true  │
        │ true ┆ false │
        └──────┴───────┘
        """
        return self._from_pyexpr(self._pyexpr.is_finite())

    def is_infinite(self) -> Expr:
        """
        Returns a boolean Series indicating which values are infinite.

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "A": [1.0, 2],
        ...         "B": [3.0, float("inf")],
        ...     }
        ... )
        >>> df.select(pl.all().is_infinite())
        shape: (2, 2)
        ┌───────┬───────┐
        │ A     ┆ B     │
        │ ---   ┆ ---   │
        │ bool  ┆ bool  │
        ╞═══════╪═══════╡
        │ false ┆ false │
        │ false ┆ true  │
        └───────┴───────┘
        """
        return self._from_pyexpr(self._pyexpr.is_infinite())

    def is_nan(self) -> Expr:
        """
        Returns a boolean Series indicating which values are NaN.

        Notes
        -----
        Floating point `NaN` (Not A Number) should not be confused
        with missing data represented as `Null/None`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, None, 1, 5],
        ...         "b": [1.0, 2.0, float("nan"), 1.0, 5.0],
        ...     }
        ... )
        >>> df.with_columns(pl.col(pl.Float64).is_nan().name.suffix("_isnan"))
        shape: (5, 3)
        ┌──────┬─────┬─────────┐
        │ a    ┆ b   ┆ b_isnan │
        │ ---  ┆ --- ┆ ---     │
        │ i64  ┆ f64 ┆ bool    │
        ╞══════╪═════╪═════════╡
        │ 1    ┆ 1.0 ┆ false   │
        │ 2    ┆ 2.0 ┆ false   │
        │ null ┆ NaN ┆ true    │
        │ 1    ┆ 1.0 ┆ false   │
        │ 5    ┆ 5.0 ┆ false   │
        └──────┴─────┴─────────┘
        """
        return self._from_pyexpr(self._pyexpr.is_nan())

    def is_not_nan(self) -> Expr:
        """
        Returns a boolean Series indicating which values are not NaN.

        Notes
        -----
        Floating point `NaN` (Not A Number) should not be confused
        with missing data represented as `Null/None`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, None, 1, 5],
        ...         "b": [1.0, 2.0, float("nan"), 1.0, 5.0],
        ...     }
        ... )
        >>> df.with_columns(pl.col(pl.Float64).is_not_nan().name.suffix("_is_not_nan"))
        shape: (5, 3)
        ┌──────┬─────┬──────────────┐
        │ a    ┆ b   ┆ b_is_not_nan │
        │ ---  ┆ --- ┆ ---          │
        │ i64  ┆ f64 ┆ bool         │
        ╞══════╪═════╪══════════════╡
        │ 1    ┆ 1.0 ┆ true         │
        │ 2    ┆ 2.0 ┆ true         │
        │ null ┆ NaN ┆ false        │
        │ 1    ┆ 1.0 ┆ true         │
        │ 5    ┆ 5.0 ┆ true         │
        └──────┴─────┴──────────────┘
        """
        return self._from_pyexpr(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.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "group": [
        ...             "one",
        ...             "one",
        ...             "one",
        ...             "two",
        ...             "two",
        ...             "two",
        ...         ],
        ...         "value": [94, 95, 96, 97, 97, 99],
        ...     }
        ... )
        >>> df.group_by("group", maintain_order=True).agg(pl.col("value").agg_groups())
        shape: (2, 2)
        ┌───────┬───────────┐
        │ group ┆ value     │
        │ ---   ┆ ---       │
        │ str   ┆ list[u32] │
        ╞═══════╪═══════════╡
        │ one   ┆ [0, 1, 2] │
        │ two   ┆ [3, 4, 5] │
        └───────┴───────────┘
        """
        return self._from_pyexpr(self._pyexpr.agg_groups())

    def count(self) -> Expr:
        """
        Return the number of non-null elements in the column.

        Returns
        -------
        Expr
            Expression of data type :class:`UInt32`.

        See Also
        --------
        len

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3], "b": [None, 4, 4]})
        >>> df.select(pl.all().count())
        shape: (1, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ u32 ┆ u32 │
        ╞═════╪═════╡
        │ 3   ┆ 2   │
        └─────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.count())

    def len(self) -> Expr:
        """
        Return the number of elements in the column.

        Null values count towards the total.

        Returns
        -------
        Expr
            Expression of data type :class:`UInt32`.

        See Also
        --------
        count

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3], "b": [None, 4, 4]})
        >>> df.select(pl.all().len())
        shape: (1, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ u32 ┆ u32 │
        ╞═════╪═════╡
        │ 3   ┆ 3   │
        └─────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.len())

    def slice(self, offset: int | Expr, length: int | Expr | None = None) -> Expr:
        """
        Get a slice of this expression.

        Parameters
        ----------
        offset
            Start index. Negative indexing is supported.
        length
            Length of the slice. If set to `None`, all rows starting at the offset
            will be selected.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [8, 9, 10, 11],
        ...         "b": [None, 4, 4, 4],
        ...     }
        ... )
        >>> df.select(pl.all().slice(1, 2))
        shape: (2, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ i64 ┆ i64 │
        ╞═════╪═════╡
        │ 9   ┆ 4   │
        │ 10  ┆ 4   │
        └─────┴─────┘
        """
        if not isinstance(offset, Expr):
            offset = F.lit(offset)
        if not isinstance(length, Expr):
            length = F.lit(length)
        return self._from_pyexpr(self._pyexpr.slice(offset._pyexpr, length._pyexpr))

    def append(self, other: IntoExpr, *, upcast: bool = True) -> Expr:
        """
        Append expressions.

        This is done by adding the chunks of `other` to this `Series`.

        Parameters
        ----------
        other
            Expression to append.
        upcast
            Cast both `Series` to the same supertype.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [8, 9, 10],
        ...         "b": [None, 4, 4],
        ...     }
        ... )
        >>> df.select(pl.all().head(1).append(pl.all().tail(1)))
        shape: (2, 2)
        ┌─────┬──────┐
        │ a   ┆ b    │
        │ --- ┆ ---  │
        │ i64 ┆ i64  │
        ╞═════╪══════╡
        │ 8   ┆ null │
        │ 10  ┆ 4    │
        └─────┴──────┘
        """
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr.append(other, upcast))

    def rechunk(self) -> Expr:
        """
        Create a single chunk of memory for this Series.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2]})

        Create a Series with 3 nulls, append column `a`, then rechunk.

        >>> df.select(pl.repeat(None, 3).append(pl.col("a")).rechunk())
        shape: (6, 1)
        ┌────────┐
        │ repeat │
        │ ---    │
        │ i64    │
        ╞════════╡
        │ null   │
        │ null   │
        │ null   │
        │ 1      │
        │ 1      │
        │ 2      │
        └────────┘
        """
        return self._from_pyexpr(self._pyexpr.rechunk())

    def drop_nulls(self) -> Expr:
        """
        Drop all null values.

        The original order of the remaining elements is preserved.

        See Also
        --------
        drop_nans

        Notes
        -----
        A null value is not the same as a NaN value.
        To drop NaN values, use :func:`drop_nans`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0, None, 3.0, float("nan")]})
        >>> df.select(pl.col("a").drop_nulls())
        shape: (3, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        │ 3.0 │
        │ NaN │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.drop_nulls())

    def drop_nans(self) -> Expr:
        """
        Drop all floating point NaN values.

        The original order of the remaining elements is preserved.

        See Also
        --------
        drop_nulls

        Notes
        -----
        A NaN value is not the same as a null value.
        To drop null values, use :func:`drop_nulls`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0, None, 3.0, float("nan")]})
        >>> df.select(pl.col("a").drop_nans())
        shape: (3, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ f64  │
        ╞══════╡
        │ 1.0  │
        │ null │
        │ 3.0  │
        └──────┘
        """
        return self._from_pyexpr(self._pyexpr.drop_nans())

    def cum_sum(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.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3, 4]})
        >>> df.with_columns(
        ...     pl.col("a").cum_sum().alias("cum_sum"),
        ...     pl.col("a").cum_sum(reverse=True).alias("cum_sum_reverse"),
        ... )
        shape: (4, 3)
        ┌─────┬─────────┬─────────────────┐
        │ a   ┆ cum_sum ┆ cum_sum_reverse │
        │ --- ┆ ---     ┆ ---             │
        │ i64 ┆ i64     ┆ i64             │
        ╞═════╪═════════╪═════════════════╡
        │ 1   ┆ 1       ┆ 10              │
        │ 2   ┆ 3       ┆ 9               │
        │ 3   ┆ 6       ┆ 7               │
        │ 4   ┆ 10      ┆ 4               │
        └─────┴─────────┴─────────────────┘

        Null values are excluded, but can also be filled by calling
        `fill_null(strategy="forward")`.

        >>> df = pl.DataFrame({"values": [None, 10, None, 8, 9, None, 16, None]})
        >>> df.with_columns(
        ...     pl.col("values").cum_sum().alias("value_cum_sum"),
        ...     pl.col("values")
        ...     .cum_sum()
        ...     .fill_null(strategy="forward")
        ...     .alias("value_cum_sum_all_filled"),
        ... )
        shape: (8, 3)
        ┌────────┬───────────────┬──────────────────────────┐
        │ values ┆ value_cum_sum ┆ value_cum_sum_all_filled │
        │ ---    ┆ ---           ┆ ---                      │
        │ i64    ┆ i64           ┆ i64                      │
        ╞════════╪═══════════════╪══════════════════════════╡
        │ null   ┆ null          ┆ null                     │
        │ 10     ┆ 10            ┆ 10                       │
        │ null   ┆ null          ┆ 10                       │
        │ 8      ┆ 18            ┆ 18                       │
        │ 9      ┆ 27            ┆ 27                       │
        │ null   ┆ null          ┆ 27                       │
        │ 16     ┆ 43            ┆ 43                       │
        │ null   ┆ null          ┆ 43                       │
        └────────┴───────────────┴──────────────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.cum_sum(reverse))

    def cum_prod(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.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3, 4]})
        >>> df.with_columns(
        ...     pl.col("a").cum_prod().alias("cum_prod"),
        ...     pl.col("a").cum_prod(reverse=True).alias("cum_prod_reverse"),
        ... )
        shape: (4, 3)
        ┌─────┬──────────┬──────────────────┐
        │ a   ┆ cum_prod ┆ cum_prod_reverse │
        │ --- ┆ ---      ┆ ---              │
        │ i64 ┆ i64      ┆ i64              │
        ╞═════╪══════════╪══════════════════╡
        │ 1   ┆ 1        ┆ 24               │
        │ 2   ┆ 2        ┆ 24               │
        │ 3   ┆ 6        ┆ 12               │
        │ 4   ┆ 24       ┆ 4                │
        └─────┴──────────┴──────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.cum_prod(reverse))

    def cum_min(self, *, reverse: bool = False) -> Expr:
        """
        Get an array with the cumulative min computed at every element.

        Parameters
        ----------
        reverse
            Reverse the operation.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [3, 1, 2]})
        >>> df.with_columns(
        ...     pl.col("a").cum_min().alias("cum_min"),
        ...     pl.col("a").cum_min(reverse=True).alias("cum_min_reverse"),
        ... )
        shape: (3, 3)
        ┌─────┬─────────┬─────────────────┐
        │ a   ┆ cum_min ┆ cum_min_reverse │
        │ --- ┆ ---     ┆ ---             │
        │ i64 ┆ i64     ┆ i64             │
        ╞═════╪═════════╪═════════════════╡
        │ 3   ┆ 3       ┆ 1               │
        │ 1   ┆ 1       ┆ 1               │
        │ 2   ┆ 1       ┆ 2               │
        └─────┴─────────┴─────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.cum_min(reverse))

    def cum_max(self, *, reverse: bool = False) -> Expr:
        """
        Get an array with the cumulative max computed at every element.

        Parameters
        ----------
        reverse
            Reverse the operation.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 3, 2]})
        >>> df.with_columns(
        ...     pl.col("a").cum_max().alias("cum_max"),
        ...     pl.col("a").cum_max(reverse=True).alias("cum_max_reverse"),
        ... )
        shape: (3, 3)
        ┌─────┬─────────┬─────────────────┐
        │ a   ┆ cum_max ┆ cum_max_reverse │
        │ --- ┆ ---     ┆ ---             │
        │ i64 ┆ i64     ┆ i64             │
        ╞═════╪═════════╪═════════════════╡
        │ 1   ┆ 1       ┆ 3               │
        │ 3   ┆ 3       ┆ 3               │
        │ 2   ┆ 3       ┆ 2               │
        └─────┴─────────┴─────────────────┘


        Null values are excluded, but can also be filled by calling
        `fill_null(strategy="forward")`.

        >>> df = pl.DataFrame({"values": [None, 10, None, 8, 9, None, 16, None]})
        >>> df.with_columns(
        ...     pl.col("values").cum_max().alias("cum_max"),
        ...     pl.col("values")
        ...     .cum_max()
        ...     .fill_null(strategy="forward")
        ...     .alias("cum_max_all_filled"),
        ... )
        shape: (8, 3)
        ┌────────┬─────────┬────────────────────┐
        │ values ┆ cum_max ┆ cum_max_all_filled │
        │ ---    ┆ ---     ┆ ---                │
        │ i64    ┆ i64     ┆ i64                │
        ╞════════╪═════════╪════════════════════╡
        │ null   ┆ null    ┆ null               │
        │ 10     ┆ 10      ┆ 10                 │
        │ null   ┆ null    ┆ 10                 │
        │ 8      ┆ 10      ┆ 10                 │
        │ 9      ┆ 10      ┆ 10                 │
        │ null   ┆ null    ┆ 10                 │
        │ 16     ┆ 16      ┆ 16                 │
        │ null   ┆ null    ┆ 16                 │
        └────────┴─────────┴────────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.cum_max(reverse))

    def cum_count(self, *, reverse: bool = False) -> Expr:
        """
        Return the cumulative count of the non-null values in the column.

        Parameters
        ----------
        reverse
            Reverse the operation.

        Examples
        --------
        >>> df = pl.DataFrame({"a": ["x", "k", None, "d"]})
        >>> df.with_columns(
        ...     pl.col("a").cum_count().alias("cum_count"),
        ...     pl.col("a").cum_count(reverse=True).alias("cum_count_reverse"),
        ... )
        shape: (4, 3)
        ┌──────┬───────────┬───────────────────┐
        │ a    ┆ cum_count ┆ cum_count_reverse │
        │ ---  ┆ ---       ┆ ---               │
        │ str  ┆ u32       ┆ u32               │
        ╞══════╪═══════════╪═══════════════════╡
        │ x    ┆ 1         ┆ 3                 │
        │ k    ┆ 2         ┆ 2                 │
        │ null ┆ 2         ┆ 1                 │
        │ d    ┆ 3         ┆ 1                 │
        └──────┴───────────┴───────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.cum_count(reverse))

    def floor(self) -> Expr:
        """
        Rounds down to the nearest integer value.

        Only works on floating point Series.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.3, 0.5, 1.0, 1.1]})
        >>> df.select(pl.col("a").floor())
        shape: (4, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 0.0 │
        │ 0.0 │
        │ 1.0 │
        │ 1.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.floor())

    def ceil(self) -> Expr:
        """
        Rounds up to the nearest integer value.

        Only works on floating point Series.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.3, 0.5, 1.0, 1.1]})
        >>> df.select(pl.col("a").ceil())
        shape: (4, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        │ 1.0 │
        │ 1.0 │
        │ 2.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.ceil())

    def round(self, decimals: int = 0) -> Expr:
        """
        Round underlying floating point data by `decimals` digits.

        Parameters
        ----------
        decimals
            Number of decimals to round by.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.33, 0.52, 1.02, 1.17]})
        >>> df.select(pl.col("a").round(1))
        shape: (4, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 0.3 │
        │ 0.5 │
        │ 1.0 │
        │ 1.2 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.round(decimals))

    def round_sig_figs(self, digits: int) -> Expr:
        """
        Round to a number of significant figures.

        Parameters
        ----------
        digits
            Number of significant figures to round to.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.01234, 3.333, 1234.0]})
        >>> df.with_columns(pl.col("a").round_sig_figs(2).alias("round_sig_figs"))
        shape: (3, 2)
        ┌─────────┬────────────────┐
        │ a       ┆ round_sig_figs │
        │ ---     ┆ ---            │
        │ f64     ┆ f64            │
        ╞═════════╪════════════════╡
        │ 0.01234 ┆ 0.012          │
        │ 3.333   ┆ 3.3            │
        │ 1234.0  ┆ 1200.0         │
        └─────────┴────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.round_sig_figs(digits))

    def dot(self, other: Expr | str) -> Expr:
        """
        Compute the dot/inner product between two Expressions.

        Parameters
        ----------
        other
            Expression to compute dot product with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 3, 5],
        ...         "b": [2, 4, 6],
        ...     }
        ... )
        >>> df.select(pl.col("a").dot(pl.col("b")))
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 44  │
        └─────┘
        """
        other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr.dot(other))

    def mode(self) -> Expr:
        """
        Compute the most occurring value(s).

        Can return multiple Values.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 1, 2, 3],
        ...         "b": [1, 1, 2, 2],
        ...     }
        ... )
        >>> df.select(pl.all().mode().first())  # doctest: +IGNORE_RESULT
        shape: (2, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ i64 ┆ i64 │
        ╞═════╪═════╡
        │ 1   ┆ 1   │
        └─────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.mode())

    def cast(
        self,
        dtype: PolarsDataType | type[Any],
        *,
        strict: bool = True,
        wrap_numerical: bool = False,
    ) -> Expr:
        r"""
        Cast between data types.

        Parameters
        ----------
        dtype
            DataType to cast to.
        strict
            Raise if cast is invalid on rows after predicates are pushed down.
            If `False`, invalid casts will produce null values.
        wrap_numerical
            If True numeric casts wrap overflowing values instead of
            marking the cast as invalid.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 3],
        ...         "b": ["4", "5", "6"],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("a").cast(pl.Float64),
        ...     pl.col("b").cast(pl.Int32),
        ... )
        shape: (3, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ f64 ┆ i32 │
        ╞═════╪═════╡
        │ 1.0 ┆ 4   │
        │ 2.0 ┆ 5   │
        │ 3.0 ┆ 6   │
        └─────┴─────┘
        """
        dtype = parse_into_dtype(dtype)
        return self._from_pyexpr(self._pyexpr.cast(dtype, strict, wrap_numerical))

    def sort(self, *, descending: bool = False, nulls_last: bool = False) -> Expr:
        """
        Sort this column.

        When used in a projection/selection context, the whole column is sorted.
        When used in a group by context, the groups are sorted.

        Parameters
        ----------
        descending
            Sort in descending order.
        nulls_last
            Place null values last.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, None, 3, 2],
        ...     }
        ... )
        >>> df.select(pl.col("a").sort())
        shape: (4, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ i64  │
        ╞══════╡
        │ null │
        │ 1    │
        │ 2    │
        │ 3    │
        └──────┘
        >>> df.select(pl.col("a").sort(descending=True))
        shape: (4, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ i64  │
        ╞══════╡
        │ null │
        │ 3    │
        │ 2    │
        │ 1    │
        └──────┘
        >>> df.select(pl.col("a").sort(nulls_last=True))
        shape: (4, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ i64  │
        ╞══════╡
        │ 1    │
        │ 2    │
        │ 3    │
        │ null │
        └──────┘

        When sorting in a group by context, the groups are sorted.

        >>> df = pl.DataFrame(
        ...     {
        ...         "group": ["one", "one", "one", "two", "two", "two"],
        ...         "value": [1, 98, 2, 3, 99, 4],
        ...     }
        ... )
        >>> df.group_by("group").agg(pl.col("value").sort())  # doctest: +IGNORE_RESULT
        shape: (2, 2)
        ┌───────┬────────────┐
        │ group ┆ value      │
        │ ---   ┆ ---        │
        │ str   ┆ list[i64]  │
        ╞═══════╪════════════╡
        │ two   ┆ [3, 4, 99] │
        │ one   ┆ [1, 2, 98] │
        └───────┴────────────┘
        """
        return self._from_pyexpr(self._pyexpr.sort_with(descending, nulls_last))

    def top_k(self, k: int | IntoExprColumn = 5) -> Expr:
        r"""
        Return the `k` largest elements.

        Non-null elements are always preferred over null elements. The output
        is not guaranteed to be in any particular order, call :func:`sort`
        after this function if you wish the output to be sorted.

        This has time complexity:

        .. math:: O(n)

        Parameters
        ----------
        k
            Number of elements to return.

        See Also
        --------
        top_k_by
        bottom_k
        bottom_k_by

        Examples
        --------
        Get the 5 largest values in series.

        >>> df = pl.DataFrame({"value": [1, 98, 2, 3, 99, 4]})
        >>> df.select(
        ...     pl.col("value").top_k().alias("top_k"),
        ...     pl.col("value").bottom_k().alias("bottom_k"),
        ... )
        shape: (5, 2)
        ┌───────┬──────────┐
        │ top_k ┆ bottom_k │
        │ ---   ┆ ---      │
        │ i64   ┆ i64      │
        ╞═══════╪══════════╡
        │ 4     ┆ 1        │
        │ 98    ┆ 98       │
        │ 2     ┆ 2        │
        │ 3     ┆ 3        │
        │ 99    ┆ 4        │
        └───────┴──────────┘
        """
        k = parse_into_expression(k)
        return self._from_pyexpr(self._pyexpr.top_k(k))

    @deprecate_renamed_parameter("descending", "reverse", version="1.0.0")
    def top_k_by(
        self,
        by: IntoExpr | Iterable[IntoExpr],
        k: int | IntoExprColumn = 5,
        *,
        reverse: bool | Sequence[bool] = False,
    ) -> Expr:
        r"""
        Return the elements corresponding to the `k` largest elements of the `by` column(s).

        Non-null elements are always preferred over null elements, regardless of
        the value of `reverse`. The output is not guaranteed to be in any
        particular order, call :func:`sort` after this function if you wish the
        output to be sorted.

        This has time complexity:

        .. math:: O(n \log{n})

        Parameters
        ----------
        by
            Column(s) used to determine the largest elements.
            Accepts expression input. Strings are parsed as column names.
        k
            Number of elements to return.
        reverse
            Consider the `k` smallest elements of the `by` column(s) (instead of the `k`
            largest). This can be specified per column by passing a sequence of
            booleans.

        See Also
        --------
        top_k
        bottom_k
        bottom_k_by

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 3, 4, 5, 6],
        ...         "b": [6, 5, 4, 3, 2, 1],
        ...         "c": ["Apple", "Orange", "Apple", "Apple", "Banana", "Banana"],
        ...     }
        ... )
        >>> df
        shape: (6, 3)
        ┌─────┬─────┬────────┐
        │ a   ┆ b   ┆ c      │
        │ --- ┆ --- ┆ ---    │
        │ i64 ┆ i64 ┆ str    │
        ╞═════╪═════╪════════╡
        │ 1   ┆ 6   ┆ Apple  │
        │ 2   ┆ 5   ┆ Orange │
        │ 3   ┆ 4   ┆ Apple  │
        │ 4   ┆ 3   ┆ Apple  │
        │ 5   ┆ 2   ┆ Banana │
        │ 6   ┆ 1   ┆ Banana │
        └─────┴─────┴────────┘

        Get the top 2 rows by column `a` or `b`.

        >>> df.select(
        ...     pl.all().top_k_by("a", 2).name.suffix("_top_by_a"),
        ...     pl.all().top_k_by("b", 2).name.suffix("_top_by_b"),
        ... )
        shape: (2, 6)
        ┌────────────┬────────────┬────────────┬────────────┬────────────┬────────────┐
        │ a_top_by_a ┆ b_top_by_a ┆ c_top_by_a ┆ a_top_by_b ┆ b_top_by_b ┆ c_top_by_b │
        │ ---        ┆ ---        ┆ ---        ┆ ---        ┆ ---        ┆ ---        │
        │ i64        ┆ i64        ┆ str        ┆ i64        ┆ i64        ┆ str        │
        ╞════════════╪════════════╪════════════╪════════════╪════════════╪════════════╡
        │ 6          ┆ 1          ┆ Banana     ┆ 1          ┆ 6          ┆ Apple      │
        │ 5          ┆ 2          ┆ Banana     ┆ 2          ┆ 5          ┆ Orange     │
        └────────────┴────────────┴────────────┴────────────┴────────────┴────────────┘

        Get the top 2 rows by multiple columns with given order.

        >>> df.select(
        ...     pl.all()
        ...     .top_k_by(["c", "a"], 2, reverse=[False, True])
        ...     .name.suffix("_by_ca"),
        ...     pl.all()
        ...     .top_k_by(["c", "b"], 2, reverse=[False, True])
        ...     .name.suffix("_by_cb"),
        ... )
        shape: (2, 6)
        ┌─────────┬─────────┬─────────┬─────────┬─────────┬─────────┐
        │ a_by_ca ┆ b_by_ca ┆ c_by_ca ┆ a_by_cb ┆ b_by_cb ┆ c_by_cb │
        │ ---     ┆ ---     ┆ ---     ┆ ---     ┆ ---     ┆ ---     │
        │ i64     ┆ i64     ┆ str     ┆ i64     ┆ i64     ┆ str     │
        ╞═════════╪═════════╪═════════╪═════════╪═════════╪═════════╡
        │ 2       ┆ 5       ┆ Orange  ┆ 2       ┆ 5       ┆ Orange  │
        │ 5       ┆ 2       ┆ Banana  ┆ 6       ┆ 1       ┆ Banana  │
        └─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘

        Get the top 2 rows by column `a` in each group.

        >>> (
        ...     df.group_by("c", maintain_order=True)
        ...     .agg(pl.all().top_k_by("a", 2))
        ...     .explode(pl.all().exclude("c"))
        ... )
        shape: (5, 3)
        ┌────────┬─────┬─────┐
        │ c      ┆ a   ┆ b   │
        │ ---    ┆ --- ┆ --- │
        │ str    ┆ i64 ┆ i64 │
        ╞════════╪═════╪═════╡
        │ Apple  ┆ 4   ┆ 3   │
        │ Apple  ┆ 3   ┆ 4   │
        │ Orange ┆ 2   ┆ 5   │
        │ Banana ┆ 6   ┆ 1   │
        │ Banana ┆ 5   ┆ 2   │
        └────────┴─────┴─────┘
        """  # noqa: W505
        k = parse_into_expression(k)
        by = parse_into_list_of_expressions(by)
        reverse = extend_bool(reverse, len(by), "reverse", "by")
        return self._from_pyexpr(self._pyexpr.top_k_by(by, k=k, reverse=reverse))

    def bottom_k(self, k: int | IntoExprColumn = 5) -> Expr:
        r"""
        Return the `k` smallest elements.

        Non-null elements are always preferred over null elements. The output is
        not guaranteed to be in any particular order, call :func:`sort` after
        this function if you wish the output to be sorted.

        This has time complexity:

        .. math:: O(n)

        Parameters
        ----------
        k
            Number of elements to return.

        See Also
        --------
        top_k
        top_k_by
        bottom_k_by

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "value": [1, 98, 2, 3, 99, 4],
        ...     }
        ... )
        >>> df.select(
        ...     pl.col("value").top_k().alias("top_k"),
        ...     pl.col("value").bottom_k().alias("bottom_k"),
        ... )
        shape: (5, 2)
        ┌───────┬──────────┐
        │ top_k ┆ bottom_k │
        │ ---   ┆ ---      │
        │ i64   ┆ i64      │
        ╞═══════╪══════════╡
        │ 4     ┆ 1        │
        │ 98    ┆ 98       │
        │ 2     ┆ 2        │
        │ 3     ┆ 3        │
        │ 99    ┆ 4        │
        └───────┴──────────┘
        """
        k = parse_into_expression(k)
        return self._from_pyexpr(self._pyexpr.bottom_k(k))

    @deprecate_renamed_parameter("descending", "reverse", version="1.0.0")
    def bottom_k_by(
        self,
        by: IntoExpr | Iterable[IntoExpr],
        k: int | IntoExprColumn = 5,
        *,
        reverse: bool | Sequence[bool] = False,
    ) -> Expr:
        r"""
        Return the elements corresponding to the `k` smallest elements of the `by` column(s).

        Non-null elements are always preferred over null elements, regardless of
        the value of `reverse`. The output is not guaranteed to be in any
        particular order, call :func:`sort` after this function if you wish the
        output to be sorted.

        This has time complexity:

        .. math:: O(n \log{n})

        Parameters
        ----------
        by
            Column(s) used to determine the smallest elements.
            Accepts expression input. Strings are parsed as column names.
        k
            Number of elements to return.
        reverse
            Consider the `k` largest elements of the `by` column(s) (instead of the `k`
            smallest). This can be specified per column by passing a sequence of
            booleans.

        See Also
        --------
        top_k
        top_k_by
        bottom_k

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 3, 4, 5, 6],
        ...         "b": [6, 5, 4, 3, 2, 1],
        ...         "c": ["Apple", "Orange", "Apple", "Apple", "Banana", "Banana"],
        ...     }
        ... )
        >>> df
        shape: (6, 3)
        ┌─────┬─────┬────────┐
        │ a   ┆ b   ┆ c      │
        │ --- ┆ --- ┆ ---    │
        │ i64 ┆ i64 ┆ str    │
        ╞═════╪═════╪════════╡
        │ 1   ┆ 6   ┆ Apple  │
        │ 2   ┆ 5   ┆ Orange │
        │ 3   ┆ 4   ┆ Apple  │
        │ 4   ┆ 3   ┆ Apple  │
        │ 5   ┆ 2   ┆ Banana │
        │ 6   ┆ 1   ┆ Banana │
        └─────┴─────┴────────┘

        Get the bottom 2 rows by column `a` or `b`.

