
msgid ""
msgstr ""
"Project-Id-Version: Manim \n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
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#: ../../source/reference/manim.utils.simple_functions.rst:2
msgid "simple\\_functions"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions:1
msgid "A collection of simple functions."
msgstr ""

#: ../../source/reference/manim.utils.simple_functions.rst:20
msgid "Functions"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.binary_search:1
msgid "Searches for a value in a range by repeatedly dividing the range in half."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.binary_search:3
msgid "To be more precise, performs numerical binary search to determine the input to ``function``, between the bounds given, that outputs ``target`` to within ``tolerance`` (default of 0.0001). Returns ``None`` if no input can be found within the bounds."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.binary_search:9
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.clip:8
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.get_parameters:5
msgid "Examples"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.binary_search:10
msgid "Consider the polynomial :math:`x^2 + 3x + 1` where we search for a target value of :math:`11`. An exact solution is :math:`x = 2`."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.binary_search:22
msgid "Searching in the interval :math:`[0, 5]` for a target value of :math:`71` does not yield a solution::"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.binary_search:0
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.choose:0
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.get_parameters:0
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.sigmoid:0
msgid "Parameters"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.binary_search:0
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.choose:0
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.get_parameters:0
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.sigmoid:0
msgid "Return type"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.choose:1
msgid "The binomial coefficient n choose k."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.choose:3
msgid ":math:`\\binom{n}{k}` describes the number of possible choices of :math:`k` elements from a set of :math:`n` elements."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.choose:7
#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.sigmoid:7
msgid "References"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.choose:8
msgid "https://en.wikipedia.org/wiki/Combination"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.choose:9
msgid "https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.comb.html"
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.clip:1
msgid "Clips ``a`` to the interval [``min_a``, ``max_a``]."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.clip:3
msgid "Accepts any comparable objects (i.e. those that support <, >). Returns ``a`` if it is between ``min_a`` and ``max_a``. Otherwise, whichever of ``min_a`` and ``max_a`` is closest."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.get_parameters:1
msgid "Return the parameters of ``function`` as an ordered mapping of parameters' names to their corresponding ``Parameter`` objects."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.sigmoid:1
msgid "Returns the output of the logistic function."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.sigmoid:3
msgid "The logistic function, a common example of a sigmoid function, is defined as :math:`\\frac{1}{1 + e^{-x}}`."
msgstr ""

#: ../../../manim/utils/simple_functions.py:docstring of manim.utils.simple_functions.sigmoid:8
msgid "https://en.wikipedia.org/wiki/Sigmoid_function"
msgstr ""


