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[3.12] gh-125957: sync argument naming in sphinx docs of the cmath and help() (GH-125958) (#131963)
gh-125957: sync argument naming in sphinx docs of the cmath and help() (GH-125958)
(cherry picked from commit 0a3eb8855c)
Co-authored-by: Sergey B Kirpichev <skirpichev@gmail.com>
Co-authored-by: Bénédikt Tran <10796600+picnixz@users.noreply.github.com>
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@ -55,13 +55,13 @@ segment that joins the origin to *z*.
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The following functions can be used to convert from the native
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rectangular coordinates to polar coordinates and back.
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.. function:: phase(x)
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.. function:: phase(z)
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Return the phase of *x* (also known as the *argument* of *x*), as a float.
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``phase(x)`` is equivalent to ``math.atan2(x.imag, x.real)``. The result
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Return the phase of *z* (also known as the *argument* of *z*), as a float.
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``phase(z)`` is equivalent to ``math.atan2(z.imag, z.real)``. The result
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lies in the range [-\ *π*, *π*], and the branch cut for this operation lies
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along the negative real axis. The sign of the result is the same as the
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sign of ``x.imag``, even when ``x.imag`` is zero::
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sign of ``z.imag``, even when ``z.imag`` is zero::
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>>> phase(complex(-1.0, 0.0))
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3.141592653589793
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@ -71,147 +71,147 @@ rectangular coordinates to polar coordinates and back.
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.. note::
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The modulus (absolute value) of a complex number *x* can be
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The modulus (absolute value) of a complex number *z* can be
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computed using the built-in :func:`abs` function. There is no
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separate :mod:`cmath` module function for this operation.
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.. function:: polar(x)
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.. function:: polar(z)
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Return the representation of *x* in polar coordinates. Returns a
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pair ``(r, phi)`` where *r* is the modulus of *x* and phi is the
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phase of *x*. ``polar(x)`` is equivalent to ``(abs(x),
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phase(x))``.
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Return the representation of *z* in polar coordinates. Returns a
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pair ``(r, phi)`` where *r* is the modulus of *z* and *phi* is the
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phase of *z*. ``polar(z)`` is equivalent to ``(abs(z),
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phase(z))``.
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.. function:: rect(r, phi)
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Return the complex number *x* with polar coordinates *r* and *phi*.
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Return the complex number *z* with polar coordinates *r* and *phi*.
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Equivalent to ``complex(r * math.cos(phi), r * math.sin(phi))``.
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Power and logarithmic functions
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-------------------------------
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.. function:: exp(x)
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.. function:: exp(z)
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Return *e* raised to the power *x*, where *e* is the base of natural
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Return *e* raised to the power *z*, where *e* is the base of natural
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logarithms.
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.. function:: log(x[, base])
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.. function:: log(z[, base])
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Returns the logarithm of *x* to the given *base*. If the *base* is not
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specified, returns the natural logarithm of *x*. There is one branch cut,
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Return the logarithm of *z* to the given *base*. If the *base* is not
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specified, returns the natural logarithm of *z*. There is one branch cut,
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from 0 along the negative real axis to -∞.
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.. function:: log10(x)
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.. function:: log10(z)
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Return the base-10 logarithm of *x*. This has the same branch cut as
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Return the base-10 logarithm of *z*. This has the same branch cut as
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:func:`log`.
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.. function:: sqrt(x)
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.. function:: sqrt(z)
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Return the square root of *x*. This has the same branch cut as :func:`log`.
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Return the square root of *z*. This has the same branch cut as :func:`log`.
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Trigonometric functions
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-----------------------
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.. function:: acos(x)
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.. function:: acos(z)
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Return the arc cosine of *x*. There are two branch cuts: One extends right
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Return the arc cosine of *z*. There are two branch cuts: One extends right
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from 1 along the real axis to ∞. The other extends left from -1 along the
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real axis to -∞.
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.. function:: asin(x)
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.. function:: asin(z)
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Return the arc sine of *x*. This has the same branch cuts as :func:`acos`.
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Return the arc sine of *z*. This has the same branch cuts as :func:`acos`.
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.. function:: atan(x)
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.. function:: atan(z)
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Return the arc tangent of *x*. There are two branch cuts: One extends from
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Return the arc tangent of *z*. There are two branch cuts: One extends from
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``1j`` along the imaginary axis to ``∞j``. The other extends from ``-1j``
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along the imaginary axis to ``-∞j``.
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.. function:: cos(x)
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.. function:: cos(z)
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Return the cosine of *x*.
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Return the cosine of *z*.
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.. function:: sin(x)
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.. function:: sin(z)
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Return the sine of *x*.
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Return the sine of *z*.
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.. function:: tan(x)
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.. function:: tan(z)
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Return the tangent of *x*.
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Return the tangent of *z*.
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Hyperbolic functions
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--------------------
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.. function:: acosh(x)
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.. function:: acosh(z)
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Return the inverse hyperbolic cosine of *x*. There is one branch cut,
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Return the inverse hyperbolic cosine of *z*. There is one branch cut,
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extending left from 1 along the real axis to -∞.
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.. function:: asinh(x)
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.. function:: asinh(z)
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Return the inverse hyperbolic sine of *x*. There are two branch cuts:
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Return the inverse hyperbolic sine of *z*. There are two branch cuts:
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One extends from ``1j`` along the imaginary axis to ``∞j``. The other
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extends from ``-1j`` along the imaginary axis to ``-∞j``.
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.. function:: atanh(x)
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.. function:: atanh(z)
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Return the inverse hyperbolic tangent of *x*. There are two branch cuts: One
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Return the inverse hyperbolic tangent of *z*. There are two branch cuts: One
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extends from ``1`` along the real axis to ``∞``. The other extends from
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``-1`` along the real axis to ``-∞``.
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.. function:: cosh(x)
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.. function:: cosh(z)
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Return the hyperbolic cosine of *x*.
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Return the hyperbolic cosine of *z*.
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.. function:: sinh(x)
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.. function:: sinh(z)
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Return the hyperbolic sine of *x*.
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Return the hyperbolic sine of *z*.
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.. function:: tanh(x)
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.. function:: tanh(z)
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Return the hyperbolic tangent of *x*.
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Return the hyperbolic tangent of *z*.
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Classification functions
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------------------------
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.. function:: isfinite(x)
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.. function:: isfinite(z)
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Return ``True`` if both the real and imaginary parts of *x* are finite, and
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Return ``True`` if both the real and imaginary parts of *z* are finite, and
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``False`` otherwise.
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.. versionadded:: 3.2
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.. function:: isinf(x)
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.. function:: isinf(z)
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Return ``True`` if either the real or the imaginary part of *x* is an
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Return ``True`` if either the real or the imaginary part of *z* is an
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infinity, and ``False`` otherwise.
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.. function:: isnan(x)
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.. function:: isnan(z)
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Return ``True`` if either the real or the imaginary part of *x* is a NaN,
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Return ``True`` if either the real or the imaginary part of *z* is a NaN,
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and ``False`` otherwise.
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