        >>> df.select(
        ...     pl.all().bottom_k_by("a", 2).name.suffix("_btm_by_a"),
        ...     pl.all().bottom_k_by("b", 2).name.suffix("_btm_by_b"),
        ... )
        shape: (2, 6)
        ┌────────────┬────────────┬────────────┬────────────┬────────────┬────────────┐
        │ a_btm_by_a ┆ b_btm_by_a ┆ c_btm_by_a ┆ a_btm_by_b ┆ b_btm_by_b ┆ c_btm_by_b │
        │ ---        ┆ ---        ┆ ---        ┆ ---        ┆ ---        ┆ ---        │
        │ i64        ┆ i64        ┆ str        ┆ i64        ┆ i64        ┆ str        │
        ╞════════════╪════════════╪════════════╪════════════╪════════════╪════════════╡
        │ 1          ┆ 6          ┆ Apple      ┆ 6          ┆ 1          ┆ Banana     │
        │ 2          ┆ 5          ┆ Orange     ┆ 5          ┆ 2          ┆ Banana     │
        └────────────┴────────────┴────────────┴────────────┴────────────┴────────────┘

        Get the bottom 2 rows by multiple columns with given order.

        >>> df.select(
        ...     pl.all()
        ...     .bottom_k_by(["c", "a"], 2, reverse=[False, True])
        ...     .name.suffix("_by_ca"),
        ...     pl.all()
        ...     .bottom_k_by(["c", "b"], 2, reverse=[False, True])
        ...     .name.suffix("_by_cb"),
        ... )
        shape: (2, 6)
        ┌─────────┬─────────┬─────────┬─────────┬─────────┬─────────┐
        │ a_by_ca ┆ b_by_ca ┆ c_by_ca ┆ a_by_cb ┆ b_by_cb ┆ c_by_cb │
        │ ---     ┆ ---     ┆ ---     ┆ ---     ┆ ---     ┆ ---     │
        │ i64     ┆ i64     ┆ str     ┆ i64     ┆ i64     ┆ str     │
        ╞═════════╪═════════╪═════════╪═════════╪═════════╪═════════╡
        │ 4       ┆ 3       ┆ Apple   ┆ 1       ┆ 6       ┆ Apple   │
        │ 3       ┆ 4       ┆ Apple   ┆ 3       ┆ 4       ┆ Apple   │
        └─────────┴─────────┴─────────┴─────────┴─────────┴─────────┘

        Get the bottom 2 rows by column `a` in each group.

        >>> (
        ...     df.group_by("c", maintain_order=True)
        ...     .agg(pl.all().bottom_k_by("a", 2))
        ...     .explode(pl.all().exclude("c"))
        ... )
        shape: (5, 3)
        ┌────────┬─────┬─────┐
        │ c      ┆ a   ┆ b   │
        │ ---    ┆ --- ┆ --- │
        │ str    ┆ i64 ┆ i64 │
        ╞════════╪═════╪═════╡
        │ Apple  ┆ 1   ┆ 6   │
        │ Apple  ┆ 3   ┆ 4   │
        │ Orange ┆ 2   ┆ 5   │
        │ Banana ┆ 5   ┆ 2   │
        │ Banana ┆ 6   ┆ 1   │
        └────────┴─────┴─────┘
        """  # noqa: W505
        k = parse_into_expression(k)
        by = parse_into_list_of_expressions(by)
        reverse = extend_bool(reverse, len(by), "reverse", "by")
        return self._from_pyexpr(self._pyexpr.bottom_k_by(by, k=k, reverse=reverse))

    def arg_sort(self, *, descending: bool = False, nulls_last: bool = False) -> Expr:
        """
        Get the index values that would sort this column.

        Parameters
        ----------
        descending
            Sort in descending (descending) order.
        nulls_last
            Place null values last instead of first.

        Returns
        -------
        Expr
            Expression of data type :class:`UInt32`.

        See Also
        --------
        Expr.gather: Take values by index.
        Expr.rank : Get the rank of each row.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [20, 10, 30],
        ...         "b": [1, 2, 3],
        ...     }
        ... )
        >>> df.select(pl.col("a").arg_sort())
        shape: (3, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 1   │
        │ 0   │
        │ 2   │
        └─────┘

        Use gather to apply the arg sort to other columns.

        >>> df.select(pl.col("b").gather(pl.col("a").arg_sort()))
        shape: (3, 1)
        ┌─────┐
        │ b   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 2   │
        │ 1   │
        │ 3   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.arg_sort(descending, nulls_last))

    def arg_max(self) -> Expr:
        """
        Get the index of the maximal value.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [20, 10, 30],
        ...     }
        ... )
        >>> df.select(pl.col("a").arg_max())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 2   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.arg_max())

    def arg_min(self) -> Expr:
        """
        Get the index of the minimal value.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [20, 10, 30],
        ...     }
        ... )
        >>> df.select(pl.col("a").arg_min())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 1   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.arg_min())

    def index_of(self, element: IntoExpr) -> Expr:
        """
        Get the index of the first occurrence of a value, or ``None`` if it's not found.

        Parameters
        ----------
        element
            Value to find.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, None, 17]})
        >>> df.select(
        ...     [
        ...         pl.col("a").index_of(17).alias("seventeen"),
        ...         pl.col("a").index_of(None).alias("null"),
        ...         pl.col("a").index_of(55).alias("fiftyfive"),
        ...     ]
        ... )
        shape: (1, 3)
        ┌───────────┬──────┬───────────┐
        │ seventeen ┆ null ┆ fiftyfive │
        │ ---       ┆ ---  ┆ ---       │
        │ u32       ┆ u32  ┆ u32       │
        ╞═══════════╪══════╪═══════════╡
        │ 2         ┆ 1    ┆ null      │
        └───────────┴──────┴───────────┘
        """
        element = parse_into_expression(element, str_as_lit=True, list_as_series=False)
        return self._from_pyexpr(self._pyexpr.index_of(element))

    def search_sorted(
        self, element: IntoExpr | np.ndarray[Any, Any], side: SearchSortedSide = "any"
    ) -> Expr:
        """
        Find indices where elements should be inserted to maintain order.

        .. math:: a[i-1] < v <= a[i]

        Parameters
        ----------
        element
            Expression or scalar value.
        side : {'any', 'left', 'right'}
            If 'any', the index of the first suitable location found is given.
            If 'left', the index of the leftmost suitable location found is given.
            If 'right', return the rightmost suitable location found is given.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "values": [1, 2, 3, 5],
        ...     }
        ... )
        >>> df.select(
        ...     [
        ...         pl.col("values").search_sorted(0).alias("zero"),
        ...         pl.col("values").search_sorted(3).alias("three"),
        ...         pl.col("values").search_sorted(6).alias("six"),
        ...     ]
        ... )
        shape: (1, 3)
        ┌──────┬───────┬─────┐
        │ zero ┆ three ┆ six │
        │ ---  ┆ ---   ┆ --- │
        │ u32  ┆ u32   ┆ u32 │
        ╞══════╪═══════╪═════╡
        │ 0    ┆ 2     ┆ 4   │
        └──────┴───────┴─────┘
        """
        element = parse_into_expression(element, str_as_lit=True, list_as_series=True)  # type: ignore[arg-type]
        return self._from_pyexpr(self._pyexpr.search_sorted(element, side))

    def sort_by(
        self,
        by: IntoExpr | Iterable[IntoExpr],
        *more_by: IntoExpr,
        descending: bool | Sequence[bool] = False,
        nulls_last: bool | Sequence[bool] = False,
        multithreaded: bool = True,
        maintain_order: bool = False,
    ) -> Expr:
        """
        Sort this column by the ordering of other columns.

        When used in a projection/selection context, the whole column is sorted.
        When used in a group by context, the groups are sorted.

        Parameters
        ----------
        by
            Column(s) to sort by. Accepts expression input. Strings are parsed as column
            names.
        *more_by
            Additional columns to sort by, specified as positional arguments.
        descending
            Sort in descending order. When sorting by multiple columns, can be specified
            per column by passing a sequence of booleans.
        nulls_last
            Place null values last; can specify a single boolean applying to all columns
            or a sequence of booleans for per-column control.
        multithreaded
            Sort using multiple threads.
        maintain_order
            Whether the order should be maintained if elements are equal.

        Examples
        --------
        Pass a single column name to sort by that column.

        >>> df = pl.DataFrame(
        ...     {
        ...         "group": ["a", "a", "b", "b"],
        ...         "value1": [1, 3, 4, 2],
        ...         "value2": [8, 7, 6, 5],
        ...     }
        ... )
        >>> df.select(pl.col("group").sort_by("value1"))
        shape: (4, 1)
        ┌───────┐
        │ group │
        │ ---   │
        │ str   │
        ╞═══════╡
        │ a     │
        │ b     │
        │ a     │
        │ b     │
        └───────┘

        Sorting by expressions is also supported.

        >>> df.select(pl.col("group").sort_by(pl.col("value1") + pl.col("value2")))
        shape: (4, 1)
        ┌───────┐
        │ group │
        │ ---   │
        │ str   │
        ╞═══════╡
        │ b     │
        │ a     │
        │ a     │
        │ b     │
        └───────┘

        Sort by multiple columns by passing a list of columns.

        >>> df.select(pl.col("group").sort_by(["value1", "value2"], descending=True))
        shape: (4, 1)
        ┌───────┐
        │ group │
        │ ---   │
        │ str   │
        ╞═══════╡
        │ b     │
        │ a     │
        │ b     │
        │ a     │
        └───────┘

        Or use positional arguments to sort by multiple columns in the same way.

        >>> df.select(pl.col("group").sort_by("value1", "value2"))
        shape: (4, 1)
        ┌───────┐
        │ group │
        │ ---   │
        │ str   │
        ╞═══════╡
        │ a     │
        │ b     │
        │ a     │
        │ b     │
        └───────┘

        When sorting in a group by context, the groups are sorted.

        >>> df.group_by("group").agg(
        ...     pl.col("value1").sort_by("value2")
        ... )  # doctest: +IGNORE_RESULT
        shape: (2, 2)
        ┌───────┬───────────┐
        │ group ┆ value1    │
        │ ---   ┆ ---       │
        │ str   ┆ list[i64] │
        ╞═══════╪═══════════╡
        │ a     ┆ [3, 1]    │
        │ b     ┆ [2, 4]    │
        └───────┴───────────┘

        Take a single row from each group where a column attains its minimal value
        within that group.

        >>> df.group_by("group").agg(
        ...     pl.all().sort_by("value2").first()
        ... )  # doctest: +IGNORE_RESULT
        shape: (2, 3)
        ┌───────┬────────┬────────┐
        │ group ┆ value1 ┆ value2 |
        │ ---   ┆ ---    ┆ ---    │
        │ str   ┆ i64    ┆ i64    |
        ╞═══════╪════════╪════════╡
        │ a     ┆ 3      ┆ 7      |
        │ b     ┆ 2      ┆ 5      |
        └───────┴────────┴────────┘
        """
        by = parse_into_list_of_expressions(by, *more_by)
        descending = extend_bool(descending, len(by), "descending", "by")
        nulls_last = extend_bool(nulls_last, len(by), "nulls_last", "by")
        return self._from_pyexpr(
            self._pyexpr.sort_by(
                by, descending, nulls_last, multithreaded, maintain_order
            )
        )

    def gather(
        self, indices: int | Sequence[int] | IntoExpr | Series | np.ndarray[Any, Any]
    ) -> Expr:
        """
        Take values by index.

        Parameters
        ----------
        indices
            An expression that leads to a UInt32 dtyped Series.

        Returns
        -------
        Expr
            Expression of the same data type.

        See Also
        --------
        Expr.get : Take a single value

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "group": [
        ...             "one",
        ...             "one",
        ...             "one",
        ...             "two",
        ...             "two",
        ...             "two",
        ...         ],
        ...         "value": [1, 98, 2, 3, 99, 4],
        ...     }
        ... )
        >>> df.group_by("group", maintain_order=True).agg(
        ...     pl.col("value").gather([2, 1])
        ... )
        shape: (2, 2)
        ┌───────┬───────────┐
        │ group ┆ value     │
        │ ---   ┆ ---       │
        │ str   ┆ list[i64] │
        ╞═══════╪═══════════╡
        │ one   ┆ [2, 98]   │
        │ two   ┆ [4, 99]   │
        └───────┴───────────┘
        """
        if (isinstance(indices, Sequence) and not isinstance(indices, str)) or (
            _check_for_numpy(indices) and isinstance(indices, np.ndarray)
        ):
            indices_lit = F.lit(pl.Series("", indices, dtype=Int64))._pyexpr
        else:
            indices_lit = parse_into_expression(indices)  # type: ignore[arg-type]
        return self._from_pyexpr(self._pyexpr.gather(indices_lit))

    def get(self, index: int | Expr) -> Expr:
        """
        Return a single value by index.

        Parameters
        ----------
        index
            An expression that leads to a UInt32 index.

        Returns
        -------
        Expr
            Expression of the same data type.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "group": [
        ...             "one",
        ...             "one",
        ...             "one",
        ...             "two",
        ...             "two",
        ...             "two",
        ...         ],
        ...         "value": [1, 98, 2, 3, 99, 4],
        ...     }
        ... )
        >>> df.group_by("group", maintain_order=True).agg(pl.col("value").get(1))
        shape: (2, 2)
        ┌───────┬───────┐
        │ group ┆ value │
        │ ---   ┆ ---   │
        │ str   ┆ i64   │
        ╞═══════╪═══════╡
        │ one   ┆ 98    │
        │ two   ┆ 99    │
        └───────┴───────┘
        """
        index_lit = parse_into_expression(index)
        return self._from_pyexpr(self._pyexpr.get(index_lit))

    def shift(
        self, n: int | IntoExprColumn = 1, *, fill_value: IntoExpr | None = None
    ) -> Expr:
        """
        Shift values by the given number of indices.

        Parameters
        ----------
        n
            Number of indices to shift forward. If a negative value is passed, values
            are shifted in the opposite direction instead.
        fill_value
            Fill the resulting null values with this scalar value.

        Notes
        -----
        This method is similar to the `LAG` operation in SQL when the value for `n`
        is positive. With a negative value for `n`, it is similar to `LEAD`.

        See Also
        --------
        fill_null

        Examples
        --------
        By default, values are shifted forward by one index.

        >>> df = pl.DataFrame({"a": [1, 2, 3, 4]})
        >>> df.with_columns(shift=pl.col("a").shift())
        shape: (4, 2)
        ┌─────┬───────┐
        │ a   ┆ shift │
        │ --- ┆ ---   │
        │ i64 ┆ i64   │
        ╞═════╪═══════╡
        │ 1   ┆ null  │
        │ 2   ┆ 1     │
        │ 3   ┆ 2     │
        │ 4   ┆ 3     │
        └─────┴───────┘

        Pass a negative value to shift in the opposite direction instead.

        >>> df.with_columns(shift=pl.col("a").shift(-2))
        shape: (4, 2)
        ┌─────┬───────┐
        │ a   ┆ shift │
        │ --- ┆ ---   │
        │ i64 ┆ i64   │
        ╞═════╪═══════╡
        │ 1   ┆ 3     │
        │ 2   ┆ 4     │
        │ 3   ┆ null  │
        │ 4   ┆ null  │
        └─────┴───────┘

        Specify `fill_value` to fill the resulting null values.

        >>> df.with_columns(shift=pl.col("a").shift(-2, fill_value=100))
        shape: (4, 2)
        ┌─────┬───────┐
        │ a   ┆ shift │
        │ --- ┆ ---   │
        │ i64 ┆ i64   │
        ╞═════╪═══════╡
        │ 1   ┆ 3     │
        │ 2   ┆ 4     │
        │ 3   ┆ 100   │
        │ 4   ┆ 100   │
        └─────┴───────┘
        """
        if fill_value is not None:
            fill_value = parse_into_expression(fill_value, str_as_lit=True)
        n = parse_into_expression(n)
        return self._from_pyexpr(self._pyexpr.shift(n, fill_value))

    def fill_null(
        self,
        value: Any | Expr | None = None,
        strategy: FillNullStrategy | None = None,
        limit: int | None = None,
    ) -> Expr:
        """
        Fill null values using the specified value or strategy.

        To interpolate over null values see interpolate.
        See the examples below to fill nulls with an expression.

        Parameters
        ----------
        value
            Value used to fill null values.
        strategy : {None, 'forward', 'backward', 'min', 'max', 'mean', 'zero', 'one'}
            Strategy used to fill null values.
        limit
            Number of consecutive null values to fill when using the 'forward' or
            'backward' strategy.

        See Also
        --------
        fill_nan

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, None],
        ...         "b": [4, None, 6],
        ...     }
        ... )
        >>> df.with_columns(pl.col("b").fill_null(strategy="zero"))
        shape: (3, 2)
        ┌──────┬─────┐
        │ a    ┆ b   │
        │ ---  ┆ --- │
        │ i64  ┆ i64 │
        ╞══════╪═════╡
        │ 1    ┆ 4   │
        │ 2    ┆ 0   │
        │ null ┆ 6   │
        └──────┴─────┘
        >>> df.with_columns(pl.col("b").fill_null(99))
        shape: (3, 2)
        ┌──────┬─────┐
        │ a    ┆ b   │
        │ ---  ┆ --- │
        │ i64  ┆ i64 │
        ╞══════╪═════╡
        │ 1    ┆ 4   │
        │ 2    ┆ 99  │
        │ null ┆ 6   │
        └──────┴─────┘
        >>> df.with_columns(pl.col("b").fill_null(strategy="forward"))
        shape: (3, 2)
        ┌──────┬─────┐
        │ a    ┆ b   │
        │ ---  ┆ --- │
        │ i64  ┆ i64 │
        ╞══════╪═════╡
        │ 1    ┆ 4   │
        │ 2    ┆ 4   │
        │ null ┆ 6   │
        └──────┴─────┘
        >>> df.with_columns(pl.col("b").fill_null(pl.col("b").median()))
        shape: (3, 2)
        ┌──────┬─────┐
        │ a    ┆ b   │
        │ ---  ┆ --- │
        │ i64  ┆ f64 │
        ╞══════╪═════╡
        │ 1    ┆ 4.0 │
        │ 2    ┆ 5.0 │
        │ null ┆ 6.0 │
        └──────┴─────┘
        >>> df.with_columns(pl.all().fill_null(pl.all().median()))
        shape: (3, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ f64 ┆ f64 │
        ╞═════╪═════╡
        │ 1.0 ┆ 4.0 │
        │ 2.0 ┆ 5.0 │
        │ 1.5 ┆ 6.0 │
        └─────┴─────┘
        """
        if value is not None and strategy is not None:
            msg = "cannot specify both `value` and `strategy`"
            raise ValueError(msg)
        elif value is None and strategy is None:
            msg = "must specify either a fill `value` or `strategy`"
            raise ValueError(msg)
        elif strategy not in ("forward", "backward") and limit is not None:
            msg = "can only specify `limit` when strategy is set to 'backward' or 'forward'"
            raise ValueError(msg)

        if value is not None:
            value = parse_into_expression(value, str_as_lit=True)
            return self._from_pyexpr(self._pyexpr.fill_null(value))
        else:
            return self._from_pyexpr(
                self._pyexpr.fill_null_with_strategy(strategy, limit)
            )

    def fill_nan(self, value: int | float | Expr | None) -> Expr:
        """
        Fill floating point NaN value with a fill value.

        Parameters
        ----------
        value
            Value used to fill NaN values.

        Warnings
        --------
        Note that floating point NaNs (Not a Number) are not missing values.
        To replace missing values, use :func:`fill_null`.

        See Also
        --------
        fill_null

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1.0, None, float("nan")],
        ...         "b": [4.0, float("nan"), 6],
        ...     }
        ... )
        >>> df.with_columns(pl.col("b").fill_nan(0))
        shape: (3, 2)
        ┌──────┬─────┐
        │ a    ┆ b   │
        │ ---  ┆ --- │
        │ f64  ┆ f64 │
        ╞══════╪═════╡
        │ 1.0  ┆ 4.0 │
        │ null ┆ 0.0 │
        │ NaN  ┆ 6.0 │
        └──────┴─────┘
        """
        fill_value = parse_into_expression(value, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.fill_nan(fill_value))

    def forward_fill(self, limit: int | None = None) -> Expr:
        """
        Fill missing values with the last non-null value.

        This is an alias of `.fill_null(strategy="forward")`.

        Parameters
        ----------
        limit
            The number of consecutive null values to forward fill.

        See Also
        --------
        fill_null
        shift
        """
        return self.fill_null(strategy="forward", limit=limit)

    def backward_fill(self, limit: int | None = None) -> Expr:
        """
        Fill missing values with the next non-null value.

        This is an alias of `.fill_null(strategy="backward")`.

        Parameters
        ----------
        limit
            The number of consecutive null values to backward fill.

        See Also
        --------
        fill_null
        shift
        """
        return self.fill_null(strategy="backward", limit=limit)

    def reverse(self) -> Expr:
        """
        Reverse the selection.

        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.select(
        ...     [
        ...         pl.all(),
        ...         pl.all().reverse().name.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       │
        └─────┴────────┴─────┴────────┴───────────┴────────────────┴───────────┴──────────────┘
        """  # noqa: W505
        return self._from_pyexpr(self._pyexpr.reverse())

    def std(self, ddof: int = 1) -> Expr:
        """
        Get standard deviation.

        Parameters
        ----------
        ddof
            “Delta Degrees of Freedom”: the divisor used in the calculation is N - ddof,
            where N represents the number of elements.
            By default ddof is 1.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1, 0, 1]})
        >>> df.select(pl.col("a").std())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.std(ddof))

    def var(self, ddof: int = 1) -> Expr:
        """
        Get variance.

        Parameters
        ----------
        ddof
            “Delta Degrees of Freedom”: the divisor used in the calculation is N - ddof,
            where N represents the number of elements.
            By default ddof is 1.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1, 0, 1]})
        >>> df.select(pl.col("a").var())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.var(ddof))

    def max(self) -> Expr:
        """
        Get maximum value.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1.0, float("nan"), 1.0]})
        >>> df.select(pl.col("a").max())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.max())

    def min(self) -> Expr:
        """
        Get minimum value.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1.0, float("nan"), 1.0]})
        >>> df.select(pl.col("a").min())
        shape: (1, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ f64  │
        ╞══════╡
        │ -1.0 │
        └──────┘
        """
        return self._from_pyexpr(self._pyexpr.min())

    def nan_max(self) -> Expr:
        """
        Get maximum value, but propagate/poison encountered NaN values.

        This differs from numpy's `nanmax` as numpy defaults to propagating NaN values,
        whereas polars defaults to ignoring them.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.0, float("nan")]})
        >>> df.select(pl.col("a").nan_max())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ NaN │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.nan_max())

    def nan_min(self) -> Expr:
        """
        Get minimum value, but propagate/poison encountered NaN values.

        This differs from numpy's `nanmax` as numpy defaults to propagating NaN values,
        whereas polars defaults to ignoring them.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.0, float("nan")]})
        >>> df.select(pl.col("a").nan_min())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ NaN │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.nan_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.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1, 0, 1]})
        >>> df.select(pl.col("a").sum())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │  0  │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.sum())

    def mean(self) -> Expr:
        """
        Get mean value.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1, 0, 1]})
        >>> df.select(pl.col("a").mean())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 0.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.mean())

    def median(self) -> Expr:
        """
        Get median value using linear interpolation.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1, 0, 1]})
        >>> df.select(pl.col("a").median())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 0.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.median())

    def product(self) -> Expr:
        """
        Compute the product of an expression.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").product())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 6   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.product())

    def n_unique(self) -> Expr:
        """
        Count unique values.

        Notes
        -----
        `null` is considered to be a unique value for the purposes of this operation.

        Examples
        --------
        >>> df = pl.DataFrame({"x": [1, 1, 2, 2, 3], "y": [1, 1, 1, None, None]})
        >>> df.select(
        ...     x_unique=pl.col("x").n_unique(),
        ...     y_unique=pl.col("y").n_unique(),
        ... )
        shape: (1, 2)
        ┌──────────┬──────────┐
        │ x_unique ┆ y_unique │
        │ ---      ┆ ---      │
        │ u32      ┆ u32      │
        ╞══════════╪══════════╡
        │ 3        ┆ 2        │
        └──────────┴──────────┘
        """
        return self._from_pyexpr(self._pyexpr.n_unique())

    def approx_n_unique(self) -> Expr:
        """
        Approximate count of unique values.

        This is done using the HyperLogLog++ algorithm for cardinality estimation.

        Examples
        --------
        >>> df = pl.DataFrame({"n": [1, 1, 2]})
        >>> df.select(pl.col("n").approx_n_unique())
        shape: (1, 1)
        ┌─────┐
        │ n   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 2   │
        └─────┘
        >>> df = pl.DataFrame({"n": range(1000)})
        >>> df.select(
        ...     exact=pl.col("n").n_unique(),
        ...     approx=pl.col("n").approx_n_unique(),
        ... )  # doctest: +SKIP
        shape: (1, 2)
        ┌───────┬────────┐
        │ exact ┆ approx │
        │ ---   ┆ ---    │
        │ u32   ┆ u32    │
        ╞═══════╪════════╡
        │ 1000  ┆ 1005   │
        └───────┴────────┘
        """
        return self._from_pyexpr(self._pyexpr.approx_n_unique())

    def null_count(self) -> Expr:
        """
        Count null values.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [None, 1, None],
        ...         "b": [10, None, 300],
        ...         "c": [350, 650, 850],
        ...     }
        ... )
        >>> df.select(pl.all().null_count())
        shape: (1, 3)
        ┌─────┬─────┬─────┐
        │ a   ┆ b   ┆ c   │
        │ --- ┆ --- ┆ --- │
        │ u32 ┆ u32 ┆ u32 │
        ╞═════╪═════╪═════╡
        │ 2   ┆ 1   ┆ 0   │
        └─────┴─────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.null_count())

    def has_nulls(self) -> Expr:
        """
        Check whether the expression contains one or more null values.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [None, 1, None],
        ...         "b": [10, None, 300],
        ...         "c": [350, 650, 850],
        ...     }
        ... )
        >>> df.select(pl.all().has_nulls())
        shape: (1, 3)
        ┌──────┬──────┬───────┐
        │ a    ┆ b    ┆ c     │
        │ ---  ┆ ---  ┆ ---   │
        │ bool ┆ bool ┆ bool  │
        ╞══════╪══════╪═══════╡
        │ true ┆ true ┆ false │
        └──────┴──────┴───────┘
        """
        return self.null_count() > 0

    def arg_unique(self) -> Expr:
        """
        Get index of first unique value.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [8, 9, 10],
        ...         "b": [None, 4, 4],
        ...     }
        ... )
        >>> df.select(pl.col("a").arg_unique())
        shape: (3, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 0   │
        │ 1   │
        │ 2   │
        └─────┘
        >>> df.select(pl.col("b").arg_unique())
        shape: (2, 1)
        ┌─────┐
        │ b   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 0   │
        │ 1   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.arg_unique())

    def unique(self, *, maintain_order: bool = False) -> Expr:
        """
        Get unique values of this expression.

        Parameters
        ----------
        maintain_order
            Maintain order of data. This requires more work.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2]})
        >>> df.select(pl.col("a").unique())  # doctest: +IGNORE_RESULT
        shape: (2, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 2   │
        │ 1   │
        └─────┘
        >>> df.select(pl.col("a").unique(maintain_order=True))
        shape: (2, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 1   │
        │ 2   │
        └─────┘
        """
        if maintain_order:
            return self._from_pyexpr(self._pyexpr.unique_stable())
        return self._from_pyexpr(self._pyexpr.unique())

    def first(self) -> Expr:
        """
        Get the first value.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2]})
        >>> df.select(pl.col("a").first())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 1   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.first())

    def last(self) -> Expr:
        """
        Get the last value.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 3, 2]})
        >>> df.select(pl.col("a").last())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 2   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.last())

    def over(
        self,
        partition_by: IntoExpr | Iterable[IntoExpr],
        *more_exprs: IntoExpr,
        order_by: IntoExpr | Iterable[IntoExpr] | None = None,
        descending: bool = False,
        nulls_last: bool = False,
        mapping_strategy: WindowMappingStrategy = "group_to_rows",
    ) -> Expr:
        """
        Compute expressions over the given groups.

        This expression is similar to performing a group by aggregation and joining the
        result back into the original DataFrame.

        The outcome is similar to how `window functions
        <https://www.postgresql.org/docs/current/tutorial-window.html>`_
        work in PostgreSQL.

        Parameters
        ----------
        partition_by
            Column(s) to group by. Accepts expression input. Strings are parsed as
            column names.
        *more_exprs
            Additional columns to group by, specified as positional arguments.
        order_by
            Order the window functions/aggregations with the partitioned groups by the
            result of the expression passed to `order_by`.
        descending
            In case 'order_by' is given, indicate whether to order in
            ascending or descending order.
        nulls_last
            In case 'order_by' is given, indicate whether to order
            the nulls in last position.
        mapping_strategy: {'group_to_rows', 'join', 'explode'}
            - group_to_rows
                If the aggregation results in multiple values, assign them back to their
                position in the DataFrame. This can only be done if the group yields
                the same elements before aggregation as after.
            - join
                Join the groups as 'List<group_dtype>' to the row positions.
                warning: this can be memory intensive.
            - explode
                Explodes the grouped data into new rows, similar to the results of
                `group_by` + `agg` + `explode`. Sorting of the given groups is required
                if the groups are not part of the window operation for the operation,
                otherwise the result would not make sense. This operation changes the
                number of rows.

