diff --git a/Doc/library/cmath.rst b/Doc/library/cmath.rst index e7c027dd4d0c22..31dacae35c7748 100644 --- a/Doc/library/cmath.rst +++ b/Doc/library/cmath.rst @@ -55,13 +55,13 @@ segment that joins the origin to *z*. The following functions can be used to convert from the native rectangular coordinates to polar coordinates and back. -.. function:: phase(x) +.. function:: phase(z) - Return the phase of *x* (also known as the *argument* of *x*), as a float. - ``phase(x)`` is equivalent to ``math.atan2(x.imag, x.real)``. The result + Return the phase of *z* (also known as the *argument* of *z*), as a float. + ``phase(z)`` is equivalent to ``math.atan2(z.imag, z.real)``. The result lies in the range [-\ *π*, *π*], and the branch cut for this operation lies along the negative real axis. The sign of the result is the same as the - sign of ``x.imag``, even when ``x.imag`` is zero:: + sign of ``z.imag``, even when ``z.imag`` is zero:: >>> phase(-1+0j) 3.141592653589793 @@ -71,147 +71,147 @@ rectangular coordinates to polar coordinates and back. .. note:: - The modulus (absolute value) of a complex number *x* can be + The modulus (absolute value) of a complex number *z* can be computed using the built-in :func:`abs` function. There is no separate :mod:`cmath` module function for this operation. -.. function:: polar(x) +.. function:: polar(z) - Return the representation of *x* in polar coordinates. Returns a - pair ``(r, phi)`` where *r* is the modulus of *x* and phi is the - phase of *x*. ``polar(x)`` is equivalent to ``(abs(x), - phase(x))``. + Return the representation of *z* in polar coordinates. Returns a + pair ``(r, phi)`` where *r* is the modulus of *z* and *phi* is the + phase of *z*. ``polar(z)`` is equivalent to ``(abs(z), + phase(z))``. .. function:: rect(r, phi) - Return the complex number *x* with polar coordinates *r* and *phi*. + Return the complex number *z* with polar coordinates *r* and *phi*. Equivalent to ``complex(r * math.cos(phi), r * math.sin(phi))``. Power and logarithmic functions ------------------------------- -.. function:: exp(x) +.. function:: exp(z) - Return *e* raised to the power *x*, where *e* is the base of natural + Return *e* raised to the power *z*, where *e* is the base of natural logarithms. -.. function:: log(x[, base]) +.. function:: log(z[, base]) - Returns the logarithm of *x* to the given *base*. If the *base* is not - specified, returns the natural logarithm of *x*. There is one branch cut, + Return the logarithm of *z* to the given *base*. If the *base* is not + specified, returns the natural logarithm of *z*. There is one branch cut, from 0 along the negative real axis to -∞. -.. function:: log10(x) +.. function:: log10(z) - Return the base-10 logarithm of *x*. This has the same branch cut as + Return the base-10 logarithm of *z*. This has the same branch cut as :func:`log`. -.. function:: sqrt(x) +.. function:: sqrt(z) - Return the square root of *x*. This has the same branch cut as :func:`log`. + Return the square root of *z*. This has the same branch cut as :func:`log`. Trigonometric functions ----------------------- -.. function:: acos(x) +.. function:: acos(z) - Return the arc cosine of *x*. There are two branch cuts: One extends right + Return the arc cosine of *z*. There are two branch cuts: One extends right from 1 along the real axis to ∞. The other extends left from -1 along the real axis to -∞. -.. function:: asin(x) +.. function:: asin(z) - Return the arc sine of *x*. This has the same branch cuts as :func:`acos`. + Return the arc sine of *z*. This has the same branch cuts as :func:`acos`. -.. function:: atan(x) +.. function:: atan(z) - Return the arc tangent of *x*. There are two branch cuts: One extends from + Return the arc tangent of *z*. There are two branch cuts: One extends from ``1j`` along the imaginary axis to ``∞j``. The other extends from ``-1j`` along the imaginary axis to ``-∞j``. -.. function:: cos(x) +.. function:: cos(z) - Return the cosine of *x*. + Return the cosine of *z*. -.. function:: sin(x) +.. function:: sin(z) - Return the sine of *x*. + Return the sine of *z*. -.. function:: tan(x) +.. function:: tan(z) - Return the tangent of *x*. + Return the tangent of *z*. Hyperbolic functions -------------------- -.. function:: acosh(x) +.. function:: acosh(z) - Return the inverse hyperbolic cosine of *x*. There is one branch cut, + Return the inverse hyperbolic cosine of *z*. There is one branch cut, extending left from 1 along the real axis to -∞. -.. function:: asinh(x) +.. function:: asinh(z) - Return the inverse hyperbolic sine of *x*. There are two branch cuts: + Return the inverse hyperbolic sine of *z*. There are two branch cuts: One extends from ``1j`` along the imaginary axis to ``∞j``. The other extends from ``-1j`` along the imaginary axis to ``-∞j``. -.. function:: atanh(x) +.. function:: atanh(z) - Return the inverse hyperbolic tangent of *x*. There are two branch cuts: One + Return the inverse hyperbolic tangent of *z*. There are two branch cuts: One extends from ``1`` along the real axis to ``∞``. The other extends from ``-1`` along the real axis to ``-∞``. -.. function:: cosh(x) +.. function:: cosh(z) - Return the hyperbolic cosine of *x*. + Return the hyperbolic cosine of *z*. -.. function:: sinh(x) +.. function:: sinh(z) - Return the hyperbolic sine of *x*. + Return the hyperbolic sine of *z*. -.. function:: tanh(x) +.. function:: tanh(z) - Return the hyperbolic tangent of *x*. + Return the hyperbolic tangent of *z*. Classification functions ------------------------ -.. function:: isfinite(x) +.. function:: isfinite(z) - Return ``True`` if both the real and imaginary parts of *x* are finite, and + Return ``True`` if both the real and imaginary parts of *z* are finite, and ``False`` otherwise. .. versionadded:: 3.2 -.. function:: isinf(x) +.. function:: isinf(z) - Return ``True`` if either the real or the imaginary part of *x* is an + Return ``True`` if either the real or the imaginary part of *z* is an infinity, and ``False`` otherwise. -.. function:: isnan(x) +.. function:: isnan(z) - Return ``True`` if either the real or the imaginary part of *x* is a NaN, + Return ``True`` if either the real or the imaginary part of *z* is a NaN, and ``False`` otherwise. pFad - Phonifier reborn

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