Mercurial > cpython-lru_cache-weakref

annotate Doc/library/cmath.rst @ 54294:dba767bc3155 legacy-trunk

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
remove mention of old ctypes version
author Benjamin Peterson <benjamin@python.org>
date Sat, 23 May 2009 20:59:09 +0000
parents ee9ced92843a
children 7fd9adc81280 7422d789fdca
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
1
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
2 :mod:`cmath` --- Mathematical functions for complex numbers
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
3 ===========================================================
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
4
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
5 .. module:: cmath
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
6 :synopsis: Mathematical functions for complex numbers.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
7
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
8
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
9 This module is always available. It provides access to mathematical functions
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
10 for complex numbers. The functions in this module accept integers,
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
11 floating-point numbers or complex numbers as arguments. They will also accept
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
12 any Python object that has either a :meth:`__complex__` or a :meth:`__float__`
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
13 method: these methods are used to convert the object to a complex or
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
14 floating-point number, respectively, and the function is then applied to the
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
15 result of the conversion.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
16
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
17 .. note::
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
18
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
19 On platforms with hardware and system-level support for signed
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
20 zeros, functions involving branch cuts are continuous on *both*
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
21 sides of the branch cut: the sign of the zero distinguishes one
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
22 side of the branch cut from the other. On platforms that do not
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
23 support signed zeros the continuity is as specified below.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
24
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
25
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
26 Complex coordinates
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
27 -------------------
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
28
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
29 Complex numbers can be expressed by two important coordinate systems.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
30 Python's :class:`complex` type uses rectangular coordinates where a number
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
31 on the complex plain is defined by two floats, the real part and the imaginary
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
32 part.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
33
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
34 Definition::
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
35
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
36 z = x + 1j * y
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
37
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
38 x := real(z)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
39 y := imag(z)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
40
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
41 In engineering the polar coordinate system is popular for complex numbers. In
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
42 polar coordinates a complex number is defined by the radius *r* and the phase
47809
b11b09c1efef Write out "phi" consistently.
Georg Brandl <georg@python.org>
parents: 46473
diff changeset
43 angle *phi*. The radius *r* is the absolute value of the complex, which can be
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
44 viewed as distance from (0, 0). The radius *r* is always 0 or a positive float.
47809
b11b09c1efef Write out "phi" consistently.
Georg Brandl <georg@python.org>
parents: 46473
diff changeset
45 The phase angle *phi* is the counter clockwise angle from the positive x axis,
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
46 e.g. *1* has the angle *0*, *1j* has the angle *π/2* and *-1* the angle *-π*.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
47
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
48 .. note::
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
49 While :func:`phase` and func:`polar` return *+π* for a negative real they
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
50 may return *-π* for a complex with a very small negative imaginary
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
51 part, e.g. *-1-1E-300j*.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
52
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
53
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
54 Definition::
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
55
47809
b11b09c1efef Write out "phi" consistently.
Georg Brandl <georg@python.org>
parents: 46473
diff changeset
56 z = r * exp(1j * phi)
b11b09c1efef Write out "phi" consistently.
Georg Brandl <georg@python.org>
parents: 46473
diff changeset
57 z = r * cis(phi)
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
58
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
59 r := abs(z) := sqrt(real(z)**2 + imag(z)**2)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
60 phi := phase(z) := atan2(imag(z), real(z))
47809
b11b09c1efef Write out "phi" consistently.
Georg Brandl <georg@python.org>
parents: 46473
diff changeset
61 cis(phi) := cos(phi) + 1j * sin(phi)
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
62
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
63
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
64 .. function:: phase(x)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
65
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
66 Return phase, also known as the argument, of a complex.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
67
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
68 .. versionadded:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
69
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
70
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
71 .. function:: polar(x)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
72
50522
ee9ced92843a Merged revisions 68133-68134,68141-68142,68145-68146,68148-68149,68159-68162,68166,68171-68174,68179,68195-68196,68210,68214-68215,68217-68222 via svnmerge from
Georg Brandl <georg@python.org>
parents: 47809
diff changeset
73 Convert a :class:`complex` from rectangular coordinates to polar
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
74 coordinates. The function returns a tuple with the two elements
50522
ee9ced92843a Merged revisions 68133-68134,68141-68142,68145-68146,68148-68149,68159-68162,68166,68171-68174,68179,68195-68196,68210,68214-68215,68217-68222 via svnmerge from
Georg Brandl <georg@python.org>
parents: 47809
diff changeset
75 *r* and *phi*. *r* is the distance from 0 and *phi* the phase
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
76 angle.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
77
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
78 .. versionadded:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
79
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
80
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
81 .. function:: rect(r, phi)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
82
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
83 Convert from polar coordinates to rectangular coordinates and return
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
84 a :class:`complex`.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
85
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
86 .. versionadded:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
87
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
88
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
89
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
90 cmath functions
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
91 ---------------
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
92
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
93 .. function:: acos(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
94
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
95 Return the arc cosine of *x*. There are two branch cuts: One extends right from
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
96 1 along the real axis to ∞, continuous from below. The other extends left from
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
97 -1 along the real axis to -∞, continuous from above.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
98
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
99
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
100 .. function:: acosh(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
101
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
102 Return the hyperbolic arc cosine of *x*. There is one branch cut, extending left
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
103 from 1 along the real axis to -∞, continuous from above.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
104
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
105
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
106 .. function:: asin(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
107
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
108 Return the arc sine of *x*. This has the same branch cuts as :func:`acos`.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
109
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
110
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
111 .. function:: asinh(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
112
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
113 Return the hyperbolic arc sine of *x*. There are two branch cuts:
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
114 One extends from ``1j`` along the imaginary axis to ``∞j``,
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
115 continuous from the right. The other extends from ``-1j`` along
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
116 the imaginary axis to ``-∞j``, continuous from the left.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
117