        Examples
        --------
        Pass the name of a column to compute the expression over that column.

        >>> df = pl.DataFrame(
        ...     {
        ...         "a": ["a", "a", "b", "b", "b"],
        ...         "b": [1, 2, 3, 5, 3],
        ...         "c": [5, 4, 3, 2, 1],
        ...     }
        ... )
        >>> df.with_columns(c_max=pl.col("c").max().over("a"))
        shape: (5, 4)
        ┌─────┬─────┬─────┬───────┐
        │ a   ┆ b   ┆ c   ┆ c_max │
        │ --- ┆ --- ┆ --- ┆ ---   │
        │ str ┆ i64 ┆ i64 ┆ i64   │
        ╞═════╪═════╪═════╪═══════╡
        │ a   ┆ 1   ┆ 5   ┆ 5     │
        │ a   ┆ 2   ┆ 4   ┆ 5     │
        │ b   ┆ 3   ┆ 3   ┆ 3     │
        │ b   ┆ 5   ┆ 2   ┆ 3     │
        │ b   ┆ 3   ┆ 1   ┆ 3     │
        └─────┴─────┴─────┴───────┘

        Expression input is also supported.

        >>> df.with_columns(c_max=pl.col("c").max().over(pl.col("b") // 2))
        shape: (5, 4)
        ┌─────┬─────┬─────┬───────┐
        │ a   ┆ b   ┆ c   ┆ c_max │
        │ --- ┆ --- ┆ --- ┆ ---   │
        │ str ┆ i64 ┆ i64 ┆ i64   │
        ╞═════╪═════╪═════╪═══════╡
        │ a   ┆ 1   ┆ 5   ┆ 5     │
        │ a   ┆ 2   ┆ 4   ┆ 4     │
        │ b   ┆ 3   ┆ 3   ┆ 4     │
        │ b   ┆ 5   ┆ 2   ┆ 2     │
        │ b   ┆ 3   ┆ 1   ┆ 4     │
        └─────┴─────┴─────┴───────┘

        Group by multiple columns by passing multiple column names or expressions.

        >>> df.with_columns(c_min=pl.col("c").min().over("a", pl.col("b") % 2))
        shape: (5, 4)
        ┌─────┬─────┬─────┬───────┐
        │ a   ┆ b   ┆ c   ┆ c_min │
        │ --- ┆ --- ┆ --- ┆ ---   │
        │ str ┆ i64 ┆ i64 ┆ i64   │
        ╞═════╪═════╪═════╪═══════╡
        │ a   ┆ 1   ┆ 5   ┆ 5     │
        │ a   ┆ 2   ┆ 4   ┆ 4     │
        │ b   ┆ 3   ┆ 3   ┆ 1     │
        │ b   ┆ 5   ┆ 2   ┆ 1     │
        │ b   ┆ 3   ┆ 1   ┆ 1     │
        └─────┴─────┴─────┴───────┘

        You can use non-elementwise expressions with `over` too. By default they are
        evaluated using row-order, but you can specify a different one using `order_by`.

        >>> from datetime import date
        >>> df = pl.DataFrame(
        ...     {
        ...         "store_id": ["a", "a", "b", "b"],
        ...         "date": [
        ...             date(2024, 9, 18),
        ...             date(2024, 9, 17),
        ...             date(2024, 9, 18),
        ...             date(2024, 9, 16),
        ...         ],
        ...         "sales": [7, 9, 8, 10],
        ...     }
        ... )
        >>> df.with_columns(
        ...     cumulative_sales=pl.col("sales")
        ...     .cum_sum()
        ...     .over("store_id", order_by="date")
        ... )
        shape: (4, 4)
        ┌──────────┬────────────┬───────┬──────────────────┐
        │ store_id ┆ date       ┆ sales ┆ cumulative_sales │
        │ ---      ┆ ---        ┆ ---   ┆ ---              │
        │ str      ┆ date       ┆ i64   ┆ i64              │
        ╞══════════╪════════════╪═══════╪══════════════════╡
        │ a        ┆ 2024-09-18 ┆ 7     ┆ 16               │
        │ a        ┆ 2024-09-17 ┆ 9     ┆ 9                │
        │ b        ┆ 2024-09-18 ┆ 8     ┆ 18               │
        │ b        ┆ 2024-09-16 ┆ 10    ┆ 10               │
        └──────────┴────────────┴───────┴──────────────────┘

        If you don't require that the group order be preserved, then the more performant
        option is to use `mapping_strategy='explode'` - be careful however to only ever
        use this in a `select` statement, not a `with_columns` one.

        >>> window = {
        ...     "partition_by": "store_id",
        ...     "order_by": "date",
        ...     "mapping_strategy": "explode",
        ... }
        >>> df.select(
        ...     pl.all().over(**window),
        ...     cumulative_sales=pl.col("sales").cum_sum().over(**window),
        ... )
        shape: (4, 4)
        ┌──────────┬────────────┬───────┬──────────────────┐
        │ store_id ┆ date       ┆ sales ┆ cumulative_sales │
        │ ---      ┆ ---        ┆ ---   ┆ ---              │
        │ str      ┆ date       ┆ i64   ┆ i64              │
        ╞══════════╪════════════╪═══════╪══════════════════╡
        │ a        ┆ 2024-09-17 ┆ 9     ┆ 9                │
        │ a        ┆ 2024-09-18 ┆ 7     ┆ 16               │
        │ b        ┆ 2024-09-16 ┆ 10    ┆ 10               │
        │ b        ┆ 2024-09-18 ┆ 8     ┆ 18               │
        └──────────┴────────────┴───────┴──────────────────┘
        """
        partition_by = parse_into_list_of_expressions(partition_by, *more_exprs)
        if order_by is not None:
            order_by = parse_into_list_of_expressions(order_by)
        return self._from_pyexpr(
            self._pyexpr.over(
                partition_by,
                order_by=order_by,
                order_by_descending=descending,
                order_by_nulls_last=False,  # does not work yet
                mapping_strategy=mapping_strategy,
            )
        )

    def rolling(
        self,
        index_column: str,
        *,
        period: str | timedelta,
        offset: str | timedelta | None = None,
        closed: ClosedInterval = "right",
    ) -> Expr:
        """
        Create rolling groups based on a temporal or integer column.

        If you have a time series `<t_0, t_1, ..., t_n>`, then by default the
        windows created will be

            * (t_0 - period, t_0]
            * (t_1 - period, t_1]
            * ...
            * (t_n - period, t_n]

        whereas if you pass a non-default `offset`, then the windows will be

            * (t_0 + offset, t_0 + offset + period]
            * (t_1 + offset, t_1 + offset + period]
            * ...
            * (t_n + offset, t_n + offset + period]

        The `period` and `offset` arguments are created either from a timedelta, or
        by using the following string language:

        - 1ns   (1 nanosecond)
        - 1us   (1 microsecond)
        - 1ms   (1 millisecond)
        - 1s    (1 second)
        - 1m    (1 minute)
        - 1h    (1 hour)
        - 1d    (1 calendar day)
        - 1w    (1 calendar week)
        - 1mo   (1 calendar month)
        - 1q    (1 calendar quarter)
        - 1y    (1 calendar year)
        - 1i    (1 index count)

        Or combine them:
        "3d12h4m25s" # 3 days, 12 hours, 4 minutes, and 25 seconds

        By "calendar day", we mean the corresponding time on the next day (which may
        not be 24 hours, due to daylight savings). Similarly for "calendar week",
        "calendar month", "calendar quarter", and "calendar year".

        Parameters
        ----------
        index_column
            Column used to group based on the time window.
            Often of type Date/Datetime.
            This column must be sorted in ascending order.
            In case of a rolling group by on indices, dtype needs to be one of
            {UInt32, UInt64, Int32, Int64}. Note that the first three get temporarily
            cast to Int64, so if performance matters use an Int64 column.
        period
            Length of the window - must be non-negative.
        offset
            Offset of the window. Default is `-period`.
        closed : {'right', 'left', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive).

        Examples
        --------
        >>> dates = [
        ...     "2020-01-01 13:45:48",
        ...     "2020-01-01 16:42:13",
        ...     "2020-01-01 16:45:09",
        ...     "2020-01-02 18:12:48",
        ...     "2020-01-03 19:45:32",
        ...     "2020-01-08 23:16:43",
        ... ]
        >>> df = pl.DataFrame({"dt": dates, "a": [3, 7, 5, 9, 2, 1]}).with_columns(
        ...     pl.col("dt").str.strptime(pl.Datetime).set_sorted()
        ... )
        >>> df.with_columns(
        ...     sum_a=pl.sum("a").rolling(index_column="dt", period="2d"),
        ...     min_a=pl.min("a").rolling(index_column="dt", period="2d"),
        ...     max_a=pl.max("a").rolling(index_column="dt", period="2d"),
        ... )
        shape: (6, 5)
        ┌─────────────────────┬─────┬───────┬───────┬───────┐
        │ dt                  ┆ a   ┆ sum_a ┆ min_a ┆ max_a │
        │ ---                 ┆ --- ┆ ---   ┆ ---   ┆ ---   │
        │ datetime[μs]        ┆ i64 ┆ i64   ┆ i64   ┆ i64   │
        ╞═════════════════════╪═════╪═══════╪═══════╪═══════╡
        │ 2020-01-01 13:45:48 ┆ 3   ┆ 3     ┆ 3     ┆ 3     │
        │ 2020-01-01 16:42:13 ┆ 7   ┆ 10    ┆ 3     ┆ 7     │
        │ 2020-01-01 16:45:09 ┆ 5   ┆ 15    ┆ 3     ┆ 7     │
        │ 2020-01-02 18:12:48 ┆ 9   ┆ 24    ┆ 3     ┆ 9     │
        │ 2020-01-03 19:45:32 ┆ 2   ┆ 11    ┆ 2     ┆ 9     │
        │ 2020-01-08 23:16:43 ┆ 1   ┆ 1     ┆ 1     ┆ 1     │
        └─────────────────────┴─────┴───────┴───────┴───────┘
        """
        if offset is None:
            offset = negate_duration_string(parse_as_duration_string(period))

        period = parse_as_duration_string(period)
        offset = parse_as_duration_string(offset)

        return self._from_pyexpr(
            self._pyexpr.rolling(index_column, period, offset, closed)
        )

    def is_unique(self) -> Expr:
        """
        Get mask of unique values.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2]})
        >>> df.select(pl.col("a").is_unique())
        shape: (3, 1)
        ┌───────┐
        │ a     │
        │ ---   │
        │ bool  │
        ╞═══════╡
        │ false │
        │ false │
        │ true  │
        └───────┘
        """
        return self._from_pyexpr(self._pyexpr.is_unique())

    def is_first_distinct(self) -> Expr:
        """
        Return a boolean mask indicating the first occurrence of each distinct value.

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2, 3, 2]})
        >>> df.with_columns(pl.col("a").is_first_distinct().alias("first"))
        shape: (5, 2)
        ┌─────┬───────┐
        │ a   ┆ first │
        │ --- ┆ ---   │
        │ i64 ┆ bool  │
        ╞═════╪═══════╡
        │ 1   ┆ true  │
        │ 1   ┆ false │
        │ 2   ┆ true  │
        │ 3   ┆ true  │
        │ 2   ┆ false │
        └─────┴───────┘
        """
        return self._from_pyexpr(self._pyexpr.is_first_distinct())

    def is_last_distinct(self) -> Expr:
        """
        Return a boolean mask indicating the last occurrence of each distinct value.

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2, 3, 2]})
        >>> df.with_columns(pl.col("a").is_last_distinct().alias("last"))
        shape: (5, 2)
        ┌─────┬───────┐
        │ a   ┆ last  │
        │ --- ┆ ---   │
        │ i64 ┆ bool  │
        ╞═════╪═══════╡
        │ 1   ┆ false │
        │ 1   ┆ true  │
        │ 2   ┆ false │
        │ 3   ┆ true  │
        │ 2   ┆ true  │
        └─────┴───────┘
        """
        return self._from_pyexpr(self._pyexpr.is_last_distinct())

    def is_duplicated(self) -> Expr:
        """
        Return a boolean mask indicating duplicated values.

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2]})
        >>> df.select(pl.col("a").is_duplicated())
        shape: (3, 1)
        ┌───────┐
        │ a     │
        │ ---   │
        │ bool  │
        ╞═══════╡
        │ true  │
        │ true  │
        │ false │
        └───────┘
        """
        return self._from_pyexpr(self._pyexpr.is_duplicated())

    def peak_max(self) -> Expr:
        """
        Get a boolean mask of the local maximum peaks.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3, 4, 5]})
        >>> df.select(pl.col("a").peak_max())
        shape: (5, 1)
        ┌───────┐
        │ a     │
        │ ---   │
        │ bool  │
        ╞═══════╡
        │ false │
        │ false │
        │ false │
        │ false │
        │ true  │
        └───────┘
        """
        return self._from_pyexpr(self._pyexpr.peak_max())

    def peak_min(self) -> Expr:
        """
        Get a boolean mask of the local minimum peaks.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [4, 1, 3, 2, 5]})
        >>> df.select(pl.col("a").peak_min())
        shape: (5, 1)
        ┌───────┐
        │ a     │
        │ ---   │
        │ bool  │
        ╞═══════╡
        │ false │
        │ true  │
        │ false │
        │ true  │
        │ false │
        └───────┘
        """
        return self._from_pyexpr(self._pyexpr.peak_min())

    def quantile(
        self,
        quantile: float | Expr,
        interpolation: RollingInterpolationMethod = "nearest",
    ) -> Expr:
        """
        Get quantile value.

        Parameters
        ----------
        quantile
            Quantile between 0.0 and 1.0.
        interpolation : {'nearest', 'higher', 'lower', 'midpoint', 'linear'}
            Interpolation method.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0, 1, 2, 3, 4, 5]})
        >>> df.select(pl.col("a").quantile(0.3))
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 2.0 │
        └─────┘
        >>> df.select(pl.col("a").quantile(0.3, interpolation="higher"))
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 2.0 │
        └─────┘
        >>> df.select(pl.col("a").quantile(0.3, interpolation="lower"))
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        └─────┘
        >>> df.select(pl.col("a").quantile(0.3, interpolation="midpoint"))
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.5 │
        └─────┘
        >>> df.select(pl.col("a").quantile(0.3, interpolation="linear"))
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.5 │
        └─────┘
        """
        quantile = parse_into_expression(quantile)
        return self._from_pyexpr(self._pyexpr.quantile(quantile, interpolation))

    @unstable()
    def cut(
        self,
        breaks: Sequence[float],
        *,
        labels: Sequence[str] | None = None,
        left_closed: bool = False,
        include_breaks: bool = False,
    ) -> Expr:
        """
        Bin continuous values into discrete categories.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Parameters
        ----------
        breaks
            List of unique cut points.
        labels
            Names of the categories. The number of labels must be equal to the number
            of cut points plus one.
        left_closed
            Set the intervals to be left-closed instead of right-closed.
        include_breaks
            Include a column with the right endpoint of the bin each observation falls
            in. This will change the data type of the output from a
            :class:`Categorical` to a :class:`Struct`.

        Returns
        -------
        Expr
            Expression of data type :class:`Categorical` if `include_breaks` is set to
            `False` (default), otherwise an expression of data type :class:`Struct`.

        See Also
        --------
        qcut

        Examples
        --------
        Divide a column into three categories.

        >>> df = pl.DataFrame({"foo": [-2, -1, 0, 1, 2]})
        >>> df.with_columns(
        ...     pl.col("foo").cut([-1, 1], labels=["a", "b", "c"]).alias("cut")
        ... )
        shape: (5, 2)
        ┌─────┬─────┐
        │ foo ┆ cut │
        │ --- ┆ --- │
        │ i64 ┆ cat │
        ╞═════╪═════╡
        │ -2  ┆ a   │
        │ -1  ┆ a   │
        │ 0   ┆ b   │
        │ 1   ┆ b   │
        │ 2   ┆ c   │
        └─────┴─────┘

        Add both the category and the breakpoint.

        >>> df.with_columns(
        ...     pl.col("foo").cut([-1, 1], include_breaks=True).alias("cut")
        ... ).unnest("cut")
        shape: (5, 3)
        ┌─────┬────────────┬────────────┐
        │ foo ┆ breakpoint ┆ category   │
        │ --- ┆ ---        ┆ ---        │
        │ i64 ┆ f64        ┆ cat        │
        ╞═════╪════════════╪════════════╡
        │ -2  ┆ -1.0       ┆ (-inf, -1] │
        │ -1  ┆ -1.0       ┆ (-inf, -1] │
        │ 0   ┆ 1.0        ┆ (-1, 1]    │
        │ 1   ┆ 1.0        ┆ (-1, 1]    │
        │ 2   ┆ inf        ┆ (1, inf]   │
        └─────┴────────────┴────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.cut(breaks, labels, left_closed, include_breaks)
        )

    @unstable()
    def qcut(
        self,
        quantiles: Sequence[float] | int,
        *,
        labels: Sequence[str] | None = None,
        left_closed: bool = False,
        allow_duplicates: bool = False,
        include_breaks: bool = False,
    ) -> Expr:
        """
        Bin continuous values into discrete categories based on their quantiles.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Parameters
        ----------
        quantiles
            Either a list of quantile probabilities between 0 and 1 or a positive
            integer determining the number of bins with uniform probability.
        labels
            Names of the categories. The number of labels must be equal to the number
            of categories.
        left_closed
            Set the intervals to be left-closed instead of right-closed.
        allow_duplicates
            If set to `True`, duplicates in the resulting quantiles are dropped,
            rather than raising a `DuplicateError`. This can happen even with unique
            probabilities, depending on the data.
        include_breaks
            Include a column with the right endpoint of the bin each observation falls
            in. This will change the data type of the output from a
            :class:`Categorical` to a :class:`Struct`.

        Returns
        -------
        Expr
            Expression of data type :class:`Categorical` if `include_breaks` is set to
            `False` (default), otherwise an expression of data type :class:`Struct`.

        See Also
        --------
        cut

        Examples
        --------
        Divide a column into three categories according to pre-defined quantile
        probabilities.

        >>> df = pl.DataFrame({"foo": [-2, -1, 0, 1, 2]})
        >>> df.with_columns(
        ...     pl.col("foo").qcut([0.25, 0.75], labels=["a", "b", "c"]).alias("qcut")
        ... )
        shape: (5, 2)
        ┌─────┬──────┐
        │ foo ┆ qcut │
        │ --- ┆ ---  │
        │ i64 ┆ cat  │
        ╞═════╪══════╡
        │ -2  ┆ a    │
        │ -1  ┆ a    │
        │ 0   ┆ b    │
        │ 1   ┆ b    │
        │ 2   ┆ c    │
        └─────┴──────┘

        Divide a column into two categories using uniform quantile probabilities.

        >>> df.with_columns(
        ...     pl.col("foo")
        ...     .qcut(2, labels=["low", "high"], left_closed=True)
        ...     .alias("qcut")
        ... )
        shape: (5, 2)
        ┌─────┬──────┐
        │ foo ┆ qcut │
        │ --- ┆ ---  │
        │ i64 ┆ cat  │
        ╞═════╪══════╡
        │ -2  ┆ low  │
        │ -1  ┆ low  │
        │ 0   ┆ high │
        │ 1   ┆ high │
        │ 2   ┆ high │
        └─────┴──────┘

        Add both the category and the breakpoint.

        >>> df.with_columns(
        ...     pl.col("foo").qcut([0.25, 0.75], include_breaks=True).alias("qcut")
        ... ).unnest("qcut")
        shape: (5, 3)
        ┌─────┬────────────┬────────────┐
        │ foo ┆ breakpoint ┆ category   │
        │ --- ┆ ---        ┆ ---        │
        │ i64 ┆ f64        ┆ cat        │
        ╞═════╪════════════╪════════════╡
        │ -2  ┆ -1.0       ┆ (-inf, -1] │
        │ -1  ┆ -1.0       ┆ (-inf, -1] │
        │ 0   ┆ 1.0        ┆ (-1, 1]    │
        │ 1   ┆ 1.0        ┆ (-1, 1]    │
        │ 2   ┆ inf        ┆ (1, inf]   │
        └─────┴────────────┴────────────┘
        """
        if isinstance(quantiles, int):
            pyexpr = self._pyexpr.qcut_uniform(
                quantiles, labels, left_closed, allow_duplicates, include_breaks
            )
        else:
            pyexpr = self._pyexpr.qcut(
                quantiles, labels, left_closed, allow_duplicates, include_breaks
            )

        return self._from_pyexpr(pyexpr)

    def rle(self) -> Expr:
        """
        Compress the column data using run-length encoding.

        Run-length encoding (RLE) encodes data by storing each *run* of identical values
        as a single value and its length.

        Returns
        -------
        Expr
            Expression of data type `Struct` with fields `len` of data type `UInt32`
            and `value` of the original data type.

        See Also
        --------
        rle_id

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 1, 2, 1, None, 1, 3, 3]})
        >>> df.select(pl.col("a").rle()).unnest("a")
        shape: (6, 2)
        ┌─────┬───────┐
        │ len ┆ value │
        │ --- ┆ ---   │
        │ u32 ┆ i64   │
        ╞═════╪═══════╡
        │ 2   ┆ 1     │
        │ 1   ┆ 2     │
        │ 1   ┆ 1     │
        │ 1   ┆ null  │
        │ 1   ┆ 1     │
        │ 2   ┆ 3     │
        └─────┴───────┘
        """
        return self._from_pyexpr(self._pyexpr.rle())

    def rle_id(self) -> Expr:
        """
        Get a distinct integer ID for each run of identical values.

        The ID starts at 0 and increases by one each time the value of the column
        changes.

        Returns
        -------
        Expr
            Expression of data type `UInt32`.

        See Also
        --------
        rle

        Notes
        -----
        This functionality is especially useful for defining a new group for every time
        a column's value changes, rather than for every distinct value of that column.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 1, 1, 1],
        ...         "b": ["x", "x", None, "y", "y"],
        ...     }
        ... )
        >>> df.with_columns(
        ...     rle_id_a=pl.col("a").rle_id(),
        ...     rle_id_ab=pl.struct("a", "b").rle_id(),
        ... )
        shape: (5, 4)
        ┌─────┬──────┬──────────┬───────────┐
        │ a   ┆ b    ┆ rle_id_a ┆ rle_id_ab │
        │ --- ┆ ---  ┆ ---      ┆ ---       │
        │ i64 ┆ str  ┆ u32      ┆ u32       │
        ╞═════╪══════╪══════════╪═══════════╡
        │ 1   ┆ x    ┆ 0        ┆ 0         │
        │ 2   ┆ x    ┆ 1        ┆ 1         │
        │ 1   ┆ null ┆ 2        ┆ 2         │
        │ 1   ┆ y    ┆ 2        ┆ 3         │
        │ 1   ┆ y    ┆ 2        ┆ 3         │
        └─────┴──────┴──────────┴───────────┘
        """
        return self._from_pyexpr(self._pyexpr.rle_id())

    def filter(
        self,
        *predicates: IntoExprColumn | Iterable[IntoExprColumn],
        **constraints: Any,
    ) -> Expr:
        """
        Filter the expression based on one or more predicate expressions.

        The original order of the remaining elements is preserved.

        Elements where the filter does not evaluate to True are discarded, including
        nulls.

        Mostly useful in an aggregation context. If you want to filter on a DataFrame
        level, use `LazyFrame.filter`.

        Parameters
        ----------
        predicates
            Expression(s) that evaluates to a boolean Series.
        constraints
            Column filters; use `name = value` to filter columns by the supplied value.
            Each constraint will behave the same as `pl.col(name).eq(value)`, and
            be implicitly joined with the other filter conditions using `&`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "group_col": ["g1", "g1", "g2"],
        ...         "b": [1, 2, 3],
        ...     }
        ... )
        >>> df.group_by("group_col").agg(
        ...     lt=pl.col("b").filter(pl.col("b") < 2).sum(),
        ...     gte=pl.col("b").filter(pl.col("b") >= 2).sum(),
        ... ).sort("group_col")
        shape: (2, 3)
        ┌───────────┬─────┬─────┐
        │ group_col ┆ lt  ┆ gte │
        │ ---       ┆ --- ┆ --- │
        │ str       ┆ i64 ┆ i64 │
        ╞═══════════╪═════╪═════╡
        │ g1        ┆ 1   ┆ 2   │
        │ g2        ┆ 0   ┆ 3   │
        └───────────┴─────┴─────┘

        Filter expressions can also take constraints as keyword arguments.

        >>> df = pl.DataFrame(
        ...     {
        ...         "key": ["a", "a", "a", "a", "b", "b", "b", "b", "b"],
        ...         "n": [1, 2, 2, 3, 1, 3, 3, 2, 3],
        ...     },
        ... )
        >>> df.group_by("key").agg(
        ...     n_1=pl.col("n").filter(n=1).sum(),
        ...     n_2=pl.col("n").filter(n=2).sum(),
        ...     n_3=pl.col("n").filter(n=3).sum(),
        ... ).sort(by="key")
        shape: (2, 4)
        ┌─────┬─────┬─────┬─────┐
        │ key ┆ n_1 ┆ n_2 ┆ n_3 │
        │ --- ┆ --- ┆ --- ┆ --- │
        │ str ┆ i64 ┆ i64 ┆ i64 │
        ╞═════╪═════╪═════╪═════╡
        │ a   ┆ 1   ┆ 4   ┆ 3   │
        │ b   ┆ 1   ┆ 2   ┆ 9   │
        └─────┴─────┴─────┴─────┘
        """
        predicate = parse_predicates_constraints_into_expression(
            *predicates, **constraints
        )
        return self._from_pyexpr(self._pyexpr.filter(predicate))

    @deprecate_function("Use `filter` instead.", version="0.20.4")
    def where(self, predicate: Expr) -> Expr:
        """
        Filter a single column.

        .. deprecated:: 0.20.4
            Use :func:`filter` instead.

        Alias for :func:`filter`.

        Parameters
        ----------
        predicate
            Boolean expression.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "group_col": ["g1", "g1", "g2"],
        ...         "b": [1, 2, 3],
        ...     }
        ... )
        >>> df.group_by("group_col").agg(  # doctest: +SKIP
        ...     [
        ...         pl.col("b").where(pl.col("b") < 2).sum().alias("lt"),
        ...         pl.col("b").where(pl.col("b") >= 2).sum().alias("gte"),
        ...     ]
        ... ).sort("group_col")
        shape: (2, 3)
        ┌───────────┬─────┬─────┐
        │ group_col ┆ lt  ┆ gte │
        │ ---       ┆ --- ┆ --- │
        │ str       ┆ i64 ┆ i64 │
        ╞═══════════╪═════╪═════╡
        │ g1        ┆ 1   ┆ 2   │
        │ g2        ┆ 0   ┆ 3   │
        └───────────┴─────┴─────┘
        """
        return self.filter(predicate)

    class _map_batches_wrapper:
        def __init__(
            self,
            function: Callable[[Series], Series | Any],
            return_dtype: PolarsDataType | None,
        ) -> None:
            self.function = function
            self.return_dtype = return_dtype

        def __call__(self, *args: Any, **kwargs: Any) -> Any:
            result = self.function(*args, **kwargs)
            if _check_for_numpy(result) and isinstance(result, np.ndarray):
                result = pl.Series(result, dtype=self.return_dtype)
            return result

    def map_batches(
        self,
        function: Callable[[Series], Series | Any],
        return_dtype: PolarsDataType | None = None,
        *,
        agg_list: bool = False,
        is_elementwise: bool = False,
        returns_scalar: bool = False,
    ) -> Expr:
        """
        Apply a custom python function to a whole Series or sequence of Series.

        The output of this custom function is presumed to be either a Series,
        or a NumPy array (in which case it will be automatically converted into
        a Series), or a scalar that will be converted into a Series. If the
        result is a scalar and you want it to stay as a scalar, pass in
        ``returns_scalar=True``. If you want to apply a
        custom function elementwise over single values, see :func:`map_elements`.
        A reasonable use case for `map` functions is transforming the values
        represented by an expression using a third-party library.

        Parameters
        ----------
        function
            Lambda/function to apply.
        return_dtype
            Dtype of the output Series.
            If not set, the dtype will be inferred based on the first non-null value
            that is returned by the function.
        agg_list
            Aggregate the values of the expression into a list before applying the
            function. This parameter only works in a group-by context.
            The function will be invoked only once on a list of groups, rather than
            once per group.
        is_elementwise
            If set to true this can run in the streaming engine, but may yield
            incorrect results in group-by. Ensure you know what you are doing!
        returns_scalar
            If the function returns a scalar, by default it will be wrapped in
            a list in the output, since the assumption is that the function
            always returns something Series-like. If you want to keep the
            result as a scalar, set this argument to True.

        Warnings
        --------
        If `return_dtype` is not provided, this may lead to unexpected results.
        We allow this, but it is considered a bug in the user's query.

        See Also
        --------
        map_elements
        replace

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "sine": [0.0, 1.0, 0.0, -1.0],
        ...         "cosine": [1.0, 0.0, -1.0, 0.0],
        ...     }
        ... )
        >>> df.select(pl.all().map_batches(lambda x: x.to_numpy().argmax()))
        shape: (1, 2)
        ┌──────┬────────┐
        │ sine ┆ cosine │
        │ ---  ┆ ---    │
        │ i64  ┆ i64    │
        ╞══════╪════════╡
        │ 1    ┆ 0      │
        └──────┴────────┘

        In a group-by context, the `agg_list` parameter can improve performance if used
        correctly. The following example has `agg_list` set to `False`, which causes
        the function to be applied once per group. The input of the function is a
        Series of type `Int64`. This is less efficient.

