332 lines
8.1 KiB
Python
332 lines
8.1 KiB
Python
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from __future__ import annotations
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from typing import (
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Any,
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Callable,
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Literal,
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Optional,
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overload,
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)
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import numpy
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_IntegerType = int | numpy.integer
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_FloatingType = float | numpy.floating
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_PointsAndWeights = tuple[numpy.ndarray, numpy.ndarray]
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_PointsAndWeightsAndMu = tuple[numpy.ndarray, numpy.ndarray, float]
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_ArrayLike0D = bool | int | float | complex | str | bytes | numpy.generic
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__all__ = [
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'legendre',
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'chebyt',
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'chebyu',
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'chebyc',
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'chebys',
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'jacobi',
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'laguerre',
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'genlaguerre',
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'hermite',
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'hermitenorm',
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'gegenbauer',
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'sh_legendre',
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'sh_chebyt',
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'sh_chebyu',
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'sh_jacobi',
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'roots_legendre',
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'roots_chebyt',
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'roots_chebyu',
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'roots_chebyc',
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'roots_chebys',
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'roots_jacobi',
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'roots_laguerre',
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'roots_genlaguerre',
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'roots_hermite',
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'roots_hermitenorm',
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'roots_gegenbauer',
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'roots_sh_legendre',
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'roots_sh_chebyt',
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'roots_sh_chebyu',
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'roots_sh_jacobi',
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]
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@overload
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def roots_jacobi(
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n: _IntegerType,
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alpha: _FloatingType,
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beta: _FloatingType,
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) -> _PointsAndWeights: ...
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@overload
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def roots_jacobi(
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n: _IntegerType,
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alpha: _FloatingType,
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beta: _FloatingType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_jacobi(
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n: _IntegerType,
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alpha: _FloatingType,
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beta: _FloatingType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_sh_jacobi(
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n: _IntegerType,
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p1: _FloatingType,
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q1: _FloatingType,
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) -> _PointsAndWeights: ...
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@overload
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def roots_sh_jacobi(
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n: _IntegerType,
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p1: _FloatingType,
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q1: _FloatingType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_sh_jacobi(
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n: _IntegerType,
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p1: _FloatingType,
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q1: _FloatingType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_genlaguerre(
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n: _IntegerType,
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alpha: _FloatingType,
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) -> _PointsAndWeights: ...
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@overload
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def roots_genlaguerre(
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n: _IntegerType,
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alpha: _FloatingType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_genlaguerre(
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n: _IntegerType,
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alpha: _FloatingType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_laguerre(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_laguerre(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_laguerre(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_hermite(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_hermite(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_hermite(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_hermitenorm(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_hermitenorm(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_hermitenorm(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_gegenbauer(
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n: _IntegerType,
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alpha: _FloatingType,
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) -> _PointsAndWeights: ...
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@overload
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def roots_gegenbauer(
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n: _IntegerType,
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alpha: _FloatingType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_gegenbauer(
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n: _IntegerType,
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alpha: _FloatingType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_chebyt(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_chebyt(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_chebyu(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_chebyu(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_chebyc(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_chebyc(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_chebyc(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_chebys(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_chebys(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_chebys(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_sh_chebyt(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_sh_chebyt(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_sh_chebyt(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_sh_chebyu(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_sh_chebyu(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_sh_chebyu(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_legendre(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_legendre(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_legendre(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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@overload
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def roots_sh_legendre(n: _IntegerType) -> _PointsAndWeights: ...
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@overload
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def roots_sh_legendre(
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n: _IntegerType,
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mu: Literal[False],
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) -> _PointsAndWeights: ...
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@overload
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def roots_sh_legendre(
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n: _IntegerType,
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mu: Literal[True],
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) -> _PointsAndWeightsAndMu: ...
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class orthopoly1d(numpy.poly1d):
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def __init__(
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self,
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roots: numpy.typing.ArrayLike,
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weights: numpy.typing.ArrayLike | None,
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hn: float = ...,
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kn: float = ...,
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wfunc = Optional[Callable[[float], float]], # noqa: UP007
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limits = tuple[float, float] | None,
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monic: bool = ...,
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eval_func: numpy.ufunc = ...,
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) -> None: ...
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@property
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def limits(self) -> tuple[float, float]: ...
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def weight_func(self, x: float) -> float: ...
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@overload
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def __call__(self, x: _ArrayLike0D) -> Any: ...
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@overload
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def __call__(self, x: numpy.poly1d) -> numpy.poly1d: ... # type: ignore[misc]
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@overload
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def __call__(self, x: numpy.typing.ArrayLike) -> numpy.ndarray: ...
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def legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def chebyc(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def chebys(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def jacobi(
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n: _IntegerType,
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alpha: _FloatingType,
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beta: _FloatingType,
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monic: bool = ...,
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) -> orthopoly1d: ...
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def laguerre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def genlaguerre(
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n: _IntegerType,
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alpha: _FloatingType,
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monic: bool = ...,
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) -> orthopoly1d: ...
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def hermite(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def hermitenorm(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def gegenbauer(
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n: _IntegerType,
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alpha: _FloatingType,
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monic: bool = ...,
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) -> orthopoly1d: ...
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def sh_legendre(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def sh_chebyt(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def sh_chebyu(n: _IntegerType, monic: bool = ...) -> orthopoly1d: ...
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def sh_jacobi(
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n: _IntegerType,
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p: _FloatingType,
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q: _FloatingType,
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monic: bool = ...,
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) -> orthopoly1d: ...
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# These functions are not public, but still need stubs because they
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# get checked in the tests.
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def _roots_hermite_asy(n: _IntegerType) -> _PointsAndWeights: ...
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