1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
|
<html lang="en">
<head>
<title>Cubic Equations - GNU Scientific Library -- Reference Manual</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="GNU Scientific Library -- Reference Manual">
<meta name="generator" content="makeinfo 4.8">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Polynomials.html" title="Polynomials">
<link rel="prev" href="Quadratic-Equations.html" title="Quadratic Equations">
<link rel="next" href="General-Polynomial-Equations.html" title="General Polynomial Equations">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<!--
Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 or
any later version published by the Free Software Foundation; with the
Invariant Sections being ``GNU General Public License'' and ``Free Software
Needs Free Documentation'', the Front-Cover text being ``A GNU Manual'',
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled ``GNU Free Documentation
License''.
(a) The Back-Cover Text is: ``You have freedom to copy and modify this
GNU Manual, like GNU software.''-->
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
pre.display { font-family:inherit }
pre.format { font-family:inherit }
pre.smalldisplay { font-family:inherit; font-size:smaller }
pre.smallformat { font-family:inherit; font-size:smaller }
pre.smallexample { font-size:smaller }
pre.smalllisp { font-size:smaller }
span.sc { font-variant:small-caps }
span.roman { font-family:serif; font-weight:normal; }
span.sansserif { font-family:sans-serif; font-weight:normal; }
--></style>
</head>
<body>
<div class="node">
<p>
<a name="Cubic-Equations"></a>
Next: <a rel="next" accesskey="n" href="General-Polynomial-Equations.html">General Polynomial Equations</a>,
Previous: <a rel="previous" accesskey="p" href="Quadratic-Equations.html">Quadratic Equations</a>,
Up: <a rel="up" accesskey="u" href="Polynomials.html">Polynomials</a>
<hr>
</div>
<h3 class="section">6.4 Cubic Equations</h3>
<p><a name="index-cubic-equation_002c-solving-231"></a>
<div class="defun">
— Function: int <b>gsl_poly_solve_cubic</b> (<var>double a, double b, double c, double * x0, double * x1, double * x2</var>)<var><a name="index-gsl_005fpoly_005fsolve_005fcubic-232"></a></var><br>
<blockquote>
<p>This function finds the real roots of the cubic equation,
<pre class="example"> x^3 + a x^2 + b x + c = 0
</pre>
<p class="noindent">with a leading coefficient of unity. The number of real roots (either
one or three) is returned, and their locations are stored in <var>x0</var>,
<var>x1</var> and <var>x2</var>. If one real root is found then only <var>x0</var> is
modified. When three real roots are found they are stored in <var>x0</var>,
<var>x1</var> and <var>x2</var> in ascending order. The case of coincident roots
is not considered special. For example, the equation (x-1)^3=0
will have three roots with exactly equal values.
</blockquote></div>
<div class="defun">
— Function: int <b>gsl_poly_complex_solve_cubic</b> (<var>double a, double b, double c, gsl_complex * z0, gsl_complex * z1, gsl_complex * z2</var>)<var><a name="index-gsl_005fpoly_005fcomplex_005fsolve_005fcubic-233"></a></var><br>
<blockquote>
<p>This function finds the complex roots of the cubic equation,
<pre class="example"> z^3 + a z^2 + b z + c = 0
</pre>
<p class="noindent">The number of complex roots is returned (always three) and the locations
of the roots are stored in <var>z0</var>, <var>z1</var> and <var>z2</var>. The roots
are returned in ascending order, sorted first by their real components
and then by their imaginary components.
</blockquote></div>
<hr>The GNU Scientific Library - a free numerical library licensed under the GNU GPL<br>Back to the <a href="/software/gsl/">GNU Scientific Library Homepage</a></body></html>
|