        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [0, 1, 0, 1],
        ...         "b": [1, 2, 3, 4],
        ...     }
        ... )
        >>> df.group_by("a").agg(
        ...     pl.col("b").map_batches(lambda x: x + 2, agg_list=False)
        ... )  # doctest: +IGNORE_RESULT
        shape: (2, 2)
        ┌─────┬───────────┐
        │ a   ┆ b         │
        │ --- ┆ ---       │
        │ i64 ┆ list[i64] │
        ╞═════╪═══════════╡
        │ 1   ┆ [4, 6]    │
        │ 0   ┆ [3, 5]    │
        └─────┴───────────┘

        Using `agg_list=True` would be more efficient. In this example, the input of
        the function is a Series of type `List(Int64)`.

        >>> df.group_by("a").agg(
        ...     pl.col("b").map_batches(
        ...         lambda x: x.list.eval(pl.element() + 2), agg_list=True
        ...     )
        ... )  # doctest: +IGNORE_RESULT
        shape: (2, 2)
        ┌─────┬───────────┐
        │ a   ┆ b         │
        │ --- ┆ ---       │
        │ i64 ┆ list[i64] │
        ╞═════╪═══════════╡
        │ 0   ┆ [3, 5]    │
        │ 1   ┆ [4, 6]    │
        └─────┴───────────┘

        Here's an example of a function that returns a scalar, where we want it
        to stay as a scalar:

        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [0, 1, 0, 1],
        ...         "b": [1, 2, 3, 4],
        ...     }
        ... )
        >>> df.group_by("a").agg(
        ...     pl.col("b").map_batches(lambda x: x.max(), returns_scalar=True)
        ... )  # doctest: +IGNORE_RESULT
        shape: (2, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ i64 ┆ i64 │
        ╞═════╪═════╡
        │ 1   ┆ 4   │
        │ 0   ┆ 3   │
        └─────┴─────┘

        Call a function that takes multiple arguments by creating a `struct` and
        referencing its fields inside the function call.

        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [5, 1, 0, 3],
        ...         "b": [4, 2, 3, 4],
        ...     }
        ... )
        >>> df.with_columns(
        ...     a_times_b=pl.struct("a", "b").map_batches(
        ...         lambda x: np.multiply(x.struct.field("a"), x.struct.field("b"))
        ...     )
        ... )
        shape: (4, 3)
        ┌─────┬─────┬───────────┐
        │ a   ┆ b   ┆ a_times_b │
        │ --- ┆ --- ┆ ---       │
        │ i64 ┆ i64 ┆ i64       │
        ╞═════╪═════╪═══════════╡
        │ 5   ┆ 4   ┆ 20        │
        │ 1   ┆ 2   ┆ 2         │
        │ 0   ┆ 3   ┆ 0         │
        │ 3   ┆ 4   ┆ 12        │
        └─────┴─────┴───────────┘
        """
        if return_dtype is not None:
            return_dtype = parse_into_dtype(return_dtype)

        return self._from_pyexpr(
            self._pyexpr.map_batches(
                self._map_batches_wrapper(function, return_dtype),
                return_dtype,
                agg_list,
                is_elementwise,
                returns_scalar,
            )
        )

    def map_elements(
        self,
        function: Callable[[Any], Any],
        return_dtype: PolarsDataType | None = None,
        *,
        skip_nulls: bool = True,
        pass_name: bool = False,
        strategy: MapElementsStrategy = "thread_local",
        returns_scalar: bool = False,
    ) -> Expr:
        """
        Map a custom/user-defined function (UDF) to each element of a column.

        .. warning::
            This method is much slower than the native expressions API.
            Only use it if you cannot implement your logic otherwise.

            Suppose that the function is: `x ↦ sqrt(x)`:

            - For mapping elements of a series, consider:
              `pl.col("col_name").sqrt()`.
            - For mapping inner elements of lists, consider:
              `pl.col("col_name").list.eval(pl.element().sqrt())`.
            - For mapping elements of struct fields, consider:
              `pl.col("col_name").struct.field("field_name").sqrt()`.

            If you want to replace the original column or field,
            consider :meth:`.with_columns <polars.DataFrame.with_columns>`
            and :meth:`.with_fields <polars.Expr.struct.with_fields>`.

        The UDF is applied to each element of a column. Note that, in a GroupBy
        context, the column will have been pre-aggregated and so each element
        will itself be a Series. Therefore, depending on the context,
        requirements for `function` differ:

        * Selection
            Expects `function` to be of type `Callable[[Any], Any]`.
            Applies a Python function to each individual value in the column.
        * GroupBy
            Expects `function` to be of type `Callable[[Series], Any]`.
            For each group, applies a Python function to the slice of the column
            corresponding to that group.

        Parameters
        ----------
        function
            Lambda/function to map.
        return_dtype
            Dtype of the output Series.
            If not set, the dtype will be inferred based on the first non-null value
            that is returned by the function.
        skip_nulls
            Don't map the function over values that contain nulls (this is faster).
        pass_name
            Pass the Series name to the custom function (this is more expensive).
        returns_scalar
            If the function passed does a reduction
            (e.g. sum, min, etc), Polars must be informed of this otherwise
            the schema might be incorrect.
        strategy : {'thread_local', 'threading'}
            The threading strategy to use.

            - 'thread_local': run the python function on a single thread.
            - 'threading': run the python function on separate threads. Use with
              care as this can slow performance. This might only speed up
              your code if the amount of work per element is significant
              and the python function releases the GIL (e.g. via calling
              a c function)

            .. warning::
                This functionality is considered **unstable**. It may be changed
                at any point without it being considered a breaking change.

        Warnings
        --------
        If `return_dtype` is not provided, this may lead to unexpected results.
        We allow this, but it is considered a bug in the user's query.

        Notes
        -----
        * Using `map_elements` is strongly discouraged as you will be effectively
          running python "for" loops, which will be very slow. Wherever possible you
          should prefer the native expression API to achieve the best performance.

        * If your function is expensive and you don't want it to be called more than
          once for a given input, consider applying an `@lru_cache` decorator to it.
          If your data is suitable you may achieve *significant* speedups.

        * Window function application using `over` is considered a GroupBy context
          here, so `map_elements` can be used to map functions over window groups.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 3, 1],
        ...         "b": ["a", "b", "c", "c"],
        ...     }
        ... )

        The function is applied to each element of column `'a'`:

        >>> df.with_columns(  # doctest: +SKIP
        ...     pl.col("a")
        ...     .map_elements(lambda x: x * 2, return_dtype=pl.Int64)
        ...     .alias("a_times_2"),
        ... )
        shape: (4, 3)
        ┌─────┬─────┬───────────┐
        │ a   ┆ b   ┆ a_times_2 │
        │ --- ┆ --- ┆ ---       │
        │ i64 ┆ str ┆ i64       │
        ╞═════╪═════╪═══════════╡
        │ 1   ┆ a   ┆ 2         │
        │ 2   ┆ b   ┆ 4         │
        │ 3   ┆ c   ┆ 6         │
        │ 1   ┆ c   ┆ 2         │
        └─────┴─────┴───────────┘

        Tip: it is better to implement this with an expression:

        >>> df.with_columns(
        ...     (pl.col("a") * 2).alias("a_times_2"),
        ... )  # doctest: +IGNORE_RESULT

        In a GroupBy context, each element of the column is itself a Series:

        >>> (
        ...     df.lazy().group_by("b").agg(pl.col("a")).collect()
        ... )  # doctest: +IGNORE_RESULT
        shape: (3, 2)
        ┌─────┬───────────┐
        │ b   ┆ a         │
        │ --- ┆ ---       │
        │ str ┆ list[i64] │
        ╞═════╪═══════════╡
        │ a   ┆ [1]       │
        │ b   ┆ [2]       │
        │ c   ┆ [3, 1]    │
        └─────┴───────────┘

        Therefore, from the user's point-of-view, the function is applied per-group:

        >>> (
        ...     df.lazy()
        ...     .group_by("b")
        ...     .agg(pl.col("a").map_elements(lambda x: x.sum(), return_dtype=pl.Int64))
        ...     .collect()
        ... )  # doctest: +IGNORE_RESULT
        shape: (3, 2)
        ┌─────┬─────┐
        │ b   ┆ a   │
        │ --- ┆ --- │
        │ str ┆ i64 │
        ╞═════╪═════╡
        │ a   ┆ 1   │
        │ b   ┆ 2   │
        │ c   ┆ 4   │
        └─────┴─────┘

        Tip: again, it is better to implement this with an expression:

        >>> (
        ...     df.lazy()
        ...     .group_by("b", maintain_order=True)
        ...     .agg(pl.col("a").sum())
        ...     .collect()
        ... )  # doctest: +IGNORE_RESULT

        Window function application using `over` will behave as a GroupBy
        context, with your function receiving individual window groups:

        >>> df = pl.DataFrame(
        ...     {
        ...         "key": ["x", "x", "y", "x", "y", "z"],
        ...         "val": [1, 1, 1, 1, 1, 1],
        ...     }
        ... )
        >>> df.with_columns(
        ...     scaled=pl.col("val")
        ...     .map_elements(lambda s: s * len(s), return_dtype=pl.List(pl.Int64))
        ...     .over("key"),
        ... ).sort("key")
        shape: (6, 3)
        ┌─────┬─────┬────────┐
        │ key ┆ val ┆ scaled │
        │ --- ┆ --- ┆ ---    │
        │ str ┆ i64 ┆ i64    │
        ╞═════╪═════╪════════╡
        │ x   ┆ 1   ┆ 3      │
        │ x   ┆ 1   ┆ 3      │
        │ x   ┆ 1   ┆ 3      │
        │ y   ┆ 1   ┆ 2      │
        │ y   ┆ 1   ┆ 2      │
        │ z   ┆ 1   ┆ 1      │
        └─────┴─────┴────────┘

        Note that this function would *also* be better-implemented natively:

        >>> df.with_columns(
        ...     scaled=(pl.col("val") * pl.col("val").count()).over("key"),
        ... ).sort("key")  # doctest: +IGNORE_RESULT
        """
        if strategy == "threading":
            issue_unstable_warning(
                "The 'threading' strategy for `map_elements` is considered unstable."
            )

        # input x: Series of type list containing the group values
        from polars._utils.udfs import warn_on_inefficient_map

        root_names = self.meta.root_names()
        if len(root_names) > 0:
            warn_on_inefficient_map(function, columns=root_names, map_target="expr")

        if pass_name:

            def wrap_f(x: Series) -> Series:  # pragma: no cover
                def inner(s: Series | Any) -> Series:  # pragma: no cover
                    if isinstance(s, pl.Series):
                        s = s.alias(x.name)
                    return function(s)

                with warnings.catch_warnings():
                    warnings.simplefilter("ignore", PolarsInefficientMapWarning)
                    return x.map_elements(
                        inner, return_dtype=return_dtype, skip_nulls=skip_nulls
                    )

        else:

            def wrap_f(x: Series) -> Series:  # pragma: no cover
                with warnings.catch_warnings():
                    warnings.simplefilter("ignore", PolarsInefficientMapWarning)
                    return x.map_elements(
                        function, return_dtype=return_dtype, skip_nulls=skip_nulls
                    )

        if strategy == "thread_local":
            return self.map_batches(
                wrap_f,
                agg_list=True,
                return_dtype=return_dtype,
                returns_scalar=returns_scalar,
            )
        elif strategy == "threading":

            def wrap_threading(x: Series) -> Series:
                def get_lazy_promise(df: DataFrame) -> LazyFrame:
                    return df.lazy().select(
                        F.col("x").map_batches(
                            wrap_f,
                            agg_list=True,
                            return_dtype=return_dtype,
                            returns_scalar=returns_scalar,
                        )
                    )

                df = x.to_frame("x")

                if x.len() == 0:
                    return get_lazy_promise(df).collect().to_series()

                n_threads = thread_pool_size()
                chunk_size = x.len() // n_threads
                remainder = x.len() % n_threads
                if chunk_size == 0:
                    chunk_sizes = [1 for _ in range(remainder)]
                else:
                    chunk_sizes = [
                        chunk_size + 1 if i < remainder else chunk_size
                        for i in range(n_threads)
                    ]

                # create partitions with LazyFrames
                # these are promises on a computation
                partitions = []
                b = 0
                for step in chunk_sizes:
                    a = b
                    b = b + step
                    partition_df = df[a:b, :]
                    partitions.append(get_lazy_promise(partition_df))

                out = [df.to_series() for df in F.collect_all(partitions)]
                return F.concat(out, rechunk=False)

            return self.map_batches(
                wrap_threading,
                agg_list=True,
                return_dtype=return_dtype,
                returns_scalar=returns_scalar,
            )
        else:
            msg = f"strategy {strategy!r} is not supported"
            raise ValueError(msg)

    def flatten(self) -> Expr:
        """
        Flatten a list or string column.

        Alias for :func:`Expr.list.explode`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "group": ["a", "b", "b"],
        ...         "values": [[1, 2], [2, 3], [4]],
        ...     }
        ... )
        >>> df.group_by("group").agg(pl.col("values").flatten())  # doctest: +SKIP
        shape: (2, 2)
        ┌───────┬───────────┐
        │ group ┆ values    │
        │ ---   ┆ ---       │
        │ str   ┆ list[i64] │
        ╞═══════╪═══════════╡
        │ a     ┆ [1, 2]    │
        │ b     ┆ [2, 3, 4] │
        └───────┴───────────┘
        """
        return self._from_pyexpr(self._pyexpr.explode())

    def explode(self) -> Expr:
        """
        Explode a list expression.

        This means that every item is expanded to a new row.

        Returns
        -------
        Expr
            Expression with the data type of the list elements.

        See Also
        --------
        Expr.list.explode : Explode a list column.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "group": ["a", "b"],
        ...         "values": [
        ...             [1, 2],
        ...             [3, 4],
        ...         ],
        ...     }
        ... )
        >>> df.select(pl.col("values").explode())
        shape: (4, 1)
        ┌────────┐
        │ values │
        │ ---    │
        │ i64    │
        ╞════════╡
        │ 1      │
        │ 2      │
        │ 3      │
        │ 4      │
        └────────┘
        """
        return self._from_pyexpr(self._pyexpr.explode())

    def implode(self) -> Expr:
        """
        Aggregate values into a list.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 3],
        ...         "b": [4, 5, 6],
        ...     }
        ... )
        >>> df.select(pl.all().implode())
        shape: (1, 2)
        ┌───────────┬───────────┐
        │ a         ┆ b         │
        │ ---       ┆ ---       │
        │ list[i64] ┆ list[i64] │
        ╞═══════════╪═══════════╡
        │ [1, 2, 3] ┆ [4, 5, 6] │
        └───────────┴───────────┘
        """
        return self._from_pyexpr(self._pyexpr.implode())

    def gather_every(self, n: int, offset: int = 0) -> Expr:
        """
        Take every nth value in the Series and return as a new Series.

        Parameters
        ----------
        n
            Gather every *n*-th row.
        offset
            Starting index.

        Examples
        --------
        >>> df = pl.DataFrame({"foo": [1, 2, 3, 4, 5, 6, 7, 8, 9]})
        >>> df.select(pl.col("foo").gather_every(3))
        shape: (3, 1)
        ┌─────┐
        │ foo │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 1   │
        │ 4   │
        │ 7   │
        └─────┘

        >>> df.select(pl.col("foo").gather_every(3, offset=1))
        shape: (3, 1)
        ┌─────┐
        │ foo │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 2   │
        │ 5   │
        │ 8   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.gather_every(n, offset))

    def head(self, n: int | Expr = 10) -> Expr:
        """
        Get the first `n` rows.

        Parameters
        ----------
        n
            Number of rows to return.

        Examples
        --------
        >>> df = pl.DataFrame({"foo": [1, 2, 3, 4, 5, 6, 7]})
        >>> df.select(pl.col("foo").head(3))
        shape: (3, 1)
        ┌─────┐
        │ foo │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 1   │
        │ 2   │
        │ 3   │
        └─────┘
        """
        return self.slice(0, n)

    def tail(self, n: int | Expr = 10) -> Expr:
        """
        Get the last `n` rows.

        Parameters
        ----------
        n
            Number of rows to return.

        Examples
        --------
        >>> df = pl.DataFrame({"foo": [1, 2, 3, 4, 5, 6, 7]})
        >>> df.select(pl.col("foo").tail(3))
        shape: (3, 1)
        ┌─────┐
        │ foo │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 5   │
        │ 6   │
        │ 7   │
        └─────┘
        """
        # This cast enables tail with expressions that return unsigned integers,
        # for which negate otherwise raises InvalidOperationError.
        offset = -self._from_pyexpr(
            parse_into_expression(n).cast(Int64, strict=False, wrap_numerical=True)
        )
        return self.slice(offset, n)

    def limit(self, n: int | Expr = 10) -> Expr:
        """
        Get the first `n` rows (alias for :func:`Expr.head`).

        Parameters
        ----------
        n
            Number of rows to return.

        Examples
        --------
        >>> df = pl.DataFrame({"foo": [1, 2, 3, 4, 5, 6, 7]})
        >>> df.select(pl.col("foo").limit(3))
        shape: (3, 1)
        ┌─────┐
        │ foo │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 1   │
        │ 2   │
        │ 3   │
        └─────┘
        """
        return self.head(n)

    def and_(self, *others: Any) -> Expr:
        """
        Method equivalent of bitwise "and" operator `expr & other & ...`.

        Parameters
        ----------
        *others
            One or more integer or boolean expressions to evaluate/combine.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [5, 6, 7, 4, 8],
        ...         "y": [1.5, 2.5, 1.0, 4.0, -5.75],
        ...         "z": [-9, 2, -1, 4, 8],
        ...     }
        ... )
        >>> df.select(
        ...     (pl.col("x") >= pl.col("z"))
        ...     .and_(
        ...         pl.col("y") >= pl.col("z"),
        ...         pl.col("y") == pl.col("y"),
        ...         pl.col("z") <= pl.col("x"),
        ...         pl.col("y") != pl.col("x"),
        ...     )
        ...     .alias("all")
        ... )
        shape: (5, 1)
        ┌───────┐
        │ all   │
        │ ---   │
        │ bool  │
        ╞═══════╡
        │ true  │
        │ true  │
        │ true  │
        │ false │
        │ false │
        └───────┘
        """
        return reduce(operator.and_, (self, *others))

    def or_(self, *others: Any) -> Expr:
        """
        Method equivalent of bitwise "or" operator `expr | other | ...`.

        Parameters
        ----------
        *others
            One or more integer or boolean expressions to evaluate/combine.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [5, 6, 7, 4, 8],
        ...         "y": [1.5, 2.5, 1.0, 4.0, -5.75],
        ...         "z": [-9, 2, -1, 4, 8],
        ...     }
        ... )
        >>> df.select(
        ...     (pl.col("x") == pl.col("y"))
        ...     .or_(
        ...         pl.col("x") == pl.col("y"),
        ...         pl.col("y") == pl.col("z"),
        ...         pl.col("y").cast(int) == pl.col("z"),
        ...     )
        ...     .alias("any")
        ... )
        shape: (5, 1)
        ┌───────┐
        │ any   │
        │ ---   │
        │ bool  │
        ╞═══════╡
        │ false │
        │ true  │
        │ false │
        │ true  │
        │ false │
        └───────┘
        """
        return reduce(operator.or_, (self,) + others)

    def eq(self, other: Any) -> Expr:
        """
        Method equivalent of equality operator `expr == other`.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [1.0, 2.0, float("nan"), 4.0],
        ...         "y": [2.0, 2.0, float("nan"), 4.0],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").eq(pl.col("y")).alias("x == y"),
        ... )
        shape: (4, 3)
        ┌─────┬─────┬────────┐
        │ x   ┆ y   ┆ x == y │
        │ --- ┆ --- ┆ ---    │
        │ f64 ┆ f64 ┆ bool   │
        ╞═════╪═════╪════════╡
        │ 1.0 ┆ 2.0 ┆ false  │
        │ 2.0 ┆ 2.0 ┆ true   │
        │ NaN ┆ NaN ┆ true   │
        │ 4.0 ┆ 4.0 ┆ true   │
        └─────┴─────┴────────┘
        """
        return self.__eq__(other)

    def eq_missing(self, other: Any) -> Expr:
        """
        Method equivalent of equality operator `expr == other` where `None == None`.

        This differs from default `eq` where null values are propagated.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [1.0, 2.0, float("nan"), 4.0, None, None],
        ...         "y": [2.0, 2.0, float("nan"), 4.0, 5.0, None],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").eq(pl.col("y")).alias("x eq y"),
        ...     pl.col("x").eq_missing(pl.col("y")).alias("x eq_missing y"),
        ... )
        shape: (6, 4)
        ┌──────┬──────┬────────┬────────────────┐
        │ x    ┆ y    ┆ x eq y ┆ x eq_missing y │
        │ ---  ┆ ---  ┆ ---    ┆ ---            │
        │ f64  ┆ f64  ┆ bool   ┆ bool           │
        ╞══════╪══════╪════════╪════════════════╡
        │ 1.0  ┆ 2.0  ┆ false  ┆ false          │
        │ 2.0  ┆ 2.0  ┆ true   ┆ true           │
        │ NaN  ┆ NaN  ┆ true   ┆ true           │
        │ 4.0  ┆ 4.0  ┆ true   ┆ true           │
        │ null ┆ 5.0  ┆ null   ┆ false          │
        │ null ┆ null ┆ null   ┆ true           │
        └──────┴──────┴────────┴────────────────┘
        """
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.eq_missing(other))

    def ge(self, other: Any) -> Expr:
        """
        Method equivalent of "greater than or equal" operator `expr >= other`.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [5.0, 4.0, float("nan"), 2.0],
        ...         "y": [5.0, 3.0, float("nan"), 1.0],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").ge(pl.col("y")).alias("x >= y"),
        ... )
        shape: (4, 3)
        ┌─────┬─────┬────────┐
        │ x   ┆ y   ┆ x >= y │
        │ --- ┆ --- ┆ ---    │
        │ f64 ┆ f64 ┆ bool   │
        ╞═════╪═════╪════════╡
        │ 5.0 ┆ 5.0 ┆ true   │
        │ 4.0 ┆ 3.0 ┆ true   │
        │ NaN ┆ NaN ┆ true   │
        │ 2.0 ┆ 1.0 ┆ true   │
        └─────┴─────┴────────┘
        """
        return self.__ge__(other)

    def gt(self, other: Any) -> Expr:
        """
        Method equivalent of "greater than" operator `expr > other`.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [5.0, 4.0, float("nan"), 2.0],
        ...         "y": [5.0, 3.0, float("nan"), 1.0],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").gt(pl.col("y")).alias("x > y"),
        ... )
        shape: (4, 3)
        ┌─────┬─────┬───────┐
        │ x   ┆ y   ┆ x > y │
        │ --- ┆ --- ┆ ---   │
        │ f64 ┆ f64 ┆ bool  │
        ╞═════╪═════╪═══════╡
        │ 5.0 ┆ 5.0 ┆ false │
        │ 4.0 ┆ 3.0 ┆ true  │
        │ NaN ┆ NaN ┆ false │
        │ 2.0 ┆ 1.0 ┆ true  │
        └─────┴─────┴───────┘
        """
        return self.__gt__(other)

    def le(self, other: Any) -> Expr:
        """
        Method equivalent of "less than or equal" operator `expr <= other`.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [5.0, 4.0, float("nan"), 0.5],
        ...         "y": [5.0, 3.5, float("nan"), 2.0],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").le(pl.col("y")).alias("x <= y"),
        ... )
        shape: (4, 3)
        ┌─────┬─────┬────────┐
        │ x   ┆ y   ┆ x <= y │
        │ --- ┆ --- ┆ ---    │
        │ f64 ┆ f64 ┆ bool   │
        ╞═════╪═════╪════════╡
        │ 5.0 ┆ 5.0 ┆ true   │
        │ 4.0 ┆ 3.5 ┆ false  │
        │ NaN ┆ NaN ┆ true   │
        │ 0.5 ┆ 2.0 ┆ true   │
        └─────┴─────┴────────┘
        """
        return self.__le__(other)

    def lt(self, other: Any) -> Expr:
        """
        Method equivalent of "less than" operator `expr < other`.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [1.0, 2.0, float("nan"), 3.0],
        ...         "y": [2.0, 2.0, float("nan"), 4.0],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").lt(pl.col("y")).alias("x < y"),
        ... )
        shape: (4, 3)
        ┌─────┬─────┬───────┐
        │ x   ┆ y   ┆ x < y │
        │ --- ┆ --- ┆ ---   │
        │ f64 ┆ f64 ┆ bool  │
        ╞═════╪═════╪═══════╡
        │ 1.0 ┆ 2.0 ┆ true  │
        │ 2.0 ┆ 2.0 ┆ false │
        │ NaN ┆ NaN ┆ false │
        │ 3.0 ┆ 4.0 ┆ true  │
        └─────┴─────┴───────┘
        """
        return self.__lt__(other)

    def ne(self, other: Any) -> Expr:
        """
        Method equivalent of inequality operator `expr != other`.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [1.0, 2.0, float("nan"), 4.0],
        ...         "y": [2.0, 2.0, float("nan"), 4.0],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").ne(pl.col("y")).alias("x != y"),
        ... )
        shape: (4, 3)
        ┌─────┬─────┬────────┐
        │ x   ┆ y   ┆ x != y │
        │ --- ┆ --- ┆ ---    │
        │ f64 ┆ f64 ┆ bool   │
        ╞═════╪═════╪════════╡
        │ 1.0 ┆ 2.0 ┆ true   │
        │ 2.0 ┆ 2.0 ┆ false  │
        │ NaN ┆ NaN ┆ false  │
        │ 4.0 ┆ 4.0 ┆ false  │
        └─────┴─────┴────────┘
        """
        return self.__ne__(other)

    def ne_missing(self, other: Any) -> Expr:
        """
        Method equivalent of equality operator `expr != other` where `None == None`.

        This differs from default `ne` where null values are propagated.

        Parameters
        ----------
        other
            A literal or expression value to compare with.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={
        ...         "x": [1.0, 2.0, float("nan"), 4.0, None, None],
        ...         "y": [2.0, 2.0, float("nan"), 4.0, 5.0, None],
        ...     }
        ... )
        >>> df.with_columns(
        ...     pl.col("x").ne(pl.col("y")).alias("x ne y"),
        ...     pl.col("x").ne_missing(pl.col("y")).alias("x ne_missing y"),
        ... )
        shape: (6, 4)
        ┌──────┬──────┬────────┬────────────────┐
        │ x    ┆ y    ┆ x ne y ┆ x ne_missing y │
        │ ---  ┆ ---  ┆ ---    ┆ ---            │
        │ f64  ┆ f64  ┆ bool   ┆ bool           │
        ╞══════╪══════╪════════╪════════════════╡
        │ 1.0  ┆ 2.0  ┆ true   ┆ true           │
        │ 2.0  ┆ 2.0  ┆ false  ┆ false          │
        │ NaN  ┆ NaN  ┆ false  ┆ false          │
        │ 4.0  ┆ 4.0  ┆ false  ┆ false          │
        │ null ┆ 5.0  ┆ null   ┆ true           │
        │ null ┆ null ┆ null   ┆ false          │
        └──────┴──────┴────────┴────────────────┘
        """
        other = parse_into_expression(other, str_as_lit=True)
        return self._from_pyexpr(self._pyexpr.neq_missing(other))

    def add(self, other: Any) -> Expr:
        """
        Method equivalent of addition operator `expr + other`.

        Parameters
        ----------
        other
            numeric or string value; accepts expression input.

        Examples
        --------
        >>> df = pl.DataFrame({"x": [1, 2, 3, 4, 5]})
        >>> df.with_columns(
        ...     pl.col("x").add(2).alias("x+int"),
        ...     pl.col("x").add(pl.col("x").cum_prod()).alias("x+expr"),
        ... )
        shape: (5, 3)
        ┌─────┬───────┬────────┐
        │ x   ┆ x+int ┆ x+expr │
        │ --- ┆ ---   ┆ ---    │
        │ i64 ┆ i64   ┆ i64    │
        ╞═════╪═══════╪════════╡
        │ 1   ┆ 3     ┆ 2      │
        │ 2   ┆ 4     ┆ 4      │
        │ 3   ┆ 5     ┆ 9      │
        │ 4   ┆ 6     ┆ 28     │
        │ 5   ┆ 7     ┆ 125    │
        └─────┴───────┴────────┘

        >>> df = pl.DataFrame(
        ...     {"x": ["a", "d", "g"], "y": ["b", "e", "h"], "z": ["c", "f", "i"]}
        ... )
        >>> df.with_columns(pl.col("x").add(pl.col("y")).add(pl.col("z")).alias("xyz"))
        shape: (3, 4)
        ┌─────┬─────┬─────┬─────┐
        │ x   ┆ y   ┆ z   ┆ xyz │
        │ --- ┆ --- ┆ --- ┆ --- │
        │ str ┆ str ┆ str ┆ str │
        ╞═════╪═════╪═════╪═════╡
        │ a   ┆ b   ┆ c   ┆ abc │
        │ d   ┆ e   ┆ f   ┆ def │
        │ g   ┆ h   ┆ i   ┆ ghi │
        └─────┴─────┴─────┴─────┘
        """
        return self.__add__(other)

    def floordiv(self, other: Any) -> Expr:
        """
        Method equivalent of integer division operator `expr // other`.

        Parameters
        ----------
        other
            Numeric literal or expression value.

