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@@ -4,7 +4,7 @@ | |
This module provides lazy implementations of basic operators on | ||
streams. The classes implemented in this module can be used to build | ||
up more complex streams for different kinds of series (Laurent, | ||
Dirichlet, etc). | ||
Dirichlet, etc.). | ||
EXAMPLES: | ||
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@@ -85,6 +85,8 @@ | |
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# **************************************************************************** | ||
# Copyright (C) 2019 Kwankyu Lee <[email protected]> | ||
# 2022 Martin Rubey <martin.rubey at tuwien.ac.at> | ||
# 2022 Travis Scrimshaw <tcscrims at gmail.com> | ||
# | ||
# This program is free software: you can redistribute it and/or modify | ||
# it under the terms of the GNU General Public License as published by | ||
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@@ -1025,7 +1027,7 @@ def __eq__(self, other): | |
INPUT: | ||
- ``other`` -- a stream of coefficients | ||
- ``other`` -- a :class:`Stream` of coefficients | ||
EXAMPLES:: | ||
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@@ -1088,7 +1090,7 @@ def __eq__(self, other): | |
INPUT: | ||
- ``other`` -- a stream of coefficients | ||
- ``other`` -- a :class:`Stream` of coefficients | ||
EXAMPLES:: | ||
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@@ -1213,8 +1215,8 @@ class Stream_add(Stream_binaryCommutative): | |
INPUT: | ||
- ``left`` -- stream of coefficients on the left side of the operator | ||
- ``right`` -- stream of coefficients on the right side of the operator | ||
- ``left`` -- :class:`Stream` of coefficients on the left side of the operator | ||
- ``right`` -- :class:`Stream` of coefficients on the right side of the operator | ||
EXAMPLES:: | ||
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@@ -1273,8 +1275,8 @@ class Stream_sub(Stream_binary): | |
INPUT: | ||
- ``left`` -- stream of coefficients on the left side of the operator | ||
- ``right`` -- stream of coefficients on the right side of the operator | ||
- ``left`` -- :class:`Stream` of coefficients on the left side of the operator | ||
- ``right`` -- :class:`Stream` of coefficients on the right side of the operator | ||
EXAMPLES:: | ||
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@@ -1338,8 +1340,8 @@ class Stream_cauchy_mul(Stream_binary): | |
INPUT: | ||
- ``left`` -- stream of coefficients on the left side of the operator | ||
- ``right`` -- stream of coefficients on the right side of the operator | ||
- ``left`` -- :class:`Stream` of coefficients on the left side of the operator | ||
- ``right`` -- :class:`Stream` of coefficients on the right side of the operator | ||
EXAMPLES:: | ||
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@@ -1424,8 +1426,8 @@ class Stream_dirichlet_convolve(Stream_binary): | |
INPUT: | ||
- ``left`` -- stream of coefficients on the left side of the operator | ||
- ``right`` -- stream of coefficients on the right side of the operator | ||
- ``left`` -- :class:`Stream` of coefficients on the left side of the operator | ||
- ``right`` -- :class:`Stream` of coefficients on the right side of the operator | ||
The coefficient of `n^{-s}` in the convolution of `l` and `r` | ||
equals `\sum_{k | n} l_k r_{n/k}`. | ||
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@@ -104,6 +104,8 @@ | |
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# **************************************************************************** | ||
# Copyright (C) 2019 Kwankyu Lee <[email protected]> | ||
# 2022 Martin Rubey <martin.rubey at tuwien.ac.at> | ||
# 2022 Travis Scrimshaw <tcscrims at gmail.com> | ||
# | ||
# This program is free software: you can redistribute it and/or modify | ||
# it under the terms of the GNU General Public License as published by | ||
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@@ -1474,7 +1476,7 @@ def tan(self): | |
r""" | ||
Return the tangent of ``self``. | ||
EXAMPLES: | ||
EXAMPLES:: | ||
sage: L.<z> = LazyLaurentSeriesRing(QQ) | ||
sage: tan(z) | ||
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@@ -3281,7 +3283,7 @@ def __call__(self, *g, check=True): | |
INPUT: | ||
- ``g`` -- other series, all of the same parent. | ||
- ``g`` -- other series, all can be coerced into the same parent | ||
EXAMPLES:: | ||
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@@ -3638,7 +3640,7 @@ def __call__(self, *args, check=True): | |
INPUT: | ||
- ``args`` -- other (lazy) symmetric functions. | ||
- ``args`` -- other (lazy) symmetric functions | ||
EXAMPLES:: | ||
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@@ -22,6 +22,8 @@ | |
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# **************************************************************************** | ||
# Copyright (C) 2019 Kwankyu Lee <[email protected]> | ||
# 2022 Martin Rubey <martin.rubey at tuwien.ac.at> | ||
# 2022 Travis Scrimshaw <tcscrims at gmail.com> | ||
# | ||
# This program is free software: you can redistribute it and/or modify | ||
# it under the terms of the GNU General Public License as published by | ||
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@@ -442,7 +444,7 @@ def _element_constructor_(self, x=None, valuation=None, degree=None, constant=No | |
raise ValueError(f"unable to convert {x} into {self}") | ||
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def undefined(self, valuation=None): | ||
""" | ||
r""" | ||
Return an uninitialized series. | ||
INPUT: | ||
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@@ -451,7 +453,7 @@ def undefined(self, valuation=None): | |
Power series can be defined recursively (see | ||
:meth:`sage.rings.lazy_series.LazyModuleElement.define()` for | ||
more examples):: | ||
more examples). | ||
EXAMPLES:: | ||
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@@ -467,13 +469,13 @@ def undefined(self, valuation=None): | |
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class options(GlobalOptions): | ||
r""" | ||
Set and display the options for Lazy Laurent series. | ||
Set and display the options for lazy series. | ||
If no parameters are set, then the function returns a copy of | ||
the options dictionary. | ||
The ``options`` to Lazy Laurent series can be accessed as using | ||
:class:`LazyLaurentSeriesRing.options` of :class:`LazyLaurentSeriesRing`. | ||
The ``options`` to lazy series can be accessed as using | ||
:class:`LazySeriesRing.options`. | ||
@OPTIONS@ | ||
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