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
118 .. versionchanged:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
119 branch cuts moved to match those recommended by the C99 standard
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
120
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
121
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
122 .. function:: atan(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
123
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
124 Return the arc tangent of *x*. There are two branch cuts: One extends from
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
125 ``1j`` along the imaginary axis to ``∞j``, continuous from the right. The
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
126 other extends from ``-1j`` along the imaginary axis to ``-∞j``, continuous
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
127 from the left.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
128
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
129 .. versionchanged:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
130 direction of continuity of upper cut reversed
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
131
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
132
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
133 .. function:: atanh(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
134
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
135 Return the hyperbolic arc tangent of *x*. There are two branch cuts: One
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
136 extends from ``1`` along the real axis to ``∞``, continuous from below. The
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
137 other extends from ``-1`` along the real axis to ``-∞``, continuous from
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
138 above.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
139
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
140 .. versionchanged:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
141 direction of continuity of right cut reversed
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
142
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
143
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
144 .. function:: cos(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
145
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
146 Return the cosine of *x*.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
147
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
148
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
149 .. function:: cosh(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
150
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
151 Return the hyperbolic cosine of *x*.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
152
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
153
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
154 .. function:: exp(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
155
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
156 Return the exponential value ``e**x``.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
157
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
158
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
159 .. function:: isinf(x)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
160
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
161 Return *True* if the real or the imaginary part of x is positive
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
162 or negative infinity.
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
163
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
164 .. versionadded:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
165
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
166
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
167 .. function:: isnan(x)
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
168
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
169 Return *True* if the real or imaginary part of x is not a number (NaN).
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
170
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
171 .. versionadded:: 2.6
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
172
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
173
42604
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
174 .. function:: log(x[, base])
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
175
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
176 Returns the logarithm of *x* to the given *base*. If the *base* is not
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
177 specified, returns the natural logarithm of *x*. There is one branch cut, from 0
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
178 along the negative real axis to -∞, continuous from above.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
179
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
180 .. versionchanged:: 2.4
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
181 *base* argument added.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
182
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
183
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
184 .. function:: log10(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
185
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
186 Return the base-10 logarithm of *x*. This has the same branch cut as
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
187 :func:`log`.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
188
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
189
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
190 .. function:: sin(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
191
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
192 Return the sine of *x*.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
193
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
194
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
195 .. function:: sinh(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
196
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
197 Return the hyperbolic sine of *x*.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
198
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
199
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
200 .. function:: sqrt(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
201
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
202 Return the square root of *x*. This has the same branch cut as :func:`log`.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
203
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
204
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
205 .. function:: tan(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
206
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
207 Return the tangent of *x*.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
208
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
209
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
210 .. function:: tanh(x)
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
211
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
212 Return the hyperbolic tangent of *x*.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
213
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
214 The module also defines two mathematical constants:
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
215
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
216
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
217 .. data:: pi
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
218
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
219 The mathematical constant *pi*, as a float.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
220
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
221
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
222 .. data:: e
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
223
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
224 The mathematical constant *e*, as a float.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
225
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
226 .. index:: module: math
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
227
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
228 Note that the selection of functions is similar, but not identical, to that in
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
229 module :mod:`math`. The reason for having two modules is that some users aren't
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
230 interested in complex numbers, and perhaps don't even know what they are. They
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
231 would rather have ``math.sqrt(-1)`` raise an exception than return a complex
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
232 number. Also note that the functions defined in :mod:`cmath` always return a
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
233 complex number, even if the answer can be expressed as a real number (in which
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
234 case the complex number has an imaginary part of zero).
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
235
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
236 A note on branch cuts: They are curves along which the given function fails to
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
237 be continuous. They are a necessary feature of many complex functions. It is
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
238 assumed that if you need to compute with complex functions, you will understand
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
239 about branch cuts. Consult almost any (not too elementary) book on complex
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
240 variables for enlightenment. For information of the proper choice of branch
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
241 cuts for numerical purposes, a good reference should be the following:
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
242
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
243
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
244 .. seealso::
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
245
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
246 Kahan, W: Branch cuts for complex elementary functions; or, Much ado about
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
247 nothing's sign bit. In Iserles, A., and Powell, M. (eds.), The state of the art
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
248 in numerical analysis. Clarendon Press (1987) pp165-211.
9e1529bf0442 Move the 3k reST doc tree in place.
Georg Brandl <georg@python.org>
parents:
diff changeset
249
46473
5bc7b20dc04a I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.
Christian Heimes <christian@cheimes.de>
parents: 42604
diff changeset
250