        See Also
        --------
        truediv

        Examples
        --------
        >>> df = pl.DataFrame({"x": [1, 2, 3, 4, 5]})
        >>> df.with_columns(
        ...     pl.col("x").truediv(2).alias("x/2"),
        ...     pl.col("x").floordiv(2).alias("x//2"),
        ... )
        shape: (5, 3)
        ┌─────┬─────┬──────┐
        │ x   ┆ x/2 ┆ x//2 │
        │ --- ┆ --- ┆ ---  │
        │ i64 ┆ f64 ┆ i64  │
        ╞═════╪═════╪══════╡
        │ 1   ┆ 0.5 ┆ 0    │
        │ 2   ┆ 1.0 ┆ 1    │
        │ 3   ┆ 1.5 ┆ 1    │
        │ 4   ┆ 2.0 ┆ 2    │
        │ 5   ┆ 2.5 ┆ 2    │
        └─────┴─────┴──────┘

        Note that Polars' `floordiv` is subtly different from Python's floor division.
        For example, consider 6.0 floor-divided by 0.1.
        Python gives:

        >>> 6.0 // 0.1
        59.0

        because `0.1` is not represented internally as that exact value,
        but a slightly larger value.
        So the result of the division is slightly less than 60,
        meaning the flooring operation returns 59.0.

        Polars instead first does the floating-point division,
        resulting in a floating-point value of 60.0,
        and then performs the flooring operation using :any:`floor`:

        >>> df = pl.DataFrame({"x": [6.0, 6.03]})
        >>> df.with_columns(
        ...     pl.col("x").truediv(0.1).alias("x/0.1"),
        ... ).with_columns(
        ...     pl.col("x/0.1").floor().alias("x/0.1 floor"),
        ... )
        shape: (2, 3)
        ┌──────┬───────┬─────────────┐
        │ x    ┆ x/0.1 ┆ x/0.1 floor │
        │ ---  ┆ ---   ┆ ---         │
        │ f64  ┆ f64   ┆ f64         │
        ╞══════╪═══════╪═════════════╡
        │ 6.0  ┆ 60.0  ┆ 60.0        │
        │ 6.03 ┆ 60.3  ┆ 60.0        │
        └──────┴───────┴─────────────┘

        yielding the more intuitive result 60.0.
        The row with x = 6.03 is included to demonstrate
        the effect of the flooring operation.

        `floordiv` combines those two steps
        to give the same result with one expression:

        >>> df.with_columns(
        ...     pl.col("x").floordiv(0.1).alias("x//0.1"),
        ... )
        shape: (2, 2)
        ┌──────┬────────┐
        │ x    ┆ x//0.1 │
        │ ---  ┆ ---    │
        │ f64  ┆ f64    │
        ╞══════╪════════╡
        │ 6.0  ┆ 60.0   │
        │ 6.03 ┆ 60.0   │
        └──────┴────────┘
        """
        return self.__floordiv__(other)

    def mod(self, other: Any) -> Expr:
        """
        Method equivalent of modulus operator `expr % other`.

        Parameters
        ----------
        other
            Numeric literal or expression value.

        Examples
        --------
        >>> df = pl.DataFrame({"x": [0, 1, 2, 3, 4]})
        >>> df.with_columns(pl.col("x").mod(2).alias("x%2"))
        shape: (5, 2)
        ┌─────┬─────┐
        │ x   ┆ x%2 │
        │ --- ┆ --- │
        │ i64 ┆ i64 │
        ╞═════╪═════╡
        │ 0   ┆ 0   │
        │ 1   ┆ 1   │
        │ 2   ┆ 0   │
        │ 3   ┆ 1   │
        │ 4   ┆ 0   │
        └─────┴─────┘
        """
        return self.__mod__(other)

    def mul(self, other: Any) -> Expr:
        """
        Method equivalent of multiplication operator `expr * other`.

        Parameters
        ----------
        other
            Numeric literal or expression value.

        Examples
        --------
        >>> df = pl.DataFrame({"x": [1, 2, 4, 8, 16]})
        >>> df.with_columns(
        ...     pl.col("x").mul(2).alias("x*2"),
        ...     pl.col("x").mul(pl.col("x").log(2)).alias("x * xlog2"),
        ... )
        shape: (5, 3)
        ┌─────┬─────┬───────────┐
        │ x   ┆ x*2 ┆ x * xlog2 │
        │ --- ┆ --- ┆ ---       │
        │ i64 ┆ i64 ┆ f64       │
        ╞═════╪═════╪═══════════╡
        │ 1   ┆ 2   ┆ 0.0       │
        │ 2   ┆ 4   ┆ 2.0       │
        │ 4   ┆ 8   ┆ 8.0       │
        │ 8   ┆ 16  ┆ 24.0      │
        │ 16  ┆ 32  ┆ 64.0      │
        └─────┴─────┴───────────┘
        """
        return self.__mul__(other)

    def sub(self, other: Any) -> Expr:
        """
        Method equivalent of subtraction operator `expr - other`.

        Parameters
        ----------
        other
            Numeric literal or expression value.

        Examples
        --------
        >>> df = pl.DataFrame({"x": [0, 1, 2, 3, 4]})
        >>> df.with_columns(
        ...     pl.col("x").sub(2).alias("x-2"),
        ...     pl.col("x").sub(pl.col("x").cum_sum()).alias("x-expr"),
        ... )
        shape: (5, 3)
        ┌─────┬─────┬────────┐
        │ x   ┆ x-2 ┆ x-expr │
        │ --- ┆ --- ┆ ---    │
        │ i64 ┆ i64 ┆ i64    │
        ╞═════╪═════╪════════╡
        │ 0   ┆ -2  ┆ 0      │
        │ 1   ┆ -1  ┆ 0      │
        │ 2   ┆ 0   ┆ -1     │
        │ 3   ┆ 1   ┆ -3     │
        │ 4   ┆ 2   ┆ -6     │
        └─────┴─────┴────────┘
        """
        return self.__sub__(other)

    def neg(self) -> Expr:
        """
        Method equivalent of unary minus operator `-expr`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-1, 0, 2, None]})
        >>> df.with_columns(pl.col("a").neg())
        shape: (4, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ i64  │
        ╞══════╡
        │ 1    │
        │ 0    │
        │ -2   │
        │ null │
        └──────┘
        """
        return self.__neg__()

    def truediv(self, other: Any) -> Expr:
        """
        Method equivalent of float division operator `expr / other`.

        Parameters
        ----------
        other
            Numeric literal or expression value.

        Notes
        -----
        Zero-division behaviour follows IEEE-754:

        0/0: Invalid operation - mathematically undefined, returns NaN.
        n/0: On finite operands gives an exact infinite result, eg: ±infinity.

        See Also
        --------
        floordiv

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     data={"x": [-2, -1, 0, 1, 2], "y": [0.5, 0.0, 0.0, -4.0, -0.5]}
        ... )
        >>> df.with_columns(
        ...     pl.col("x").truediv(2).alias("x/2"),
        ...     pl.col("x").truediv(pl.col("y")).alias("x/y"),
        ... )
        shape: (5, 4)
        ┌─────┬──────┬──────┬───────┐
        │ x   ┆ y    ┆ x/2  ┆ x/y   │
        │ --- ┆ ---  ┆ ---  ┆ ---   │
        │ i64 ┆ f64  ┆ f64  ┆ f64   │
        ╞═════╪══════╪══════╪═══════╡
        │ -2  ┆ 0.5  ┆ -1.0 ┆ -4.0  │
        │ -1  ┆ 0.0  ┆ -0.5 ┆ -inf  │
        │ 0   ┆ 0.0  ┆ 0.0  ┆ NaN   │
        │ 1   ┆ -4.0 ┆ 0.5  ┆ -0.25 │
        │ 2   ┆ -0.5 ┆ 1.0  ┆ -4.0  │
        └─────┴──────┴──────┴───────┘
        """
        return self.__truediv__(other)

    def pow(self, exponent: IntoExprColumn | int | float) -> Expr:
        """
        Method equivalent of exponentiation operator `expr ** exponent`.

        If the exponent is float, the result follows the dtype of exponent.
        Otherwise, it follows dtype of base.

        Parameters
        ----------
        exponent
            Numeric literal or expression exponent value.

        Examples
        --------
        >>> df = pl.DataFrame({"x": [1, 2, 4, 8]})
        >>> df.with_columns(
        ...     pl.col("x").pow(3).alias("cube"),
        ...     pl.col("x").pow(pl.col("x").log(2)).alias("x ** xlog2"),
        ... )
        shape: (4, 3)
        ┌─────┬──────┬────────────┐
        │ x   ┆ cube ┆ x ** xlog2 │
        │ --- ┆ ---  ┆ ---        │
        │ i64 ┆ i64  ┆ f64        │
        ╞═════╪══════╪════════════╡
        │ 1   ┆ 1    ┆ 1.0        │
        │ 2   ┆ 8    ┆ 2.0        │
        │ 4   ┆ 64   ┆ 16.0       │
        │ 8   ┆ 512  ┆ 512.0      │
        └─────┴──────┴────────────┘

        Raising an integer to a positive integer results in an integer - in order
        to raise to a negative integer, you can cast either the base or the exponent
        to float first:

        >>> df.with_columns(
        ...     x_squared=pl.col("x").pow(2),
        ...     x_inverse=pl.col("x").pow(-1.0),
        ... )
        shape: (4, 3)
        ┌─────┬───────────┬───────────┐
        │ x   ┆ x_squared ┆ x_inverse │
        │ --- ┆ ---       ┆ ---       │
        │ i64 ┆ i64       ┆ f64       │
        ╞═════╪═══════════╪═══════════╡
        │ 1   ┆ 1         ┆ 1.0       │
        │ 2   ┆ 4         ┆ 0.5       │
        │ 4   ┆ 16        ┆ 0.25      │
        │ 8   ┆ 64        ┆ 0.125     │
        └─────┴───────────┴───────────┘
        """
        return self.__pow__(exponent)

    def xor(self, other: Any) -> Expr:
        """
        Method equivalent of bitwise exclusive-or operator `expr ^ other`.

        Parameters
        ----------
        other
            Integer or boolean value; accepts expression input.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {"x": [True, False, True, False], "y": [True, True, False, False]}
        ... )
        >>> df.with_columns(pl.col("x").xor(pl.col("y")).alias("x ^ y"))
        shape: (4, 3)
        ┌───────┬───────┬───────┐
        │ x     ┆ y     ┆ x ^ y │
        │ ---   ┆ ---   ┆ ---   │
        │ bool  ┆ bool  ┆ bool  │
        ╞═══════╪═══════╪═══════╡
        │ true  ┆ true  ┆ false │
        │ false ┆ true  ┆ true  │
        │ true  ┆ false ┆ true  │
        │ false ┆ false ┆ false │
        └───────┴───────┴───────┘

        >>> def binary_string(n: int) -> str:
        ...     return bin(n)[2:].zfill(8)
        >>>
        >>> df = pl.DataFrame(
        ...     data={"x": [10, 8, 250, 66], "y": [1, 2, 3, 4]},
        ...     schema={"x": pl.UInt8, "y": pl.UInt8},
        ... )
        >>> df.with_columns(
        ...     pl.col("x")
        ...     .map_elements(binary_string, return_dtype=pl.String)
        ...     .alias("bin_x"),
        ...     pl.col("y")
        ...     .map_elements(binary_string, return_dtype=pl.String)
        ...     .alias("bin_y"),
        ...     pl.col("x").xor(pl.col("y")).alias("xor_xy"),
        ...     pl.col("x")
        ...     .xor(pl.col("y"))
        ...     .map_elements(binary_string, return_dtype=pl.String)
        ...     .alias("bin_xor_xy"),
        ... )
        shape: (4, 6)
        ┌─────┬─────┬──────────┬──────────┬────────┬────────────┐
        │ x   ┆ y   ┆ bin_x    ┆ bin_y    ┆ xor_xy ┆ bin_xor_xy │
        │ --- ┆ --- ┆ ---      ┆ ---      ┆ ---    ┆ ---        │
        │ u8  ┆ u8  ┆ str      ┆ str      ┆ u8     ┆ str        │
        ╞═════╪═════╪══════════╪══════════╪════════╪════════════╡
        │ 10  ┆ 1   ┆ 00001010 ┆ 00000001 ┆ 11     ┆ 00001011   │
        │ 8   ┆ 2   ┆ 00001000 ┆ 00000010 ┆ 10     ┆ 00001010   │
        │ 250 ┆ 3   ┆ 11111010 ┆ 00000011 ┆ 249    ┆ 11111001   │
        │ 66  ┆ 4   ┆ 01000010 ┆ 00000100 ┆ 70     ┆ 01000110   │
        └─────┴─────┴──────────┴──────────┴────────┴────────────┘
        """
        return self.__xor__(other)

    def is_in(
        self,
        other: Expr | Collection[Any] | Series,
        *,
        nulls_equal: bool = False,
    ) -> Expr:
        """
        Check if elements of this expression are present in the other Series.

        Parameters
        ----------
        other
            Series or sequence of primitive type.
        nulls_equal : bool, default False
            If True, treat null as a distinct value. Null values will not propagate.

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {"sets": [[1, 2, 3], [1, 2], [9, 10]], "optional_members": [1, 2, 3]}
        ... )
        >>> df.with_columns(contains=pl.col("optional_members").is_in("sets"))
        shape: (3, 3)
        ┌───────────┬──────────────────┬──────────┐
        │ sets      ┆ optional_members ┆ contains │
        │ ---       ┆ ---              ┆ ---      │
        │ list[i64] ┆ i64              ┆ bool     │
        ╞═══════════╪══════════════════╪══════════╡
        │ [1, 2, 3] ┆ 1                ┆ true     │
        │ [1, 2]    ┆ 2                ┆ true     │
        │ [9, 10]   ┆ 3                ┆ false    │
        └───────────┴──────────────────┴──────────┘
        """
        if isinstance(other, Collection) and not isinstance(other, str):
            if not isinstance(other, (Sequence, pl.Series, pl.DataFrame)):
                other = list(other)  # eg: set, frozenset, etc
            other = F.lit(pl.Series(other))._pyexpr
        else:
            other = parse_into_expression(other)
        return self._from_pyexpr(self._pyexpr.is_in(other, nulls_equal))

    def repeat_by(self, by: pl.Series | Expr | str | int) -> Expr:
        """
        Repeat the elements in this Series as specified in the given expression.

        The repeated 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
        -------
        Expr
            Expression of data type :class:`List`, where the inner data type is equal
            to the original data type.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": ["x", "y", "z"],
        ...         "n": [1, 2, 3],
        ...     }
        ... )
        >>> df.select(pl.col("a").repeat_by("n"))
        shape: (3, 1)
        ┌─────────────────┐
        │ a               │
        │ ---             │
        │ list[str]       │
        ╞═════════════════╡
        │ ["x"]           │
        │ ["y", "y"]      │
        │ ["z", "z", "z"] │
        └─────────────────┘
        """
        by = parse_into_expression(by)
        return self._from_pyexpr(self._pyexpr.repeat_by(by))

    def is_between(
        self,
        lower_bound: IntoExpr,
        upper_bound: IntoExpr,
        closed: ClosedInterval = "both",
    ) -> Expr:
        """
        Check if this expression is between the given lower and upper bounds.

        Parameters
        ----------
        lower_bound
            Lower bound value. Accepts expression input. Strings are parsed as column
            names, other non-expression inputs are parsed as literals.
        upper_bound
            Upper bound value. Accepts expression input. Strings are parsed as column
            names, other non-expression inputs are parsed as literals.
        closed : {'both', 'left', 'right', 'none'}
            Define which sides of the interval are closed (inclusive).

        Notes
        -----
        If the value of the `lower_bound` is greater than that of the `upper_bound`
        then the result will be False, as no value can satisfy the condition.

        Returns
        -------
        Expr
            Expression of data type :class:`Boolean`.

        Examples
        --------
        >>> df = pl.DataFrame({"num": [1, 2, 3, 4, 5]})
        >>> df.with_columns(pl.col("num").is_between(2, 4).alias("is_between"))
        shape: (5, 2)
        ┌─────┬────────────┐
        │ num ┆ is_between │
        │ --- ┆ ---        │
        │ i64 ┆ bool       │
        ╞═════╪════════════╡
        │ 1   ┆ false      │
        │ 2   ┆ true       │
        │ 3   ┆ true       │
        │ 4   ┆ true       │
        │ 5   ┆ false      │
        └─────┴────────────┘

        Use the `closed` argument to include or exclude the values at the bounds:

        >>> df.with_columns(
        ...     pl.col("num").is_between(2, 4, closed="left").alias("is_between")
        ... )
        shape: (5, 2)
        ┌─────┬────────────┐
        │ num ┆ is_between │
        │ --- ┆ ---        │
        │ i64 ┆ bool       │
        ╞═════╪════════════╡
        │ 1   ┆ false      │
        │ 2   ┆ true       │
        │ 3   ┆ true       │
        │ 4   ┆ false      │
        │ 5   ┆ false      │
        └─────┴────────────┘

        You can also use strings as well as numeric/temporal values (note: ensure that
        string literals are wrapped with `lit` so as not to conflate them with
        column names):

        >>> df = pl.DataFrame({"a": ["a", "b", "c", "d", "e"]})
        >>> df.with_columns(
        ...     pl.col("a")
        ...     .is_between(pl.lit("a"), pl.lit("c"), closed="both")
        ...     .alias("is_between")
        ... )
        shape: (5, 2)
        ┌─────┬────────────┐
        │ a   ┆ is_between │
        │ --- ┆ ---        │
        │ str ┆ bool       │
        ╞═════╪════════════╡
        │ a   ┆ true       │
        │ b   ┆ true       │
        │ c   ┆ true       │
        │ d   ┆ false      │
        │ e   ┆ false      │
        └─────┴────────────┘

        Use column expressions as lower/upper bounds, comparing to a literal value:

        >>> df = pl.DataFrame({"a": [1, 2, 3, 4, 5], "b": [5, 4, 3, 2, 1]})
        >>> df.with_columns(
        ...     pl.lit(3).is_between(pl.col("a"), pl.col("b")).alias("between_ab")
        ... )
        shape: (5, 3)
        ┌─────┬─────┬────────────┐
        │ a   ┆ b   ┆ between_ab │
        │ --- ┆ --- ┆ ---        │
        │ i64 ┆ i64 ┆ bool       │
        ╞═════╪═════╪════════════╡
        │ 1   ┆ 5   ┆ true       │
        │ 2   ┆ 4   ┆ true       │
        │ 3   ┆ 3   ┆ true       │
        │ 4   ┆ 2   ┆ false      │
        │ 5   ┆ 1   ┆ false      │
        └─────┴─────┴────────────┘
        """
        lower_bound = parse_into_expression(lower_bound)
        upper_bound = parse_into_expression(upper_bound)

        return self._from_pyexpr(
            self._pyexpr.is_between(lower_bound, upper_bound, closed)
        )

    def hash(
        self,
        seed: int = 0,
        seed_1: int | None = None,
        seed_2: int | None = None,
        seed_3: int | None = None,
    ) -> Expr:
        """
        Hash the elements in the selection.

        The hash value is of type `UInt64`.

        Parameters
        ----------
        seed
            Random seed parameter. Defaults to 0.
        seed_1
            Random seed parameter. Defaults to `seed` if not set.
        seed_2
            Random seed parameter. Defaults to `seed` if not set.
        seed_3
            Random seed parameter. Defaults to `seed` if not set.

        Notes
        -----
        This implementation of `hash` does not guarantee stable results
        across different Polars versions. Its stability is only guaranteed within a
        single version.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, 2, None],
        ...         "b": ["x", None, "z"],
        ...     }
        ... )
        >>> df.with_columns(pl.all().hash(10, 20, 30, 40))  # doctest: +IGNORE_RESULT
        shape: (3, 2)
        ┌──────────────────────┬──────────────────────┐
        │ a                    ┆ b                    │
        │ ---                  ┆ ---                  │
        │ u64                  ┆ u64                  │
        ╞══════════════════════╪══════════════════════╡
        │ 9774092659964970114  ┆ 13614470193936745724 │
        │ 1101441246220388612  ┆ 11638928888656214026 │
        │ 11638928888656214026 ┆ 13382926553367784577 │
        └──────────────────────┴──────────────────────┘
        """
        k0 = seed
        k1 = seed_1 if seed_1 is not None else seed
        k2 = seed_2 if seed_2 is not None else seed
        k3 = seed_3 if seed_3 is not None else seed
        return self._from_pyexpr(self._pyexpr.hash(k0, k1, k2, k3))

    def reinterpret(self, *, signed: bool = True) -> 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
            If True, reinterpret as `pl.Int64`. Otherwise, reinterpret as `pl.UInt64`.

        Examples
        --------
        >>> s = pl.Series("a", [1, 1, 2], dtype=pl.UInt64)
        >>> df = pl.DataFrame([s])
        >>> df.select(
        ...     [
        ...         pl.col("a").reinterpret(signed=True).alias("reinterpreted"),
        ...         pl.col("a").alias("original"),
        ...     ]
        ... )
        shape: (3, 2)
        ┌───────────────┬──────────┐
        │ reinterpreted ┆ original │
        │ ---           ┆ ---      │
        │ i64           ┆ u64      │
        ╞═══════════════╪══════════╡
        │ 1             ┆ 1        │
        │ 1             ┆ 1        │
        │ 2             ┆ 2        │
        └───────────────┴──────────┘
        """
        return self._from_pyexpr(self._pyexpr.reinterpret(signed))

    def inspect(self, fmt: str = "{}") -> Expr:
        """
        Print the value that this expression evaluates to and pass on the value.

        Examples
        --------
        >>> df = pl.DataFrame({"foo": [1, 1, 2]})
        >>> df.select(pl.col("foo").cum_sum().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: Series) -> Series:  # pragma: no cover
            print(fmt.format(s))
            return s

        return self.map_batches(inspect, return_dtype=None, agg_list=True)

    def interpolate(self, method: InterpolationMethod = "linear") -> Expr:
        """
        Fill null values using interpolation.

        Parameters
        ----------
        method : {'linear', 'nearest'}
            Interpolation method.

        Examples
        --------
        Fill null values using linear interpolation.

        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, None, 3],
        ...         "b": [1.0, float("nan"), 3.0],
        ...     }
        ... )
        >>> df.select(pl.all().interpolate())
        shape: (3, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ f64 ┆ f64 │
        ╞═════╪═════╡
        │ 1.0 ┆ 1.0 │
        │ 2.0 ┆ NaN │
        │ 3.0 ┆ 3.0 │
        └─────┴─────┘

        Fill null values using nearest interpolation.

        >>> df.select(pl.all().interpolate("nearest"))
        shape: (3, 2)
        ┌─────┬─────┐
        │ a   ┆ b   │
        │ --- ┆ --- │
        │ i64 ┆ f64 │
        ╞═════╪═════╡
        │ 1   ┆ 1.0 │
        │ 3   ┆ NaN │
        │ 3   ┆ 3.0 │
        └─────┴─────┘

        Regrid data to a new grid.

        >>> df_original_grid = pl.DataFrame(
        ...     {
        ...         "grid_points": [1, 3, 10],
        ...         "values": [2.0, 6.0, 20.0],
        ...     }
        ... )  # Interpolate from this to the new grid
        >>> df_new_grid = pl.DataFrame({"grid_points": range(1, 11)})
        >>> df_new_grid.join(
        ...     df_original_grid, on="grid_points", how="left", coalesce=True
        ... ).with_columns(pl.col("values").interpolate())
        shape: (10, 2)
        ┌─────────────┬────────┐
        │ grid_points ┆ values │
        │ ---         ┆ ---    │
        │ i64         ┆ f64    │
        ╞═════════════╪════════╡
        │ 1           ┆ 2.0    │
        │ 2           ┆ 4.0    │
        │ 3           ┆ 6.0    │
        │ 4           ┆ 8.0    │
        │ 5           ┆ 10.0   │
        │ 6           ┆ 12.0   │
        │ 7           ┆ 14.0   │
        │ 8           ┆ 16.0   │
        │ 9           ┆ 18.0   │
        │ 10          ┆ 20.0   │
        └─────────────┴────────┘
        """
        return self._from_pyexpr(self._pyexpr.interpolate(method))

    def interpolate_by(self, by: IntoExpr) -> Expr:
        """
        Fill null values using interpolation based on another column.

        Parameters
        ----------
        by
            Column to interpolate values based on.

        Examples
        --------
        Fill null values using linear interpolation.

        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [1, None, None, 3],
        ...         "b": [1, 2, 7, 8],
        ...     }
        ... )
        >>> df.with_columns(a_interpolated=pl.col("a").interpolate_by("b"))
        shape: (4, 3)
        ┌──────┬─────┬────────────────┐
        │ a    ┆ b   ┆ a_interpolated │
        │ ---  ┆ --- ┆ ---            │
        │ i64  ┆ i64 ┆ f64            │
        ╞══════╪═════╪════════════════╡
        │ 1    ┆ 1   ┆ 1.0            │
        │ null ┆ 2   ┆ 1.285714       │
        │ null ┆ 7   ┆ 2.714286       │
        │ 3    ┆ 8   ┆ 3.0            │
        └──────┴─────┴────────────────┘
        """
        by = parse_into_expression(by)
        return self._from_pyexpr(self._pyexpr.interpolate_by(by))

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_min_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        min_samples: int = 1,
        closed: ClosedInterval = "right",
    ) -> Expr:
        """
        Apply a rolling min based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        window_size
            The length of the window. Can be a dynamic temporal
            size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling min with the temporal windows closed on the right (default)

        >>> df_temporal.with_columns(
        ...     rolling_row_min=pl.col("index").rolling_min_by("date", window_size="2h")
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_min │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ u32             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0               │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0               │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 1               │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 2               │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 3               │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 19              │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 20              │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 21              │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 22              │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 23              │
        └───────┴─────────────────────┴─────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_min_by(by, window_size, min_samples, closed)
        )

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_max_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        min_samples: int = 1,
        closed: ClosedInterval = "right",
    ) -> Expr:
        """
        Apply a rolling max based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        window_size
            The length of the window. Can be a dynamic temporal
            size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling max with the temporal windows closed on the right (default)

        >>> df_temporal.with_columns(
        ...     rolling_row_max=pl.col("index").rolling_max_by("date", window_size="2h")
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_max │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ u32             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0               │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 1               │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 2               │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 3               │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 4               │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 20              │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 21              │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 22              │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 23              │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 24              │
        └───────┴─────────────────────┴─────────────────┘

        Compute the rolling max with the closure of windows on both sides

        >>> df_temporal.with_columns(
        ...     rolling_row_max=pl.col("index").rolling_max_by(
        ...         "date", window_size="2h", closed="both"
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_max │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ u32             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0               │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 1               │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 2               │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 3               │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 4               │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 20              │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 21              │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 22              │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 23              │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 24              │
        └───────┴─────────────────────┴─────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_max_by(by, window_size, min_samples, closed)
        )

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_mean_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        min_samples: int = 1,
        closed: ClosedInterval = "right",
    ) -> Expr:
        """
        Apply a rolling mean based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        window_size
            The length of the window. Can be a dynamic temporal
            size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling mean with the temporal windows closed on the right (default)

        >>> df_temporal.with_columns(
        ...     rolling_row_mean=pl.col("index").rolling_mean_by(
        ...         "date", window_size="2h"
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬──────────────────┐
        │ index ┆ date                ┆ rolling_row_mean │
        │ ---   ┆ ---                 ┆ ---              │
        │ u32   ┆ datetime[μs]        ┆ f64              │
        ╞═══════╪═════════════════════╪══════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0.0              │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.5              │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 1.5              │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 2.5              │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 3.5              │
        │ …     ┆ …                   ┆ …                │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 19.5             │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 20.5             │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 21.5             │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 22.5             │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 23.5             │
        └───────┴─────────────────────┴──────────────────┘

        Compute the rolling mean with the closure of windows on both sides

        >>> df_temporal.with_columns(
        ...     rolling_row_mean=pl.col("index").rolling_mean_by(
        ...         "date", window_size="2h", closed="both"
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬──────────────────┐
        │ index ┆ date                ┆ rolling_row_mean │
        │ ---   ┆ ---                 ┆ ---              │
        │ u32   ┆ datetime[μs]        ┆ f64              │
        ╞═══════╪═════════════════════╪══════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0.0              │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.5              │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 1.0              │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 2.0              │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 3.0              │
        │ …     ┆ …                   ┆ …                │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 19.0             │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 20.0             │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 21.0             │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 22.0             │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 23.0             │
        └───────┴─────────────────────┴──────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_mean_by(
                by,
                window_size,
                min_samples,
                closed,
            )
        )

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_sum_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        min_samples: int = 1,
        closed: ClosedInterval = "right",
    ) -> Expr:
        """
        Apply a rolling sum based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        window_size
            The length of the window. Can be a dynamic temporal
            size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling sum with the temporal windows closed on the right (default)

        >>> df_temporal.with_columns(
        ...     rolling_row_sum=pl.col("index").rolling_sum_by("date", window_size="2h")
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_sum │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ u32             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0               │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 1               │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 3               │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 5               │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 7               │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 39              │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 41              │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 43              │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 45              │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 47              │
        └───────┴─────────────────────┴─────────────────┘

        Compute the rolling sum with the closure of windows on both sides

        >>> df_temporal.with_columns(
        ...     rolling_row_sum=pl.col("index").rolling_sum_by(
        ...         "date", window_size="2h", closed="both"
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_sum │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ u32             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0               │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 1               │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 3               │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 6               │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 9               │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 57              │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 60              │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 63              │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 66              │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 69              │
        └───────┴─────────────────────┴─────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_sum_by(by, window_size, min_samples, closed)
        )

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_std_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        min_samples: int = 1,
        closed: ClosedInterval = "right",
        ddof: int = 1,
    ) -> Expr:
        """
        Compute a rolling standard deviation based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        window_size
            The length of the window. Can be a dynamic temporal
            size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.
        ddof
            "Delta Degrees of Freedom": The divisor for a length N window is N - ddof

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling std with the temporal windows closed on the right (default)

        >>> df_temporal.with_columns(
        ...     rolling_row_std=pl.col("index").rolling_std_by("date", window_size="2h")
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_std │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ f64             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ null            │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.707107        │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 0.707107        │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 0.707107        │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 0.707107        │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 0.707107        │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 0.707107        │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 0.707107        │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 0.707107        │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 0.707107        │
        └───────┴─────────────────────┴─────────────────┘

        Compute the rolling std with the closure of windows on both sides

        >>> df_temporal.with_columns(
        ...     rolling_row_std=pl.col("index").rolling_std_by(
        ...         "date", window_size="2h", closed="both"
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_std │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ f64             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ null            │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.707107        │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 1.0             │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 1.0             │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 1.0             │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 1.0             │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 1.0             │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 1.0             │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 1.0             │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 1.0             │
        └───────┴─────────────────────┴─────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_std_by(
                by,
                window_size,
                min_samples,
                closed,
                ddof,
            )
        )

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_var_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        min_samples: int = 1,
        closed: ClosedInterval = "right",
        ddof: int = 1,
    ) -> Expr:
        """
        Compute a rolling variance based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        window_size
            The length of the window. Can be a dynamic temporal
            size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.
        ddof
            "Delta Degrees of Freedom": The divisor for a length N window is N - ddof

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling var with the temporal windows closed on the right (default)

        >>> df_temporal.with_columns(
        ...     rolling_row_var=pl.col("index").rolling_var_by("date", window_size="2h")
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_var │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ f64             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ null            │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.5             │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 0.5             │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 0.5             │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 0.5             │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 0.5             │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 0.5             │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 0.5             │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 0.5             │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 0.5             │
        └───────┴─────────────────────┴─────────────────┘

        Compute the rolling var with the closure of windows on both sides

        >>> df_temporal.with_columns(
        ...     rolling_row_var=pl.col("index").rolling_var_by(
        ...         "date", window_size="2h", closed="both"
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬─────────────────┐
        │ index ┆ date                ┆ rolling_row_var │
        │ ---   ┆ ---                 ┆ ---             │
        │ u32   ┆ datetime[μs]        ┆ f64             │
        ╞═══════╪═════════════════════╪═════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ null            │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.5             │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 1.0             │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 1.0             │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 1.0             │
        │ …     ┆ …                   ┆ …               │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 1.0             │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 1.0             │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 1.0             │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 1.0             │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 1.0             │
        └───────┴─────────────────────┴─────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_var_by(
                by,
                window_size,
                min_samples,
                closed,
                ddof,
            )
        )

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_median_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        min_samples: int = 1,
        closed: ClosedInterval = "right",
    ) -> Expr:
        """
        Compute a rolling median based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        window_size
            The length of the window. Can be a dynamic temporal
            size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling median with the temporal windows closed on the right:

        >>> df_temporal.with_columns(
        ...     rolling_row_median=pl.col("index").rolling_median_by(
        ...         "date", window_size="2h"
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬────────────────────┐
        │ index ┆ date                ┆ rolling_row_median │
        │ ---   ┆ ---                 ┆ ---                │
        │ u32   ┆ datetime[μs]        ┆ f64                │
        ╞═══════╪═════════════════════╪════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0.0                │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.5                │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 1.5                │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 2.5                │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 3.5                │
        │ …     ┆ …                   ┆ …                  │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 19.5               │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 20.5               │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 21.5               │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 22.5               │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 23.5               │
        └───────┴─────────────────────┴────────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_median_by(by, window_size, min_samples, closed)
        )

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_quantile_by(
        self,
        by: IntoExpr,
        window_size: timedelta | str,
        *,
        quantile: float,
        interpolation: RollingInterpolationMethod = "nearest",
        min_samples: int = 1,
        closed: ClosedInterval = "right",
    ) -> Expr:
        """
        Compute a rolling quantile based on another column.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Given a `by` column `<t_0, t_1, ..., t_n>`, then `closed="right"`
        (the default) means the windows will be:

            - (t_0 - window_size, t_0]
            - (t_1 - window_size, t_1]
            - ...
            - (t_n - window_size, t_n]

        Parameters
        ----------
        by
            Should be ``DateTime``, ``Date``, ``UInt64``, ``UInt32``, ``Int64``,
            or ``Int32`` data type (note that the integral ones require using `'i'`
            in `window size`).
        quantile
            Quantile between 0.0 and 1.0.
        interpolation : {'nearest', 'higher', 'lower', 'midpoint', 'linear'}
            Interpolation method.
        window_size
            The length of the window. Can be a dynamic
            temporal size indicated by a timedelta or the following string language:

            - 1ns   (1 nanosecond)
            - 1us   (1 microsecond)
            - 1ms   (1 millisecond)
            - 1s    (1 second)
            - 1m    (1 minute)
            - 1h    (1 hour)
            - 1d    (1 calendar day)
            - 1w    (1 calendar week)
            - 1mo   (1 calendar month)
            - 1q    (1 calendar quarter)
            - 1y    (1 calendar year)
            - 1i    (1 index count)

            By "calendar day", we mean the corresponding time on the next day
            (which may not be 24 hours, due to daylight savings). Similarly for
            "calendar week", "calendar month", "calendar quarter", and
            "calendar year".
        min_samples
            The number of values in the window that should be non-null before computing
            a result.
        closed : {'left', 'right', 'both', 'none'}
            Define which sides of the temporal interval are closed (inclusive),
            defaults to `'right'`.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        Create a DataFrame with a datetime column and a row number column

        >>> from datetime import timedelta, datetime
        >>> start = datetime(2001, 1, 1)
        >>> stop = datetime(2001, 1, 2)
        >>> df_temporal = pl.DataFrame(
        ...     {"date": pl.datetime_range(start, stop, "1h", eager=True)}
        ... ).with_row_index()
        >>> df_temporal
        shape: (25, 2)
        ┌───────┬─────────────────────┐
        │ index ┆ date                │
        │ ---   ┆ ---                 │
        │ u32   ┆ datetime[μs]        │
        ╞═══════╪═════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 │
        │ 1     ┆ 2001-01-01 01:00:00 │
        │ 2     ┆ 2001-01-01 02:00:00 │
        │ 3     ┆ 2001-01-01 03:00:00 │
        │ 4     ┆ 2001-01-01 04:00:00 │
        │ …     ┆ …                   │
        │ 20    ┆ 2001-01-01 20:00:00 │
        │ 21    ┆ 2001-01-01 21:00:00 │
        │ 22    ┆ 2001-01-01 22:00:00 │
        │ 23    ┆ 2001-01-01 23:00:00 │
        │ 24    ┆ 2001-01-02 00:00:00 │
        └───────┴─────────────────────┘

        Compute the rolling quantile with the temporal windows closed on the right:

        >>> df_temporal.with_columns(
        ...     rolling_row_quantile=pl.col("index").rolling_quantile_by(
        ...         "date", window_size="2h", quantile=0.3
        ...     )
        ... )
        shape: (25, 3)
        ┌───────┬─────────────────────┬──────────────────────┐
        │ index ┆ date                ┆ rolling_row_quantile │
        │ ---   ┆ ---                 ┆ ---                  │
        │ u32   ┆ datetime[μs]        ┆ f64                  │
        ╞═══════╪═════════════════════╪══════════════════════╡
        │ 0     ┆ 2001-01-01 00:00:00 ┆ 0.0                  │
        │ 1     ┆ 2001-01-01 01:00:00 ┆ 0.0                  │
        │ 2     ┆ 2001-01-01 02:00:00 ┆ 1.0                  │
        │ 3     ┆ 2001-01-01 03:00:00 ┆ 2.0                  │
        │ 4     ┆ 2001-01-01 04:00:00 ┆ 3.0                  │
        │ …     ┆ …                   ┆ …                    │
        │ 20    ┆ 2001-01-01 20:00:00 ┆ 19.0                 │
        │ 21    ┆ 2001-01-01 21:00:00 ┆ 20.0                 │
        │ 22    ┆ 2001-01-01 22:00:00 ┆ 21.0                 │
        │ 23    ┆ 2001-01-01 23:00:00 ┆ 22.0                 │
        │ 24    ┆ 2001-01-02 00:00:00 ┆ 23.0                 │
        └───────┴─────────────────────┴──────────────────────┘
        """
        window_size = _prepare_rolling_by_window_args(window_size)
        by = parse_into_expression(by)
        return self._from_pyexpr(
            self._pyexpr.rolling_quantile_by(
                by,
                quantile,
                interpolation,
                window_size,
                min_samples,
                closed,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_min(
        self,
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = 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
        `weights` vector. The resulting values will be aggregated to their min.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_min=pl.col("A").rolling_min(window_size=2),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_min │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 1.0         │
        │ 3.0 ┆ 2.0         │
        │ 4.0 ┆ 3.0         │
        │ 5.0 ┆ 4.0         │
        │ 6.0 ┆ 5.0         │
        └─────┴─────────────┘

        Specify weights to multiply the values in the window with:

        >>> df.with_columns(
        ...     rolling_min=pl.col("A").rolling_min(
        ...         window_size=2, weights=[0.25, 0.75]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_min │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 0.25        │
        │ 3.0 ┆ 0.5         │
        │ 4.0 ┆ 0.75        │
        │ 5.0 ┆ 1.0         │
        │ 6.0 ┆ 1.25        │
        └─────┴─────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_min=pl.col("A").rolling_min(window_size=3, center=True),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_min │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 1.0         │
        │ 3.0 ┆ 2.0         │
        │ 4.0 ┆ 3.0         │
        │ 5.0 ┆ 4.0         │
        │ 6.0 ┆ null        │
        └─────┴─────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_min(
                window_size,
                weights,
                min_samples,
                center=center,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_max(
        self,
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = 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
        `weights` vector. The resulting values will be aggregated to their max.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_max=pl.col("A").rolling_max(window_size=2),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_max │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 2.0         │
        │ 3.0 ┆ 3.0         │
        │ 4.0 ┆ 4.0         │
        │ 5.0 ┆ 5.0         │
        │ 6.0 ┆ 6.0         │
        └─────┴─────────────┘

        Specify weights to multiply the values in the window with:

        >>> df.with_columns(
        ...     rolling_max=pl.col("A").rolling_max(
        ...         window_size=2, weights=[0.25, 0.75]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_max │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 1.5         │
        │ 3.0 ┆ 2.25        │
        │ 4.0 ┆ 3.0         │
        │ 5.0 ┆ 3.75        │
        │ 6.0 ┆ 4.5         │
        └─────┴─────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_max=pl.col("A").rolling_max(window_size=3, center=True),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_max │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 3.0         │
        │ 3.0 ┆ 4.0         │
        │ 4.0 ┆ 5.0         │
        │ 5.0 ┆ 6.0         │
        │ 6.0 ┆ null        │
        └─────┴─────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_max(
                window_size,
                weights,
                min_samples,
                center,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_mean(
        self,
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = 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
        `weights` vector. The resulting values will be aggregated to their mean.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_mean=pl.col("A").rolling_mean(window_size=2),
        ... )
        shape: (6, 2)
        ┌─────┬──────────────┐
        │ A   ┆ rolling_mean │
        │ --- ┆ ---          │
        │ f64 ┆ f64          │
        ╞═════╪══════════════╡
        │ 1.0 ┆ null         │
        │ 2.0 ┆ 1.5          │
        │ 3.0 ┆ 2.5          │
        │ 4.0 ┆ 3.5          │
        │ 5.0 ┆ 4.5          │
        │ 6.0 ┆ 5.5          │
        └─────┴──────────────┘

        Specify weights to multiply the values in the window with:

        >>> df.with_columns(
        ...     rolling_mean=pl.col("A").rolling_mean(
        ...         window_size=2, weights=[0.25, 0.75]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬──────────────┐
        │ A   ┆ rolling_mean │
        │ --- ┆ ---          │
        │ f64 ┆ f64          │
        ╞═════╪══════════════╡
        │ 1.0 ┆ null         │
        │ 2.0 ┆ 1.75         │
        │ 3.0 ┆ 2.75         │
        │ 4.0 ┆ 3.75         │
        │ 5.0 ┆ 4.75         │
        │ 6.0 ┆ 5.75         │
        └─────┴──────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_mean=pl.col("A").rolling_mean(window_size=3, center=True),
        ... )
        shape: (6, 2)
        ┌─────┬──────────────┐
        │ A   ┆ rolling_mean │
        │ --- ┆ ---          │
        │ f64 ┆ f64          │
        ╞═════╪══════════════╡
        │ 1.0 ┆ null         │
        │ 2.0 ┆ 2.0          │
        │ 3.0 ┆ 3.0          │
        │ 4.0 ┆ 4.0          │
        │ 5.0 ┆ 5.0          │
        │ 6.0 ┆ null         │
        └─────┴──────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_mean(
                window_size,
                weights,
                min_samples,
                center,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_sum(
        self,
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = 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
        `weights` vector. The resulting values will be aggregated to their sum.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_sum=pl.col("A").rolling_sum(window_size=2),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_sum │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 3.0         │
        │ 3.0 ┆ 5.0         │
        │ 4.0 ┆ 7.0         │
        │ 5.0 ┆ 9.0         │
        │ 6.0 ┆ 11.0        │
        └─────┴─────────────┘

        Specify weights to multiply the values in the window with:

        >>> df.with_columns(
        ...     rolling_sum=pl.col("A").rolling_sum(
        ...         window_size=2, weights=[0.25, 0.75]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_sum │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 1.75        │
        │ 3.0 ┆ 2.75        │
        │ 4.0 ┆ 3.75        │
        │ 5.0 ┆ 4.75        │
        │ 6.0 ┆ 5.75        │
        └─────┴─────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_sum=pl.col("A").rolling_sum(window_size=3, center=True),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_sum │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 6.0         │
        │ 3.0 ┆ 9.0         │
        │ 4.0 ┆ 12.0        │
        │ 5.0 ┆ 15.0        │
        │ 6.0 ┆ null        │
        └─────┴─────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_sum(
                window_size,
                weights,
                min_samples,
                center,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_std(
        self,
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = None,
        center: bool = False,
        ddof: int = 1,
    ) -> Expr:
        """
        Compute a rolling standard deviation.

        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
        `weights` vector. The resulting values will be aggregated to their std.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.
        ddof
            "Delta Degrees of Freedom": The divisor for a length N window is N - ddof

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_std=pl.col("A").rolling_std(window_size=2),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_std │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 0.707107    │
        │ 3.0 ┆ 0.707107    │
        │ 4.0 ┆ 0.707107    │
        │ 5.0 ┆ 0.707107    │
        │ 6.0 ┆ 0.707107    │
        └─────┴─────────────┘

        Specify weights to multiply the values in the window with:

        >>> df.with_columns(
        ...     rolling_std=pl.col("A").rolling_std(
        ...         window_size=2, weights=[0.25, 0.75]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_std │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 0.433013    │
        │ 3.0 ┆ 0.433013    │
        │ 4.0 ┆ 0.433013    │
        │ 5.0 ┆ 0.433013    │
        │ 6.0 ┆ 0.433013    │
        └─────┴─────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_std=pl.col("A").rolling_std(window_size=3, center=True),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_std │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 1.0         │
        │ 3.0 ┆ 1.0         │
        │ 4.0 ┆ 1.0         │
        │ 5.0 ┆ 1.0         │
        │ 6.0 ┆ null        │
        └─────┴─────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_std(
                window_size,
                weights,
                min_samples,
                center=center,
                ddof=ddof,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_var(
        self,
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = None,
        center: bool = False,
        ddof: int = 1,
    ) -> 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
        `weights` vector. The resulting values will be aggregated to their var.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.
        ddof
            "Delta Degrees of Freedom": The divisor for a length N window is N - ddof

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_var=pl.col("A").rolling_var(window_size=2),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_var │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 0.5         │
        │ 3.0 ┆ 0.5         │
        │ 4.0 ┆ 0.5         │
        │ 5.0 ┆ 0.5         │
        │ 6.0 ┆ 0.5         │
        └─────┴─────────────┘

        Specify weights to multiply the values in the window with:

        >>> df.with_columns(
        ...     rolling_var=pl.col("A").rolling_var(
        ...         window_size=2, weights=[0.25, 0.75]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_var │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 0.1875      │
        │ 3.0 ┆ 0.1875      │
        │ 4.0 ┆ 0.1875      │
        │ 5.0 ┆ 0.1875      │
        │ 6.0 ┆ 0.1875      │
        └─────┴─────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_var=pl.col("A").rolling_var(window_size=3, center=True),
        ... )
        shape: (6, 2)
        ┌─────┬─────────────┐
        │ A   ┆ rolling_var │
        │ --- ┆ ---         │
        │ f64 ┆ f64         │
        ╞═════╪═════════════╡
        │ 1.0 ┆ null        │
        │ 2.0 ┆ 1.0         │
        │ 3.0 ┆ 1.0         │
        │ 4.0 ┆ 1.0         │
        │ 5.0 ┆ 1.0         │
        │ 6.0 ┆ null        │
        └─────┴─────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_var(
                window_size,
                weights,
                min_samples,
                center=center,
                ddof=ddof,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_median(
        self,
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = None,
        center: bool = False,
    ) -> Expr:
        """
        Compute a rolling median.

        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
        `weights` vector. The resulting values will be aggregated to their median.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_median=pl.col("A").rolling_median(window_size=2),
        ... )
        shape: (6, 2)
        ┌─────┬────────────────┐
        │ A   ┆ rolling_median │
        │ --- ┆ ---            │
        │ f64 ┆ f64            │
        ╞═════╪════════════════╡
        │ 1.0 ┆ null           │
        │ 2.0 ┆ 1.5            │
        │ 3.0 ┆ 2.5            │
        │ 4.0 ┆ 3.5            │
        │ 5.0 ┆ 4.5            │
        │ 6.0 ┆ 5.5            │
        └─────┴────────────────┘

        Specify weights for the values in each window:

        >>> df.with_columns(
        ...     rolling_median=pl.col("A").rolling_median(
        ...         window_size=2, weights=[0.25, 0.75]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬────────────────┐
        │ A   ┆ rolling_median │
        │ --- ┆ ---            │
        │ f64 ┆ f64            │
        ╞═════╪════════════════╡
        │ 1.0 ┆ null           │
        │ 2.0 ┆ 1.5            │
        │ 3.0 ┆ 2.5            │
        │ 4.0 ┆ 3.5            │
        │ 5.0 ┆ 4.5            │
        │ 6.0 ┆ 5.5            │
        └─────┴────────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_median=pl.col("A").rolling_median(window_size=3, center=True),
        ... )
        shape: (6, 2)
        ┌─────┬────────────────┐
        │ A   ┆ rolling_median │
        │ --- ┆ ---            │
        │ f64 ┆ f64            │
        ╞═════╪════════════════╡
        │ 1.0 ┆ null           │
        │ 2.0 ┆ 2.0            │
        │ 3.0 ┆ 3.0            │
        │ 4.0 ┆ 4.0            │
        │ 5.0 ┆ 5.0            │
        │ 6.0 ┆ null           │
        └─────┴────────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_median(
                window_size,
                weights,
                min_samples,
                center=center,
            )
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_quantile(
        self,
        quantile: float,
        interpolation: RollingInterpolationMethod = "nearest",
        window_size: int = 2,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = None,
        center: bool = False,
    ) -> Expr:
        """
        Compute a rolling quantile.

        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
        `weights` vector. The resulting values will be aggregated to their quantile.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        quantile
            Quantile between 0.0 and 1.0.
        interpolation : {'nearest', 'higher', 'lower', 'midpoint', 'linear'}
            Interpolation method.
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.

        Notes
        -----
        If you want to compute multiple aggregation statistics over the same dynamic
        window, consider using `rolling` - this method can cache the window size
        computation.

        Examples
        --------
        >>> df = pl.DataFrame({"A": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]})
        >>> df.with_columns(
        ...     rolling_quantile=pl.col("A").rolling_quantile(
        ...         quantile=0.25, window_size=4
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬──────────────────┐
        │ A   ┆ rolling_quantile │
        │ --- ┆ ---              │
        │ f64 ┆ f64              │
        ╞═════╪══════════════════╡
        │ 1.0 ┆ null             │
        │ 2.0 ┆ null             │
        │ 3.0 ┆ null             │
        │ 4.0 ┆ 2.0              │
        │ 5.0 ┆ 3.0              │
        │ 6.0 ┆ 4.0              │
        └─────┴──────────────────┘

        Specify weights for the values in each window:

        >>> df.with_columns(
        ...     rolling_quantile=pl.col("A").rolling_quantile(
        ...         quantile=0.25, window_size=4, weights=[0.2, 0.4, 0.4, 0.2]
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬──────────────────┐
        │ A   ┆ rolling_quantile │
        │ --- ┆ ---              │
        │ f64 ┆ f64              │
        ╞═════╪══════════════════╡
        │ 1.0 ┆ null             │
        │ 2.0 ┆ null             │
        │ 3.0 ┆ null             │
        │ 4.0 ┆ 2.0              │
        │ 5.0 ┆ 3.0              │
        │ 6.0 ┆ 4.0              │
        └─────┴──────────────────┘

        Specify weights and interpolation method

        >>> df.with_columns(
        ...     rolling_quantile=pl.col("A").rolling_quantile(
        ...         quantile=0.25,
        ...         window_size=4,
        ...         weights=[0.2, 0.4, 0.4, 0.2],
        ...         interpolation="linear",
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬──────────────────┐
        │ A   ┆ rolling_quantile │
        │ --- ┆ ---              │
        │ f64 ┆ f64              │
        ╞═════╪══════════════════╡
        │ 1.0 ┆ null             │
        │ 2.0 ┆ null             │
        │ 3.0 ┆ null             │
        │ 4.0 ┆ 1.625            │
        │ 5.0 ┆ 2.625            │
        │ 6.0 ┆ 3.625            │
        └─────┴──────────────────┘

        Center the values in the window

        >>> df.with_columns(
        ...     rolling_quantile=pl.col("A").rolling_quantile(
        ...         quantile=0.2, window_size=5, center=True
        ...     ),
        ... )
        shape: (6, 2)
        ┌─────┬──────────────────┐
        │ A   ┆ rolling_quantile │
        │ --- ┆ ---              │
        │ f64 ┆ f64              │
        ╞═════╪══════════════════╡
        │ 1.0 ┆ null             │
        │ 2.0 ┆ null             │
        │ 3.0 ┆ 2.0              │
        │ 4.0 ┆ 3.0              │
        │ 5.0 ┆ null             │
        │ 6.0 ┆ null             │
        └─────┴──────────────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.rolling_quantile(
                quantile,
                interpolation,
                window_size,
                weights,
                min_samples,
                center=center,
            )
        )

    @unstable()
    def rolling_skew(self, window_size: int, *, bias: bool = True) -> Expr:
        """
        Compute a rolling skew.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        The window at a given row will include the row itself, and the `window_size - 1`
        elements before it.

        Parameters
        ----------
        window_size
            Integer size of the rolling window.
        bias
            If False, the calculations are corrected for statistical bias.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 4, 2, 9]})
        >>> df.select(pl.col("a").rolling_skew(3))
        shape: (4, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ null     │
        │ null     │
        │ 0.381802 │
        │ 0.47033  │
        └──────────┘

        Note how the values match the following:

        >>> pl.Series([1, 4, 2]).skew(), pl.Series([4, 2, 9]).skew()
        (0.38180177416060584, 0.47033046033698594)
        """
        return self._from_pyexpr(self._pyexpr.rolling_skew(window_size, bias))

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def rolling_map(
        self,
        function: Callable[[Series], Any],
        window_size: int,
        weights: list[float] | None = None,
        *,
        min_samples: int | None = None,
        center: bool = False,
    ) -> Expr:
        """
        Compute a custom rolling window function.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Parameters
        ----------
        function
            Custom aggregation function.
        window_size
            The length of the window in number of elements.
        weights
            An optional slice with the same length as the window that will be multiplied
            elementwise with the values in the window.
        min_samples
            The number of values in the window that should be non-null before computing
            a result. If set to `None` (default), it will be set equal to `window_size`.
        center
            Set the labels at the center of the window.

        Warnings
        --------
        Computing custom functions is extremely slow. Use specialized rolling
        functions such as :func:`Expr.rolling_sum` if at all possible.

        Examples
        --------
        >>> from numpy import nansum
        >>> df = pl.DataFrame({"a": [11.0, 2.0, 9.0, float("nan"), 8.0]})
        >>> df.select(pl.col("a").rolling_map(nansum, window_size=3))
        shape: (5, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ f64  │
        ╞══════╡
        │ null │
        │ null │
        │ 22.0 │
        │ 11.0 │
        │ 17.0 │
        └──────┘
        """
        if min_samples is None:
            min_samples = window_size
        return self._from_pyexpr(
            self._pyexpr.rolling_map(
                function, window_size, weights, min_samples, center
            )
        )

    def abs(self) -> Expr:
        """
        Compute absolute values.

        Same as `abs(expr)`.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "A": [-1.0, 0.0, 1.0, 2.0],
        ...     }
        ... )
        >>> df.select(pl.col("A").abs())
        shape: (4, 1)
        ┌─────┐
        │ A   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        │ 0.0 │
        │ 1.0 │
        │ 2.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.abs())

    def rank(
        self,
        method: RankMethod = "average",
        *,
        descending: bool = False,
        seed: int | None = None,
    ) -> Expr:
        """
        Assign ranks to data, dealing with ties appropriately.

        Parameters
        ----------
        method : {'average', 'min', 'max', 'dense', 'ordinal', 'random'}
            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 the Series.
            - 'random' : Like 'ordinal', but the rank for ties is not dependent
              on the order that the values occur in the Series.
        descending
            Rank in descending order.
        seed
            If `method="random"`, use this as seed.

        Examples
        --------
        The 'average' method:

        >>> df = pl.DataFrame({"a": [3, 6, 1, 1, 6]})
        >>> df.select(pl.col("a").rank())
        shape: (5, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 3.0 │
        │ 4.5 │
        │ 1.5 │
        │ 1.5 │
        │ 4.5 │
        └─────┘

        The 'ordinal' method:

        >>> df = pl.DataFrame({"a": [3, 6, 1, 1, 6]})
        >>> df.select(pl.col("a").rank("ordinal"))
        shape: (5, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 3   │
        │ 4   │
        │ 1   │
        │ 2   │
        │ 5   │
        └─────┘

        Use 'rank' with 'over' to rank within groups:

        >>> df = pl.DataFrame({"a": [1, 1, 2, 2, 2], "b": [6, 7, 5, 14, 11]})
        >>> df.with_columns(pl.col("b").rank().over("a").alias("rank"))
        shape: (5, 3)
        ┌─────┬─────┬──────┐
        │ a   ┆ b   ┆ rank │
        │ --- ┆ --- ┆ ---  │
        │ i64 ┆ i64 ┆ f64  │
        ╞═════╪═════╪══════╡
        │ 1   ┆ 6   ┆ 1.0  │
        │ 1   ┆ 7   ┆ 2.0  │
        │ 2   ┆ 5   ┆ 1.0  │
        │ 2   ┆ 14  ┆ 3.0  │
        │ 2   ┆ 11  ┆ 2.0  │
        └─────┴─────┴──────┘

        Divide by the length or number of non-null values
        to compute the percentile rank.

        >>> df = pl.DataFrame({"a": [6, 7, None, 14, 11]})
        >>> df.with_columns(
        ...     pct=pl.col("a").rank() / pl.len(),
        ...     pct_valid=pl.col("a").rank() / pl.count("a"),
        ... )
        shape: (5, 3)
        ┌──────┬──────┬───────────┐
        │ a    ┆ pct  ┆ pct_valid │
        │ ---  ┆ ---  ┆ ---       │
        │ i64  ┆ f64  ┆ f64       │
        ╞══════╪══════╪═══════════╡
        │ 6    ┆ 0.2  ┆ 0.25      │
        │ 7    ┆ 0.4  ┆ 0.5       │
        │ null ┆ null ┆ null      │
        │ 14   ┆ 0.8  ┆ 1.0       │
        │ 11   ┆ 0.6  ┆ 0.75      │
        └──────┴──────┴───────────┘

        """
        return self._from_pyexpr(self._pyexpr.rank(method, descending, seed))

    def diff(
        self, n: int | IntoExpr = 1, null_behavior: NullBehavior = "ignore"
    ) -> Expr:
        """
        Calculate the first discrete difference between shifted items.

        Parameters
        ----------
        n
            Number of slots to shift.
        null_behavior : {'ignore', 'drop'}
            How to handle null values.

        Examples
        --------
        >>> df = pl.DataFrame({"int": [20, 10, 30, 25, 35]})
        >>> df.with_columns(change=pl.col("int").diff())
        shape: (5, 2)
        ┌─────┬────────┐
        │ int ┆ change │
        │ --- ┆ ---    │
        │ i64 ┆ i64    │
        ╞═════╪════════╡
        │ 20  ┆ null   │
        │ 10  ┆ -10    │
        │ 30  ┆ 20     │
        │ 25  ┆ -5     │
        │ 35  ┆ 10     │
        └─────┴────────┘

        >>> df.with_columns(change=pl.col("int").diff(n=2))
        shape: (5, 2)
        ┌─────┬────────┐
        │ int ┆ change │
        │ --- ┆ ---    │
        │ i64 ┆ i64    │
        ╞═════╪════════╡
        │ 20  ┆ null   │
        │ 10  ┆ null   │
        │ 30  ┆ 10     │
        │ 25  ┆ 15     │
        │ 35  ┆ 5      │
        └─────┴────────┘

        >>> df.select(pl.col("int").diff(n=2, null_behavior="drop").alias("diff"))
        shape: (3, 1)
        ┌──────┐
        │ diff │
        │ ---  │
        │ i64  │
        ╞══════╡
        │ 10   │
        │ 15   │
        │ 5    │
        └──────┘
        """
        n = parse_into_expression(n)
        return self._from_pyexpr(self._pyexpr.diff(n, null_behavior))

    def pct_change(self, n: int | IntoExprColumn = 1) -> Expr:
        """
        Computes percentage change between values.

        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.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "a": [10, 11, 12, None, 12],
        ...     }
        ... )
        >>> df.with_columns(pl.col("a").pct_change().alias("pct_change"))
        shape: (5, 2)
        ┌──────┬────────────┐
        │ a    ┆ pct_change │
        │ ---  ┆ ---        │
        │ i64  ┆ f64        │
        ╞══════╪════════════╡
        │ 10   ┆ null       │
        │ 11   ┆ 0.1        │
        │ 12   ┆ 0.090909   │
        │ null ┆ 0.0        │
        │ 12   ┆ 0.0        │
        └──────┴────────────┘
        """
        n = parse_into_expression(n)
        return self._from_pyexpr(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, 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}}

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3, 2, 1]})
        >>> df.select(pl.col("a").skew())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.343622 │
        └──────────┘
        """
        return self._from_pyexpr(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, the calculations are corrected for statistical bias.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3, 2, 1]})
        >>> df.select(pl.col("a").kurtosis())
        shape: (1, 1)
        ┌───────────┐
        │ a         │
        │ ---       │
        │ f64       │
        ╞═══════════╡
        │ -1.153061 │
        └───────────┘
        """
        return self._from_pyexpr(self._pyexpr.kurtosis(fisher, bias))

    def clip(
        self,
        lower_bound: NumericLiteral | TemporalLiteral | IntoExprColumn | None = None,
        upper_bound: NumericLiteral | TemporalLiteral | IntoExprColumn | None = None,
    ) -> Expr:
        """
        Set values outside the given boundaries to the boundary value.

        Parameters
        ----------
        lower_bound
            Lower bound. Accepts expression input. Non-expression inputs are
            parsed as literals. Strings are parsed as column names.
        upper_bound
            Upper bound. Accepts expression input. Non-expression inputs are
            parsed as literals. Strings are parsed as column names.

        See Also
        --------
        when

        Notes
        -----
        This method only works for numeric and temporal columns. To clip other data
        types, consider writing a `when-then-otherwise` expression. See :func:`when`.

        Examples
        --------
        Specifying both a lower and upper bound:

        >>> df = pl.DataFrame({"a": [-50, 5, 50, None]})
        >>> df.with_columns(clip=pl.col("a").clip(1, 10))
        shape: (4, 2)
        ┌──────┬──────┐
        │ a    ┆ clip │
        │ ---  ┆ ---  │
        │ i64  ┆ i64  │
        ╞══════╪══════╡
        │ -50  ┆ 1    │
        │ 5    ┆ 5    │
        │ 50   ┆ 10   │
        │ null ┆ null │
        └──────┴──────┘

        Specifying only a single bound:

        >>> df.with_columns(clip=pl.col("a").clip(upper_bound=10))
        shape: (4, 2)
        ┌──────┬──────┐
        │ a    ┆ clip │
        │ ---  ┆ ---  │
        │ i64  ┆ i64  │
        ╞══════╪══════╡
        │ -50  ┆ -50  │
        │ 5    ┆ 5    │
        │ 50   ┆ 10   │
        │ null ┆ null │
        └──────┴──────┘

        Using columns as bounds:

        >>> df = pl.DataFrame(
        ...     {"a": [-50, 5, 50, None], "low": [10, 1, 0, 0], "up": [20, 4, 3, 2]}
        ... )
        >>> df.with_columns(clip=pl.col("a").clip("low", "up"))
        shape: (4, 4)
        ┌──────┬─────┬─────┬──────┐
        │ a    ┆ low ┆ up  ┆ clip │
        │ ---  ┆ --- ┆ --- ┆ ---  │
        │ i64  ┆ i64 ┆ i64 ┆ i64  │
        ╞══════╪═════╪═════╪══════╡
        │ -50  ┆ 10  ┆ 20  ┆ 10   │
        │ 5    ┆ 1   ┆ 4   ┆ 4    │
        │ 50   ┆ 0   ┆ 3   ┆ 3    │
        │ null ┆ 0   ┆ 2   ┆ null │
        └──────┴─────┴─────┴──────┘
        """
        if lower_bound is not None:
            lower_bound = parse_into_expression(lower_bound)
        if upper_bound is not None:
            upper_bound = parse_into_expression(upper_bound)
        return self._from_pyexpr(self._pyexpr.clip(lower_bound, upper_bound))

    def lower_bound(self) -> Expr:
        """
        Calculate the lower bound.

        Returns a unit Series with the lowest value possible for the dtype of this
        expression.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3, 2, 1]})
        >>> df.select(pl.col("a").lower_bound())
        shape: (1, 1)
        ┌──────────────────────┐
        │ a                    │
        │ ---                  │
        │ i64                  │
        ╞══════════════════════╡
        │ -9223372036854775808 │
        └──────────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.lower_bound())

    def upper_bound(self) -> Expr:
        """
        Calculate the upper bound.

        Returns a unit Series with the highest value possible for the dtype of this
        expression.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3, 2, 1]})
        >>> df.select(pl.col("a").upper_bound())
        shape: (1, 1)
        ┌─────────────────────┐
        │ a                   │
        │ ---                 │
        │ i64                 │
        ╞═════════════════════╡
        │ 9223372036854775807 │
        └─────────────────────┘
        """
        return self._from_pyexpr(self._pyexpr.upper_bound())

    def sign(self) -> Expr:
        """
        Compute the element-wise sign function on numeric types.

        The returned value is computed as follows:

        * -1 if x < 0.
        *  1 if x > 0.
        *  x otherwise (typically 0, but could be NaN if the input is).

        Null values are preserved as-is, and the dtype of the input is preserved.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-9.0, -0.0, 0.0, 4.0, float("nan"), None]})
        >>> df.select(pl.col.a.sign())
        shape: (6, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ f64  │
        ╞══════╡
        │ -1.0 │
        │ -0.0 │
        │ 0.0  │
        │ 1.0  │
        │ NaN  │
        │ null │
        └──────┘
        """
        return self._from_pyexpr(self._pyexpr.sign())

    def sin(self) -> Expr:
        """
        Compute the element-wise value for the sine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.0]})
        >>> df.select(pl.col("a").sin())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 0.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.sin())

    def cos(self) -> Expr:
        """
        Compute the element-wise value for the cosine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.0]})
        >>> df.select(pl.col("a").cos())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 1.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.cos())

    def tan(self) -> Expr:
        """
        Compute the element-wise value for the tangent.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").tan().round(2))
        shape: (1, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ f64  │
        ╞══════╡
        │ 1.56 │
        └──────┘
        """
        return self._from_pyexpr(self._pyexpr.tan())

    def cot(self) -> Expr:
        """
        Compute the element-wise value for the cotangent.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").cot().round(2))
        shape: (1, 1)
        ┌──────┐
        │ a    │
        │ ---  │
        │ f64  │
        ╞══════╡
        │ 0.64 │
        └──────┘
        """
        return self._from_pyexpr(self._pyexpr.cot())

    def arcsin(self) -> Expr:
        """
        Compute the element-wise value for the inverse sine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").arcsin())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.570796 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.arcsin())

    def arccos(self) -> Expr:
        """
        Compute the element-wise value for the inverse cosine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [0.0]})
        >>> df.select(pl.col("a").arccos())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.570796 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.arccos())

    def arctan(self) -> Expr:
        """
        Compute the element-wise value for the inverse tangent.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").arctan())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.785398 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.arctan())

    def sinh(self) -> Expr:
        """
        Compute the element-wise value for the hyperbolic sine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").sinh())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.175201 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.sinh())

    def cosh(self) -> Expr:
        """
        Compute the element-wise value for the hyperbolic cosine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").cosh())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.543081 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.cosh())

    def tanh(self) -> Expr:
        """
        Compute the element-wise value for the hyperbolic tangent.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").tanh())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.761594 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.tanh())

    def arcsinh(self) -> Expr:
        """
        Compute the element-wise value for the inverse hyperbolic sine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").arcsinh())
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.881374 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.arcsinh())

    def arccosh(self) -> Expr:
        """
        Compute the element-wise value for the inverse hyperbolic cosine.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").arccosh())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ 0.0 │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.arccosh())

    def arctanh(self) -> Expr:
        """
        Compute the element-wise value for the inverse hyperbolic tangent.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1.0]})
        >>> df.select(pl.col("a").arctanh())
        shape: (1, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ f64 │
        ╞═════╡
        │ inf │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.arctanh())

    def degrees(self) -> Expr:
        """
        Convert from radians to degrees.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> import math
        >>> df = pl.DataFrame({"a": [x * math.pi for x in range(-4, 5)]})
        >>> df.select(pl.col("a").degrees())
        shape: (9, 1)
        ┌────────┐
        │ a      │
        │ ---    │
        │ f64    │
        ╞════════╡
        │ -720.0 │
        │ -540.0 │
        │ -360.0 │
        │ -180.0 │
        │ 0.0    │
        │ 180.0  │
        │ 360.0  │
        │ 540.0  │
        │ 720.0  │
        └────────┘
        """
        return self._from_pyexpr(self._pyexpr.degrees())

    def radians(self) -> Expr:
        """
        Convert from degrees to radians.

        Returns
        -------
        Expr
            Expression of data type :class:`Float64`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [-720, -540, -360, -180, 0, 180, 360, 540, 720]})
        >>> df.select(pl.col("a").radians())
        shape: (9, 1)
        ┌────────────┐
        │ a          │
        │ ---        │
        │ f64        │
        ╞════════════╡
        │ -12.566371 │
        │ -9.424778  │
        │ -6.283185  │
        │ -3.141593  │
        │ 0.0        │
        │ 3.141593   │
        │ 6.283185   │
        │ 9.424778   │
        │ 12.566371  │
        └────────────┘
        """
        return self._from_pyexpr(self._pyexpr.radians())

    def reshape(self, dimensions: tuple[int, ...]) -> Expr:
        """
        Reshape this Expr to a flat column or an Array column.

        Parameters
        ----------
        dimensions
            Tuple of the dimension sizes. If a -1 is used in any of the dimensions, that
            dimension is inferred.

        Returns
        -------
        Expr
            If a single dimension is given, results in an expression of the original
            data type.
            If a multiple dimensions are given, results in an expression of data type
            :class:`Array` with shape `dimensions`.

        Examples
        --------
        >>> df = pl.DataFrame({"foo": [1, 2, 3, 4, 5, 6, 7, 8, 9]})
        >>> square = df.select(pl.col("foo").reshape((3, 3)))
        >>> square
        shape: (3, 1)
        ┌───────────────┐
        │ foo           │
        │ ---           │
        │ array[i64, 3] │
        ╞═══════════════╡
        │ [1, 2, 3]     │
        │ [4, 5, 6]     │
        │ [7, 8, 9]     │
        └───────────────┘
        >>> square.select(pl.col("foo").reshape((9,)))
        shape: (9, 1)
        ┌─────┐
        │ foo │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 1   │
        │ 2   │
        │ 3   │
        │ 4   │
        │ 5   │
        │ 6   │
        │ 7   │
        │ 8   │
        │ 9   │
        └─────┘

        See Also
        --------
        Expr.list.explode : Explode a list column.
        """
        return self._from_pyexpr(self._pyexpr.reshape(dimensions))

    def shuffle(self, seed: int | None = None) -> Expr:
        """
        Shuffle the contents of this expression.

        Note this is shuffled independently of any other column or Expression. If you
        want each row to stay the same use df.sample(shuffle=True)

        Parameters
        ----------
        seed
            Seed for the random number generator. If set to None (default), a
            random seed is generated each time the shuffle is called.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").shuffle(seed=1))
        shape: (3, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 2   │
        │ 1   │
        │ 3   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.shuffle(seed))

    def sample(
        self,
        n: int | IntoExprColumn | None = None,
        *,
        fraction: float | IntoExprColumn | None = None,
        with_replacement: bool = False,
        shuffle: bool = False,
        seed: int | None = None,
    ) -> Expr:
        """
        Sample from this expression.

        Parameters
        ----------
        n
            Number of items to return. Cannot be used with `fraction`. Defaults to 1 if
            `fraction` is None.
        fraction
            Fraction of items to return. Cannot be used with `n`.
        with_replacement
            Allow values to be sampled more than once.
        shuffle
            Shuffle the order of sampled data points.
        seed
            Seed for the random number generator. If set to None (default), a
            random seed is generated for each sample operation.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").sample(fraction=1.0, with_replacement=True, seed=1))
        shape: (3, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 3   │
        │ 1   │
        │ 1   │
        └─────┘
        """
        if n is not None and fraction is not None:
            msg = "cannot specify both `n` and `fraction`"
            raise ValueError(msg)

        if fraction is not None:
            fraction = parse_into_expression(fraction)
            return self._from_pyexpr(
                self._pyexpr.sample_frac(fraction, with_replacement, shuffle, seed)
            )

        if n is None:
            n = 1
        n = parse_into_expression(n)
        return self._from_pyexpr(
            self._pyexpr.sample_n(n, with_replacement, shuffle, seed)
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def ewm_mean(
        self,
        *,
        com: float | None = None,
        span: float | None = None,
        half_life: float | None = None,
        alpha: float | None = None,
        adjust: bool = True,
        min_samples: int = 1,
        ignore_nulls: bool = False,
    ) -> Expr:
        r"""
        Compute exponentially-weighted moving average.

        Parameters
        ----------
        com
            Specify decay in terms of center of mass, :math:`\gamma`, with

                .. math::
                    \alpha = \frac{1}{1 + \gamma} \; \forall \; \gamma \geq 0
        span
            Specify decay in terms of span, :math:`\theta`, with

                .. math::
                    \alpha = \frac{2}{\theta + 1} \; \forall \; \theta \geq 1
        half_life
            Specify decay in terms of half-life, :math:`\tau`, with

                .. math::
                    \alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \tau } \right\} \;
                    \forall \; \tau > 0
        alpha
            Specify smoothing factor alpha directly, :math:`0 < \alpha \leq 1`.
        adjust
            Divide by decaying adjustment factor in beginning periods to account for
            imbalance in relative weightings

                - When `adjust=True` (the default) the EW function is calculated
                  using weights :math:`w_i = (1 - \alpha)^i`
                - When `adjust=False` the EW function is calculated
                  recursively by

                  .. math::
                    y_0 &= x_0 \\
                    y_t &= (1 - \alpha)y_{t - 1} + \alpha x_t
        min_samples
            Minimum number of observations in window required to have a value
            (otherwise result is null).
        ignore_nulls
            Ignore missing values when calculating weights.

                - When `ignore_nulls=False` (default), weights are based on absolute
                  positions.
                  For example, the weights of :math:`x_0` and :math:`x_2` used in
                  calculating the final weighted average of
                  [:math:`x_0`, None, :math:`x_2`] are
                  :math:`(1-\alpha)^2` and :math:`1` if `adjust=True`, and
                  :math:`(1-\alpha)^2` and :math:`\alpha` if `adjust=False`.

                - When `ignore_nulls=True`, weights are based
                  on relative positions. For example, the weights of
                  :math:`x_0` and :math:`x_2` used in calculating the final weighted
                  average of [:math:`x_0`, None, :math:`x_2`] are
                  :math:`1-\alpha` and :math:`1` if `adjust=True`,
                  and :math:`1-\alpha` and :math:`\alpha` if `adjust=False`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").ewm_mean(com=1, ignore_nulls=False))
        shape: (3, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.0      │
        │ 1.666667 │
        │ 2.428571 │
        └──────────┘
        """
        alpha = _prepare_alpha(com, span, half_life, alpha)
        return self._from_pyexpr(
            self._pyexpr.ewm_mean(alpha, adjust, min_samples, ignore_nulls)
        )

    def ewm_mean_by(
        self,
        by: str | IntoExpr,
        *,
        half_life: str | timedelta,
    ) -> Expr:
        r"""
        Compute time-based exponentially weighted moving average.

        Given observations :math:`x_0, x_1, \ldots, x_{n-1}` at times
        :math:`t_0, t_1, \ldots, t_{n-1}`, the EWMA is calculated as

            .. math::

                y_0 &= x_0

                \alpha_i &= 1 - \exp \left\{ \frac{ -\ln(2)(t_i-t_{i-1}) }
                    { \tau } \right\}

                y_i &= \alpha_i x_i + (1 - \alpha_i) y_{i-1}; \quad i > 0

        where :math:`\tau` is the `half_life`.

        Parameters
        ----------
        by
            Times to calculate average by. Should be ``DateTime``, ``Date``, ``UInt64``,
            ``UInt32``, ``Int64``, or ``Int32`` data type.
        half_life
            Unit over which observation decays to half its value.

            Can be created either from a timedelta, or
            by using 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)
            - 1i    (1 index count)

            Or combine them:
            "3d12h4m25s" # 3 days, 12 hours, 4 minutes, and 25 seconds

            Note that `half_life` is treated as a constant duration - calendar
            durations such as months (or even days in the time-zone-aware case)
            are not supported, please express your duration in an approximately
            equivalent number of hours (e.g. '370h' instead of '1mo').

        Returns
        -------
        Expr
            Float32 if input is Float32, otherwise Float64.

        Examples
        --------
        >>> from datetime import date, timedelta
        >>> df = pl.DataFrame(
        ...     {
        ...         "values": [0, 1, 2, None, 4],
        ...         "times": [
        ...             date(2020, 1, 1),
        ...             date(2020, 1, 3),
        ...             date(2020, 1, 10),
        ...             date(2020, 1, 15),
        ...             date(2020, 1, 17),
        ...         ],
        ...     }
        ... ).sort("times")
        >>> df.with_columns(
        ...     result=pl.col("values").ewm_mean_by("times", half_life="4d"),
        ... )
        shape: (5, 3)
        ┌────────┬────────────┬──────────┐
        │ values ┆ times      ┆ result   │
        │ ---    ┆ ---        ┆ ---      │
        │ i64    ┆ date       ┆ f64      │
        ╞════════╪════════════╪══════════╡
        │ 0      ┆ 2020-01-01 ┆ 0.0      │
        │ 1      ┆ 2020-01-03 ┆ 0.292893 │
        │ 2      ┆ 2020-01-10 ┆ 1.492474 │
        │ null   ┆ 2020-01-15 ┆ null     │
        │ 4      ┆ 2020-01-17 ┆ 3.254508 │
        └────────┴────────────┴──────────┘
        """
        by = parse_into_expression(by)
        half_life = parse_as_duration_string(half_life)
        return self._from_pyexpr(self._pyexpr.ewm_mean_by(by, half_life))

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def ewm_std(
        self,
        *,
        com: float | None = None,
        span: float | None = None,
        half_life: float | None = None,
        alpha: float | None = None,
        adjust: bool = True,
        bias: bool = False,
        min_samples: int = 1,
        ignore_nulls: bool = False,
    ) -> Expr:
        r"""
        Compute exponentially-weighted moving standard deviation.

        Parameters
        ----------
        com
            Specify decay in terms of center of mass, :math:`\gamma`, with

                .. math::
                    \alpha = \frac{1}{1 + \gamma} \; \forall \; \gamma \geq 0
        span
            Specify decay in terms of span, :math:`\theta`, with

                .. math::
                    \alpha = \frac{2}{\theta + 1} \; \forall \; \theta \geq 1
        half_life
            Specify decay in terms of half-life, :math:`\lambda`, with

                .. math::
                    \alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \lambda } \right\} \;
                    \forall \; \lambda > 0
        alpha
            Specify smoothing factor alpha directly, :math:`0 < \alpha \leq 1`.
        adjust
            Divide by decaying adjustment factor in beginning periods to account for
            imbalance in relative weightings

                - When `adjust=True` (the default) the EW function is calculated
                  using weights :math:`w_i = (1 - \alpha)^i`
                - When `adjust=False` the EW function is calculated
                  recursively by

                  .. math::
                    y_0 &= x_0 \\
                    y_t &= (1 - \alpha)y_{t - 1} + \alpha x_t
        bias
            When `bias=False`, apply a correction to make the estimate statistically
            unbiased.
        min_samples
            Minimum number of observations in window required to have a value
            (otherwise result is null).
        ignore_nulls
            Ignore missing values when calculating weights.

                - When `ignore_nulls=False` (default), weights are based on absolute
                  positions.
                  For example, the weights of :math:`x_0` and :math:`x_2` used in
                  calculating the final weighted average of
                  [:math:`x_0`, None, :math:`x_2`] are
                  :math:`(1-\alpha)^2` and :math:`1` if `adjust=True`, and
                  :math:`(1-\alpha)^2` and :math:`\alpha` if `adjust=False`.

                - When `ignore_nulls=True`, weights are based
                  on relative positions. For example, the weights of
                  :math:`x_0` and :math:`x_2` used in calculating the final weighted
                  average of [:math:`x_0`, None, :math:`x_2`] are
                  :math:`1-\alpha` and :math:`1` if `adjust=True`,
                  and :math:`1-\alpha` and :math:`\alpha` if `adjust=False`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").ewm_std(com=1, ignore_nulls=False))
        shape: (3, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.0      │
        │ 0.707107 │
        │ 0.963624 │
        └──────────┘
        """
        alpha = _prepare_alpha(com, span, half_life, alpha)
        return self._from_pyexpr(
            self._pyexpr.ewm_std(alpha, adjust, bias, min_samples, ignore_nulls)
        )

    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def ewm_var(
        self,
        *,
        com: float | None = None,
        span: float | None = None,
        half_life: float | None = None,
        alpha: float | None = None,
        adjust: bool = True,
        bias: bool = False,
        min_samples: int = 1,
        ignore_nulls: bool = False,
    ) -> Expr:
        r"""
        Compute exponentially-weighted moving variance.

        Parameters
        ----------
        com
            Specify decay in terms of center of mass, :math:`\gamma`, with

                .. math::
                    \alpha = \frac{1}{1 + \gamma} \; \forall \; \gamma \geq 0
        span
            Specify decay in terms of span, :math:`\theta`, with

                .. math::
                    \alpha = \frac{2}{\theta + 1} \; \forall \; \theta \geq 1
        half_life
            Specify decay in terms of half-life, :math:`\lambda`, with

                .. math::
                    \alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \lambda } \right\} \;
                    \forall \; \lambda > 0
        alpha
            Specify smoothing factor alpha directly, :math:`0 < \alpha \leq 1`.
        adjust
            Divide by decaying adjustment factor in beginning periods to account for
            imbalance in relative weightings

                - When `adjust=True` (the default) the EW function is calculated
                  using weights :math:`w_i = (1 - \alpha)^i`
                - When `adjust=False` the EW function is calculated
                  recursively by

                  .. math::
                    y_0 &= x_0 \\
                    y_t &= (1 - \alpha)y_{t - 1} + \alpha x_t
        bias
            When `bias=False`, apply a correction to make the estimate statistically
            unbiased.
        min_samples
            Minimum number of observations in window required to have a value
            (otherwise result is null).
        ignore_nulls
            Ignore missing values when calculating weights.

                - When `ignore_nulls=False` (default), weights are based on absolute
                  positions.
                  For example, the weights of :math:`x_0` and :math:`x_2` used in
                  calculating the final weighted average of
                  [:math:`x_0`, None, :math:`x_2`] are
                  :math:`(1-\alpha)^2` and :math:`1` if `adjust=True`, and
                  :math:`(1-\alpha)^2` and :math:`\alpha` if `adjust=False`.

                - When `ignore_nulls=True`, weights are based
                  on relative positions. For example, the weights of
                  :math:`x_0` and :math:`x_2` used in calculating the final weighted
                  average of [:math:`x_0`, None, :math:`x_2`] are
                  :math:`1-\alpha` and :math:`1` if `adjust=True`,
                  and :math:`1-\alpha` and :math:`\alpha` if `adjust=False`.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").ewm_var(com=1, ignore_nulls=False))
        shape: (3, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.0      │
        │ 0.5      │
        │ 0.928571 │
        └──────────┘
        """
        alpha = _prepare_alpha(com, span, half_life, alpha)
        return self._from_pyexpr(
            self._pyexpr.ewm_var(alpha, adjust, bias, min_samples, ignore_nulls)
        )

    def extend_constant(self, value: IntoExpr, n: int | IntoExprColumn) -> Expr:
        """
        Extremely fast method for extending the Series with 'n' copies of a value.

        Parameters
        ----------
        value
            A constant literal value or a unit expression with which to extend the
            expression result Series; can pass None to extend with nulls.
        n
            The number of additional values that will be added.

        Examples
        --------
        >>> df = pl.DataFrame({"values": [1, 2, 3]})
        >>> df.select((pl.col("values") - 1).extend_constant(99, n=2))
        shape: (5, 1)
        ┌────────┐
        │ values │
        │ ---    │
        │ i64    │
        ╞════════╡
        │ 0      │
        │ 1      │
        │ 2      │
        │ 99     │
        │ 99     │
        └────────┘
        """
        value = parse_into_expression(value, str_as_lit=True)
        n = parse_into_expression(n)
        return self._from_pyexpr(self._pyexpr.extend_constant(value, n))

    def value_counts(
        self,
        *,
        sort: bool = False,
        parallel: bool = False,
        name: str | None = None,
        normalize: bool = False,
    ) -> Expr:
        """
        Count the occurrences of unique values.

        Parameters
        ----------
        sort
            Sort the output by count in descending order.
            If set to `False` (default), the order of the output is random.
        parallel
            Execute the computation in parallel.

            .. note::
                This option should likely not be enabled in a group by context,
                as the computation is already parallelized per group.
        name
            Give the resulting count column a specific name;
            if `normalize` is True defaults to "proportion",
            otherwise defaults to "count".
        normalize
            If true gives relative frequencies of the unique values

        Returns
        -------
        Expr
            Expression of data type :class:`Struct` with mapping of unique values to
            their count.

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {"color": ["red", "blue", "red", "green", "blue", "blue"]}
        ... )
        >>> df.select(pl.col("color").value_counts())  # doctest: +IGNORE_RESULT
        shape: (3, 1)
        ┌─────────────┐
        │ color       │
        │ ---         │
        │ struct[2]   │
        ╞═════════════╡
        │ {"red",2}   │
        │ {"green",1} │
        │ {"blue",3}  │
        └─────────────┘

        Sort the output by (descending) count and customize the count field name.

        >>> df = df.select(pl.col("color").value_counts(sort=True, name="n"))
        >>> df
        shape: (3, 1)
        ┌─────────────┐
        │ color       │
        │ ---         │
        │ struct[2]   │
        ╞═════════════╡
        │ {"blue",3}  │
        │ {"red",2}   │
        │ {"green",1} │
        └─────────────┘

        >>> df.unnest("color")
        shape: (3, 2)
        ┌───────┬─────┐
        │ color ┆ n   │
        │ ---   ┆ --- │
        │ str   ┆ u32 │
        ╞═══════╪═════╡
        │ blue  ┆ 3   │
        │ red   ┆ 2   │
        │ green ┆ 1   │
        └───────┴─────┘
        """
        if name is None:
            if normalize:
                name = "proportion"
            else:
                name = "count"
        return self._from_pyexpr(
            self._pyexpr.value_counts(sort, parallel, name, normalize)
        )

    def unique_counts(self) -> Expr:
        """
        Return a count of the unique values in the order of appearance.

        This method differs from `value_counts` in that it does not return the
        values, only the counts and might be faster

        Examples
        --------
        >>> df = pl.DataFrame(
        ...     {
        ...         "id": ["a", "b", "b", "c", "c", "c"],
        ...     }
        ... )
        >>> df.select(
        ...     [
        ...         pl.col("id").unique_counts(),
        ...     ]
        ... )
        shape: (3, 1)
        ┌─────┐
        │ id  │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 1   │
        │ 2   │
        │ 3   │
        └─────┘
        """
        return self._from_pyexpr(self._pyexpr.unique_counts())

    def log(self, base: float = math.e) -> Expr:
        """
        Compute the logarithm to a given base.

        Parameters
        ----------
        base
            Given base, defaults to `e`

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").log(base=2))
        shape: (3, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.0      │
        │ 1.0      │
        │ 1.584963 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.log(base))

    def log1p(self) -> Expr:
        """
        Compute the natural logarithm of each element plus one.

        This computes `log(1 + x)` but is more numerically stable for `x` close to zero.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").log1p())
        shape: (3, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 0.693147 │
        │ 1.098612 │
        │ 1.386294 │
        └──────────┘
        """
        return self._from_pyexpr(self._pyexpr.log1p())

    def entropy(self, base: float = math.e, *, normalize: bool = True) -> Expr:
        """
        Computes the entropy.

        Uses the formula `-sum(pk * log(pk)` where `pk` are discrete probabilities.

        Parameters
        ----------
        base
            Given base, defaults to `e`
        normalize
            Normalize pk if it doesn't sum to 1.

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 2, 3]})
        >>> df.select(pl.col("a").entropy(base=2))
        shape: (1, 1)
        ┌──────────┐
        │ a        │
        │ ---      │
        │ f64      │
        ╞══════════╡
        │ 1.459148 │
        └──────────┘
        >>> df.select(pl.col("a").entropy(base=2, normalize=False))
        shape: (1, 1)
        ┌───────────┐
        │ a         │
        │ ---       │
        │ f64       │
        ╞═══════════╡
        │ -6.754888 │
        └───────────┘
        """
        return self._from_pyexpr(self._pyexpr.entropy(base, normalize))

    @unstable()
    @deprecate_renamed_parameter("min_periods", "min_samples", version="1.21.0")
    def cumulative_eval(
        self, expr: Expr, *, min_samples: int = 1, parallel: bool = False
    ) -> Expr:
        """
        Run an expression over a sliding window that increases `1` slot every iteration.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Parameters
        ----------
        expr
            Expression to evaluate
        min_samples
            Number of valid values there should be in the window before the expression
            is evaluated. valid values = `length - null_count`
        parallel
            Run in parallel. Don't do this in a group by or another operation that
            already has much parallelization.

        Warnings
        --------
        This can be really slow as it can have `O(n^2)` complexity. Don't use this
        for operations that visit all elements.

        Examples
        --------
        >>> df = pl.DataFrame({"values": [1, 2, 3, 4, 5]})
        >>> df.select(
        ...     [
        ...         pl.col("values").cumulative_eval(
        ...             pl.element().first() - pl.element().last() ** 2
        ...         )
        ...     ]
        ... )
        shape: (5, 1)
        ┌────────┐
        │ values │
        │ ---    │
        │ i64    │
        ╞════════╡
        │ 0      │
        │ -3     │
        │ -8     │
        │ -15    │
        │ -24    │
        └────────┘
        """
        return self._from_pyexpr(
            self._pyexpr.cumulative_eval(expr._pyexpr, min_samples, parallel)
        )

    def set_sorted(self, *, descending: bool = False) -> Expr:
        """
        Flags the expression as 'sorted'.

        Enables downstream code to user fast paths for sorted arrays.

        Parameters
        ----------
        descending
            Whether the `Series` order is descending.

        Warnings
        --------
        This can lead to incorrect results if the data is NOT sorted!!
        Use with care!

        Examples
        --------
        >>> df = pl.DataFrame({"values": [1, 2, 3]})
        >>> df.select(pl.col("values").set_sorted().max())
        shape: (1, 1)
        ┌────────┐
        │ values │
        │ ---    │
        │ i64    │
        ╞════════╡
        │ 3      │
        └────────┘
        """
        return self._from_pyexpr(self._pyexpr.set_sorted_flag(descending))

    def shrink_dtype(self) -> Expr:
        """
        Shrink numeric columns to the minimal required datatype.

        Shrink to the dtype needed to fit the extrema of this [`Series`].
        This can be used to reduce memory pressure.

        Examples
        --------
        >>> pl.DataFrame(
        ...     {
        ...         "a": [1, 2, 3],
        ...         "b": [1, 2, 2 << 32],
        ...         "c": [-1, 2, 1 << 30],
        ...         "d": [-112, 2, 112],
        ...         "e": [-112, 2, 129],
        ...         "f": ["a", "b", "c"],
        ...         "g": [0.1, 1.32, 0.12],
        ...         "h": [True, None, False],
        ...     }
        ... ).select(pl.all().shrink_dtype())
        shape: (3, 8)
        ┌─────┬────────────┬────────────┬──────┬──────┬─────┬──────┬───────┐
        │ a   ┆ b          ┆ c          ┆ d    ┆ e    ┆ f   ┆ g    ┆ h     │
        │ --- ┆ ---        ┆ ---        ┆ ---  ┆ ---  ┆ --- ┆ ---  ┆ ---   │
        │ i8  ┆ i64        ┆ i32        ┆ i8   ┆ i16  ┆ str ┆ f32  ┆ bool  │
        ╞═════╪════════════╪════════════╪══════╪══════╪═════╪══════╪═══════╡
        │ 1   ┆ 1          ┆ -1         ┆ -112 ┆ -112 ┆ a   ┆ 0.1  ┆ true  │
        │ 2   ┆ 2          ┆ 2          ┆ 2    ┆ 2    ┆ b   ┆ 1.32 ┆ null  │
        │ 3   ┆ 8589934592 ┆ 1073741824 ┆ 112  ┆ 129  ┆ c   ┆ 0.12 ┆ false │
        └─────┴────────────┴────────────┴──────┴──────┴─────┴──────┴───────┘
        """
        return self._from_pyexpr(self._pyexpr.shrink_dtype())

    @unstable()
    def hist(
        self,
        bins: IntoExpr | None = None,
        *,
        bin_count: int | None = None,
        include_category: bool = False,
        include_breakpoint: bool = False,
    ) -> Expr:
        """
        Bin values into buckets and count their occurrences.

        .. warning::
            This functionality is considered **unstable**. It may be changed
            at any point without it being considered a breaking change.

        Parameters
        ----------
        bins
            Bin edges. If None given, we determine the edges based on the data.
        bin_count
            If `bins` is not provided, `bin_count` uniform bins are created that fully
            encompass the data.
        include_breakpoint
            Include a column that indicates the upper breakpoint.
        include_category
            Include a column that shows the intervals as categories.

        Returns
        -------
        DataFrame

        Examples
        --------
        >>> df = pl.DataFrame({"a": [1, 3, 8, 8, 2, 1, 3]})
        >>> df.select(pl.col("a").hist(bins=[1, 2, 3]))
        shape: (2, 1)
        ┌─────┐
        │ a   │
        │ --- │
        │ u32 │
        ╞═════╡
        │ 3   │
        │ 2   │
        └─────┘
        >>> df.select(
        ...     pl.col("a").hist(
        ...         bins=[1, 2, 3], include_breakpoint=True, include_category=True
        ...     )
        ... )
        shape: (2, 1)
        ┌──────────────────────┐
        │ a                    │
        │ ---                  │
        │ struct[3]            │
        ╞══════════════════════╡
        │ {2.0,"[1.0, 2.0]",3} │
        │ {3.0,"(2.0, 3.0]",2} │
        └──────────────────────┘
        """
        if bins is not None:
            if isinstance(bins, list):
                bins = pl.Series(bins)
            bins = parse_into_expression(bins)
        return self._from_pyexpr(
            self._pyexpr.hist(bins, bin_count, include_category, include_breakpoint)
        )

    def replace(
        self,
        old: IntoExpr | Sequence[Any] | Mapping[Any, Any],
        new: IntoExpr | Sequence[Any] | NoDefault = no_default,
        *,
        default: IntoExpr | NoDefault = no_default,
        return_dtype: PolarsDataType | None = None,
    ) -> Expr:
        """
        Replace the given values by different values of the same data type.

        Parameters
        ----------
        old
            Value or sequence of values to replace.
            Accepts expression input. Sequences are parsed as Series,
            other non-expression inputs are parsed as literals.
            Also accepts a mapping of values to their replacement as syntactic sugar for
            `replace(old=Series(mapping.keys()), new=Series(mapping.values()))`.
        new
            Value or sequence of values to replace by.
            Accepts expression input. Sequences are parsed as Series,
            other non-expression inputs are parsed as literals.
            Length must match the length of `old` or have length 1.

        default
            Set values that were not replaced to this value.
            Defaults to keeping the original value.
            Accepts expression input. Non-expression inputs are parsed as literals.

            .. deprecated:: 1.0.0
                Use :meth:`replace_strict` instead to set a default while replacing
                values.

        return_dtype
            The data type of the resulting expression. If set to `None` (default),
            the data type of the original column is preserved.

            .. deprecated:: 1.0.0
                Use :meth:`replace_strict` instead to set a return data type while
                replacing values, or explicitly call :meth:`cast` on the output.

        See Also
        --------
        replace_strict
        str.replace

        Notes
        -----
        The global string cache must be enabled when replacing categorical values.

        Examples
        --------
        Replace a single value by another value. Values that were not replaced remain
        unchanged.

        >>> df = pl.DataFrame({"a": [1, 2, 2, 3]})
        >>> df.with_columns(replaced=pl.col("a").replace(2, 100))
        shape: (4, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ i64 ┆ i64      │
        ╞═════╪══════════╡
        │ 1   ┆ 1        │
        │ 2   ┆ 100      │
        │ 2   ┆ 100      │
        │ 3   ┆ 3        │
        └─────┴──────────┘

        Replace multiple values by passing sequences to the `old` and `new` parameters.

        >>> df.with_columns(replaced=pl.col("a").replace([2, 3], [100, 200]))
        shape: (4, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ i64 ┆ i64      │
        ╞═════╪══════════╡
        │ 1   ┆ 1        │
        │ 2   ┆ 100      │
        │ 2   ┆ 100      │
        │ 3   ┆ 200      │
        └─────┴──────────┘

        Passing a mapping with replacements is also supported as syntactic sugar.

        >>> mapping = {2: 100, 3: 200}
        >>> df.with_columns(replaced=pl.col("a").replace(mapping))
        shape: (4, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ i64 ┆ i64      │
        ╞═════╪══════════╡
        │ 1   ┆ 1        │
        │ 2   ┆ 100      │
        │ 2   ┆ 100      │
        │ 3   ┆ 200      │
        └─────┴──────────┘

        The original data type is preserved when replacing by values of a different
        data type. Use :meth:`replace_strict` to replace and change the return data
        type.

        >>> df = pl.DataFrame({"a": ["x", "y", "z"]})
        >>> mapping = {"x": 1, "y": 2, "z": 3}
        >>> df.with_columns(replaced=pl.col("a").replace(mapping))
        shape: (3, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ str ┆ str      │
        ╞═════╪══════════╡
        │ x   ┆ 1        │
        │ y   ┆ 2        │
        │ z   ┆ 3        │
        └─────┴──────────┘

        Expression input is supported.

        >>> df = pl.DataFrame({"a": [1, 2, 2, 3], "b": [1.5, 2.5, 5.0, 1.0]})
        >>> df.with_columns(
        ...     replaced=pl.col("a").replace(
        ...         old=pl.col("a").max(),
        ...         new=pl.col("b").sum(),
        ...     )
        ... )
        shape: (4, 3)
        ┌─────┬─────┬──────────┐
        │ a   ┆ b   ┆ replaced │
        │ --- ┆ --- ┆ ---      │
        │ i64 ┆ f64 ┆ i64      │
        ╞═════╪═════╪══════════╡
        │ 1   ┆ 1.5 ┆ 1        │
        │ 2   ┆ 2.5 ┆ 2        │
        │ 2   ┆ 5.0 ┆ 2        │
        │ 3   ┆ 1.0 ┆ 10       │
        └─────┴─────┴──────────┘
        """
        if return_dtype is not None:
            issue_deprecation_warning(
                "The `return_dtype` parameter for `replace` is deprecated."
                " Use `replace_strict` instead to set a return data type while replacing values.",
                version="1.0.0",
            )
        if default is not no_default:
            issue_deprecation_warning(
                "The `default` parameter for `replace` is deprecated."
                " Use `replace_strict` instead to set a default while replacing values.",
                version="1.0.0",
            )
            return self.replace_strict(
                old, new, default=default, return_dtype=return_dtype
            )

        if new is no_default:
            if not isinstance(old, Mapping):
                msg = (
                    "`new` argument is required if `old` argument is not a Mapping type"
                )
                raise TypeError(msg)
            new = pl.Series(old.values())
            old = pl.Series(old.keys())
        else:
            if isinstance(old, Sequence) and not isinstance(old, (str, pl.Series)):
                old = pl.Series(old)
            if isinstance(new, Sequence) and not isinstance(new, (str, pl.Series)):
                new = pl.Series(new)

        old = parse_into_expression(old, str_as_lit=True)  # type: ignore[arg-type]
        new = parse_into_expression(new, str_as_lit=True)

        result = self._from_pyexpr(self._pyexpr.replace(old, new))

        if return_dtype is not None:
            result = result.cast(return_dtype)

        return result

    def replace_strict(
        self,
        old: IntoExpr | Sequence[Any] | Mapping[Any, Any],
        new: IntoExpr | Sequence[Any] | NoDefault = no_default,
        *,
        default: IntoExpr | NoDefault = no_default,
        return_dtype: PolarsDataType | None = None,
    ) -> Expr:
        """
        Replace all values by different values.

        Parameters
        ----------
        old
            Value or sequence of values to replace.
            Accepts expression input. Sequences are parsed as Series,
            other non-expression inputs are parsed as literals.
            Also accepts a mapping of values to their replacement as syntactic sugar for
            `replace_all(old=Series(mapping.keys()), new=Series(mapping.values()))`.
        new
            Value or sequence of values to replace by.
            Accepts expression input. Sequences are parsed as Series,
            other non-expression inputs are parsed as literals.
            Length must match the length of `old` or have length 1.
        default
            Set values that were not replaced to this value. If no default is specified,
            (default), an error is raised if any values were not replaced.
            Accepts expression input. Non-expression inputs are parsed as literals.
        return_dtype
            The data type of the resulting expression. If set to `None` (default),
            the data type is determined automatically based on the other inputs.

        Raises
        ------
        InvalidOperationError
            If any non-null values in the original column were not replaced, and no
            `default` was specified.

        See Also
        --------
        replace
        str.replace

        Notes
        -----
        The global string cache must be enabled when replacing categorical values.

        Examples
        --------
        Replace values by passing sequences to the `old` and `new` parameters.

        >>> df = pl.DataFrame({"a": [1, 2, 2, 3]})
        >>> df.with_columns(
        ...     replaced=pl.col("a").replace_strict([1, 2, 3], [100, 200, 300])
        ... )
        shape: (4, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ i64 ┆ i64      │
        ╞═════╪══════════╡
        │ 1   ┆ 100      │
        │ 2   ┆ 200      │
        │ 2   ┆ 200      │
        │ 3   ┆ 300      │
        └─────┴──────────┘

        Passing a mapping with replacements is also supported as syntactic sugar.

        >>> mapping = {1: 100, 2: 200, 3: 300}
        >>> df.with_columns(replaced=pl.col("a").replace_strict(mapping))
        shape: (4, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ i64 ┆ i64      │
        ╞═════╪══════════╡
        │ 1   ┆ 100      │
        │ 2   ┆ 200      │
        │ 2   ┆ 200      │
        │ 3   ┆ 300      │
        └─────┴──────────┘

        By default, an error is raised if any non-null values were not replaced.
        Specify a default to set all values that were not matched.

        >>> mapping = {2: 200, 3: 300}
        >>> df.with_columns(
        ...     replaced=pl.col("a").replace_strict(mapping)
        ... )  # doctest: +SKIP
        Traceback (most recent call last):
        ...
        polars.exceptions.InvalidOperationError: incomplete mapping specified for `replace_strict`
        >>> df.with_columns(replaced=pl.col("a").replace_strict(mapping, default=-1))
        shape: (4, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ i64 ┆ i64      │
        ╞═════╪══════════╡
        │ 1   ┆ -1       │
        │ 2   ┆ 200      │
        │ 2   ┆ 200      │
        │ 3   ┆ 300      │
        └─────┴──────────┘

        Replacing by values of a different data type sets the return type based on
        a combination of the `new` data type and the `default` data type.

        >>> df = pl.DataFrame({"a": ["x", "y", "z"]})
        >>> mapping = {"x": 1, "y": 2, "z": 3}
        >>> df.with_columns(replaced=pl.col("a").replace_strict(mapping))
        shape: (3, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ str ┆ i64      │
        ╞═════╪══════════╡
        │ x   ┆ 1        │
        │ y   ┆ 2        │
        │ z   ┆ 3        │
        └─────┴──────────┘
        >>> df.with_columns(replaced=pl.col("a").replace_strict(mapping, default="x"))
        shape: (3, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ str ┆ str      │
        ╞═════╪══════════╡
        │ x   ┆ 1        │
        │ y   ┆ 2        │
        │ z   ┆ 3        │
        └─────┴──────────┘

        Set the `return_dtype` parameter to control the resulting data type directly.

        >>> df.with_columns(
        ...     replaced=pl.col("a").replace_strict(mapping, return_dtype=pl.UInt8)
        ... )
        shape: (3, 2)
        ┌─────┬──────────┐
        │ a   ┆ replaced │
        │ --- ┆ ---      │
        │ str ┆ u8       │
        ╞═════╪══════════╡
        │ x   ┆ 1        │
        │ y   ┆ 2        │
        │ z   ┆ 3        │
        └─────┴──────────┘

        Expression input is supported for all parameters.

        >>> df = pl.DataFrame({"a": [1, 2, 2, 3], "b": [1.5, 2.5, 5.0, 1.0]})
        >>> df.with_columns(
        ...     replaced=pl.col("a").replace_strict(
        ...         old=pl.col("a").max(),
        ...         new=pl.col("b").sum(),
        ...         default=pl.col("b"),
        ...     )
        ... )
        shape: (4, 3)
        ┌─────┬─────┬──────────┐
        │ a   ┆ b   ┆ replaced │
        │ --- ┆ --- ┆ ---      │
        │ i64 ┆ f64 ┆ f64      │
        ╞═════╪═════╪══════════╡
        │ 1   ┆ 1.5 ┆ 1.5      │
        │ 2   ┆ 2.5 ┆ 2.5      │
        │ 2   ┆ 5.0 ┆ 5.0      │
        │ 3   ┆ 1.0 ┆ 10.0     │
        └─────┴─────┴──────────┘
        """  # noqa: W505
        if new is no_default:
            if not isinstance(old, Mapping):
                msg = (
                    "`new` argument is required if `old` argument is not a Mapping type"
                )
                raise TypeError(msg)
            new = pl.Series(old.values())
            old = pl.Series(old.keys())

        old = parse_into_expression(old, str_as_lit=True, list_as_series=True)  # type: ignore[arg-type]
        new = parse_into_expression(new, str_as_lit=True, list_as_series=True)  # type: ignore[arg-type]

        default = (
            None
            if default is no_default
            else parse_into_expression(default, str_as_lit=True)
        )

        return self._from_pyexpr(
            self._pyexpr.replace_strict(old, new, default, return_dtype)
        )

    def bitwise_count_ones(self) -> Expr:
        """Evaluate the number of set bits."""
        return self._from_pyexpr(self._pyexpr.bitwise_count_ones())

    def bitwise_count_zeros(self) -> Expr:
        """Evaluate the number of unset bits."""
        return self._from_pyexpr(self._pyexpr.bitwise_count_zeros())

    def bitwise_leading_ones(self) -> Expr:
        """Evaluate the number most-significant set bits before seeing an unset bit."""
        return self._from_pyexpr(self._pyexpr.bitwise_leading_ones())

    def bitwise_leading_zeros(self) -> Expr:
        """Evaluate the number most-significant unset bits before seeing a set bit."""
        return self._from_pyexpr(self._pyexpr.bitwise_leading_zeros())

    def bitwise_trailing_ones(self) -> Expr:
        """Evaluate the number least-significant set bits before seeing an unset bit."""
        return self._from_pyexpr(self._pyexpr.bitwise_trailing_ones())

    def bitwise_trailing_zeros(self) -> Expr:
        """Evaluate the number least-significant unset bits before seeing a set bit."""
        return self._from_pyexpr(self._pyexpr.bitwise_trailing_zeros())

    def bitwise_and(self) -> Expr:
        """Perform an aggregation of bitwise ANDs.

        Examples
        --------
        >>> df = pl.DataFrame({"n": [-1, 0, 1]})
        >>> df.select(pl.col("n").bitwise_and())
        shape: (1, 1)
        ┌─────┐
        │ n   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ 0   │
        └─────┘
        >>> df = pl.DataFrame(
        ...     {"grouper": ["a", "a", "a", "b", "b"], "n": [-1, 0, 1, -1, 1]}
        ... )
        >>> df.group_by("grouper", maintain_order=True).agg(pl.col("n").bitwise_and())
        shape: (2, 2)
        ┌─────────┬─────┐
        │ grouper ┆ n   │
        │ ---     ┆ --- │
        │ str     ┆ i64 │
        ╞═════════╪═════╡
        │ a       ┆ 0   │
        │ b       ┆ 1   │
        └─────────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.bitwise_and())

    def bitwise_or(self) -> Expr:
        """Perform an aggregation of bitwise ORs.

        Examples
        --------
        >>> df = pl.DataFrame({"n": [-1, 0, 1]})
        >>> df.select(pl.col("n").bitwise_or())
        shape: (1, 1)
        ┌─────┐
        │ n   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ -1  │
        └─────┘
        >>> df = pl.DataFrame(
        ...     {"grouper": ["a", "a", "a", "b", "b"], "n": [-1, 0, 1, -1, 1]}
        ... )
        >>> df.group_by("grouper", maintain_order=True).agg(pl.col("n").bitwise_or())
        shape: (2, 2)
        ┌─────────┬─────┐
        │ grouper ┆ n   │
        │ ---     ┆ --- │
        │ str     ┆ i64 │
        ╞═════════╪═════╡
        │ a       ┆ -1  │
        │ b       ┆ -1  │
        └─────────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.bitwise_or())

    def bitwise_xor(self) -> Expr:
        """Perform an aggregation of bitwise XORs.

        Examples
        --------
        >>> df = pl.DataFrame({"n": [-1, 0, 1]})
        >>> df.select(pl.col("n").bitwise_xor())
        shape: (1, 1)
        ┌─────┐
        │ n   │
        │ --- │
        │ i64 │
        ╞═════╡
        │ -2  │
        └─────┘
        >>> df = pl.DataFrame(
        ...     {"grouper": ["a", "a", "a", "b", "b"], "n": [-1, 0, 1, -1, 1]}
        ... )
        >>> df.group_by("grouper", maintain_order=True).agg(pl.col("n").bitwise_xor())
        shape: (2, 2)
        ┌─────────┬─────┐
        │ grouper ┆ n   │
        │ ---     ┆ --- │
        │ str     ┆ i64 │
        ╞═════════╪═════╡
        │ a       ┆ -2  │
        │ b       ┆ -2  │
        └─────────┴─────┘
        """
        return self._from_pyexpr(self._pyexpr.bitwise_xor())

    @deprecate_function(
        "Use `polars.plugins.register_plugin_function` instead.", version="0.20.16"
    )
    def register_plugin(
        self,
        *,
        lib: str,
        symbol: str,
        args: list[IntoExpr] | None = None,
        kwargs: dict[Any, Any] | None = None,
        is_elementwise: bool = False,
        input_wildcard_expansion: bool = False,
        returns_scalar: bool = False,
        cast_to_supertypes: bool = False,
        pass_name_to_apply: bool = False,
        changes_length: bool = False,
    ) -> Expr:
        """
        Register a plugin function.

        .. deprecated:: 0.20.16
            Use :func:`polars.plugins.register_plugin_function` instead.

        See the `user guide <https://docs.pola.rs/user-guide/plugins/>`_
        for more information about plugins.

        Warnings
        --------
        This method is deprecated. Use the new `polars.plugins.register_plugin_function`
        function instead.

        This is highly unsafe as this will call the C function loaded by
        `lib::symbol`.

        The parameters you set dictate how Polars will handle the function.
        Make sure they are correct!

        Parameters
        ----------
        lib
            Library to load.
        symbol
            Function to load.
        args
            Arguments (other than self) passed to this function.
            These arguments have to be of type Expression.
        kwargs
            Non-expression arguments. They must be JSON serializable.
        is_elementwise
            If the function only operates on scalars
            this will trigger fast paths.
        input_wildcard_expansion
            Expand expressions as input of this function.
        returns_scalar
            Automatically explode on unit length if it ran as final aggregation.
            this is the case for aggregations like `sum`, `min`, `covariance` etc.
        cast_to_supertypes
            Cast the input datatypes to their supertype.
        pass_name_to_apply
            if set, then the `Series` passed to the function in the group_by operation
            will ensure the name is set. This is an extra heap allocation per group.
        changes_length
            For example a `unique` or a `slice`
        """
        from polars.plugins import register_plugin_function

        if args is None:
            args = [self]
        else:
            args = [self, *list(args)]

        return register_plugin_function(
            plugin_path=lib,
            function_name=symbol,
            args=args,
            kwargs=kwargs,
            is_elementwise=is_elementwise,
            changes_length=changes_length,
            returns_scalar=returns_scalar,
            cast_to_supertype=cast_to_supertypes,
            input_wildcard_expansion=input_wildcard_expansion,
            pass_name_to_apply=pass_name_to_apply,
        )

    @classmethod
    def from_json(cls, value: str) -> Expr:
        """
        Read an expression from a JSON encoded string to construct an Expression.

        .. deprecated:: 0.20.11
            This method has been renamed to :meth:`deserialize`.
            Note that the new method operates on file-like inputs rather than strings.
            Enclose your input in `io.StringIO` to keep the same behavior.

        Parameters
        ----------
        value
            JSON encoded string value
        """
        issue_deprecation_warning(
            "`Expr.from_json` is deprecated. It has been renamed to `Expr.deserialize`."
            " Note that the new method operates on file-like inputs rather than strings."
            " Enclose your input in `io.StringIO` to keep the same behavior.",
            version="0.20.11",
        )
        return cls.deserialize(StringIO(value), format="json")

    @property
    def bin(self) -> ExprBinaryNameSpace:
        """
        Create an object namespace of all binary related methods.

        See the individual method pages for full details
        """
        return ExprBinaryNameSpace(self)

    @property
    def cat(self) -> ExprCatNameSpace:
        """
        Create an object namespace of all categorical related methods.

        See the individual method pages for full details

        Examples
        --------
        >>> df = pl.DataFrame({"values": ["a", "b"]}).select(
        ...     pl.col("values").cast(pl.Categorical)
        ... )
        >>> df.select(pl.col("values").cat.get_categories())
        shape: (2, 1)
        ┌────────┐
        │ values │
        │ ---    │
        │ str    │
        ╞════════╡
        │ a      │
        │ b      │
        └────────┘
        """
        return ExprCatNameSpace(self)

    @property
    def dt(self) -> ExprDateTimeNameSpace:
        """Create an object namespace of all datetime related methods."""
        return ExprDateTimeNameSpace(self)

    # Keep the `list` and `str` properties below at the end of the definition of Expr,
    # as to not confuse mypy with the type annotation `str` and `list`

    @property
    def list(self) -> ExprListNameSpace:
        """
        Create an object namespace of all list related methods.

        See the individual method pages for full details.
        """
        return ExprListNameSpace(self)

    @property
    def arr(self) -> ExprArrayNameSpace:
        """
        Create an object namespace of all array related methods.

        See the individual method pages for full details.
        """
        return ExprArrayNameSpace(self)

    @property
    def meta(self) -> ExprMetaNameSpace:
        """
        Create an object namespace of all meta related expression methods.

        This can be used to modify and traverse existing expressions.
        """
        return ExprMetaNameSpace(self)

    @property
    def name(self) -> ExprNameNameSpace:
        """
        Create an object namespace of all expressions that modify expression names.

        See the individual method pages for full details.
        """
        return ExprNameNameSpace(self)

    @property
    def str(self) -> ExprStringNameSpace:
        """
        Create an object namespace of all string related methods.

        See the individual method pages for full details.

        Examples
        --------
        >>> df = pl.DataFrame({"letters": ["a", "b"]})
        >>> df.select(pl.col("letters").str.to_uppercase())
        shape: (2, 1)
        ┌─────────┐
        │ letters │
        │ ---     │
        │ str     │
        ╞═════════╡
        │ A       │
        │ B       │
        └─────────┘
        """
        return ExprStringNameSpace(self)

    @property
    def struct(self) -> ExprStructNameSpace:
        """
        Create an object namespace of all struct related methods.

        See the individual method pages for full details.

        Examples
        --------
        >>> df = (
        ...     pl.DataFrame(
        ...         {
        ...             "int": [1, 2],
        ...             "str": ["a", "b"],
        ...             "bool": [True, None],
        ...             "list": [[1, 2], [3]],
        ...         }
        ...     )
        ...     .to_struct("my_struct")
        ...     .to_frame()
        ... )
        >>> df.select(pl.col("my_struct").struct.field("str"))
        shape: (2, 1)
        ┌─────┐
        │ str │
        │ --- │
        │ str │
        ╞═════╡
        │ a   │
        │ b   │
        └─────┘
        """
        return ExprStructNameSpace(self)

    def _skip_batch_predicate(self, schema: SchemaDict) -> Expr | None:
        result = self._pyexpr.skip_batch_predicate(schema)
        if result is None:
            return None
        return self._from_pyexpr(result)


def _prepare_alpha(
    com: float | int | None = None,
    span: float | int | None = None,
    half_life: float | int | None = None,
    alpha: float | int | None = None,
) -> float:
    """Normalise EWM decay specification in terms of smoothing factor 'alpha'."""
    if sum((param is not None) for param in (com, span, half_life, alpha)) > 1:
        msg = (
            "parameters `com`, `span`, `half_life`, and `alpha` are mutually exclusive"
        )
        raise ValueError(msg)
    if com is not None:
        if com < 0.0:
            msg = f"require `com` >= 0 (found {com!r})"
            raise ValueError(msg)
        alpha = 1.0 / (1.0 + com)

    elif span is not None:
        if span < 1.0:
            msg = f"require `span` >= 1 (found {span!r})"
            raise ValueError(msg)
        alpha = 2.0 / (span + 1.0)

    elif half_life is not None:
        if half_life <= 0.0:
            msg = f"require `half_life` > 0 (found {half_life!r})"
            raise ValueError(msg)
        alpha = 1.0 - math.exp(-math.log(2.0) / half_life)

    elif alpha is None:
        msg = "one of `com`, `span`, `half_life`, or `alpha` must be set"
        raise ValueError(msg)

    elif not (0 < alpha <= 1):
        msg = f"require 0 < `alpha` <= 1 (found {alpha!r})"
        raise ValueError(msg)

    return alpha


def _prepare_rolling_by_window_args(window_size: timedelta | str) -> str:
    if isinstance(window_size, timedelta):
        window_size = parse_as_duration_string(window_size)
    return window_size
