annotate doc/interpreter/arith.txi @ 20628:3af34e1ef330

Preliminary inclusion of uixx objects properties in the manual (bug #46076) * doc/interpreter/genpropdoc.m: add uixx objects to the list of supported graphics objects * doc/interpreter/genpropdoc.m (get_doc): add uixx objects and their specific properties (currently empty documentation) * doc/interpreter/plot.txi("Interacting with Plots"): add a note and a reference about ui* family of functions. * doc/interpreter/plot.txi("Interacting with Plots"): for consistency, remove "uimenu" reference. All the other uixx are already in the gui section * doc/interpreter/plot.txi("graphics data structure"): add uixx objects * doc/interpreter/gui.txi("UI Elements"): add "uimenu" function reference * doc/module.mk: add rules to build uixx properties texi files. * graphics.in.h: make uixx "__object__" property (Octave internal) hidden so that it does not appear in the documentation.
author Pantxo Diribarne <pantxo.diribarne@gmail.com>
date Fri, 09 Oct 2015 16:25:27 +0200
parents 45565ecec019
children
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1 @c Copyright (C) 1996-2015 John W. Eaton
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2 @c
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3 @c This file is part of Octave.
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4 @c
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5 @c Octave is free software; you can redistribute it and/or modify it
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6 @c under the terms of the GNU General Public License as published by the
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7 @c Free Software Foundation; either version 3 of the License, or (at
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8 @c your option) any later version.
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9 @c
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10 @c Octave is distributed in the hope that it will be useful, but WITHOUT
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11 @c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 @c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 @c for more details.
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14 @c
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15 @c You should have received a copy of the GNU General Public License
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16 @c along with Octave; see the file COPYING. If not, see
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17 @c <http://www.gnu.org/licenses/>.
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18
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19 @node Arithmetic
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20 @chapter Arithmetic
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21
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22 Unless otherwise noted, all of the functions described in this chapter
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23 will work for real and complex scalar, vector, or matrix arguments. Functions
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24 described as @dfn{mapping functions} apply the given operation individually to
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25 each element when given a matrix argument. For example:
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26
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27 @example
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28 @group
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29 sin ([1, 2; 3, 4])
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30 @result{} 0.84147 0.90930
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31 0.14112 -0.75680
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32 @end group
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33 @end example
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34
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35 @menu
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36 * Exponents and Logarithms::
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37 * Complex Arithmetic::
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38 * Trigonometry::
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39 * Sums and Products::
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40 * Utility Functions::
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41 * Special Functions::
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42 * Rational Approximations::
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43 * Coordinate Transformations::
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44 * Mathematical Constants::
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45 @end menu
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46
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47 @node Exponents and Logarithms
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48 @section Exponents and Logarithms
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49
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50 @DOCSTRING(exp)
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51
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52 @DOCSTRING(expm1)
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53
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54 @DOCSTRING(log)
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55
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56 @DOCSTRING(reallog)
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57
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58 @DOCSTRING(log1p)
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59
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60 @DOCSTRING(log10)
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61
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62 @DOCSTRING(log2)
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63
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64 @DOCSTRING(pow2)
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65
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66 @DOCSTRING(nextpow2)
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67
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68 @DOCSTRING(realpow)
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69
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70 @DOCSTRING(sqrt)
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71
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72 @DOCSTRING(realsqrt)
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73
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74 @DOCSTRING(cbrt)
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75
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76 @DOCSTRING(nthroot)
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77
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78 @node Complex Arithmetic
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79 @section Complex Arithmetic
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80
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81 In the descriptions of the following functions,
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82 @tex
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83 $z$ is the complex number $x + iy$, where $i$ is defined as
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84 $\sqrt{-1}$.
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85 @end tex
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86 @ifnottex
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87 @var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is
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88 defined as @code{sqrt (-1)}.
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89 @end ifnottex
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90
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91 @DOCSTRING(abs)
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92
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93 @DOCSTRING(arg)
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94
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95 @DOCSTRING(conj)
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96
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97 @DOCSTRING(cplxpair)
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98
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99 @DOCSTRING(imag)
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100
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101 @DOCSTRING(real)
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102
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103 @node Trigonometry
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104 @section Trigonometry
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105
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106 Octave provides the following trigonometric functions where angles are
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107 specified in radians. To convert from degrees to radians multiply by
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108 @tex
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109 $\pi/180$
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110 @end tex
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111 @ifnottex
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112 @code{pi/180}
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113 @end ifnottex
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114 (e.g., @code{sin (30 * pi/180)} returns the sine of 30 degrees). As
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115 an alternative, Octave provides a number of trigonometric functions
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116 which work directly on an argument specified in degrees. These functions
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117 are named after the base trigonometric function with a @samp{d} suffix. For
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118 example, @code{sin} expects an angle in radians while @code{sind} expects an
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119 angle in degrees.
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120
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121 Octave uses the C library trigonometric functions. It is expected that these
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122 functions are defined by the ISO/IEC 9899 Standard. This Standard is available
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123 at: @url{http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf}.
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124 Section F.9.1 deals with the trigonometric functions. The behavior of most of
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125 the functions is relatively straightforward. However, there are some
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126 exceptions to the standard behavior. Many of the exceptions involve the
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127 behavior for -0. The most complex case is atan2. Octave exactly implements
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128 the behavior given in the Standard. Including
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129 @tex
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130 $atan2(\pm0, -0)$ returns $\pm \pi$.
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131 @end tex
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132 @ifnottex
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133 @code{atan2(+- 0, 0)} returns @code{+- pi}.
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134 @end ifnottex
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135
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136 It should be noted that @sc{matlab} uses different definitions which apparently
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137 do not distinguish -0.
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138
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139 @DOCSTRING(sin)
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140 @DOCSTRING(cos)
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141 @DOCSTRING(tan)
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142 @DOCSTRING(sec)
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143 @DOCSTRING(csc)
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144 @DOCSTRING(cot)
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145
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146 @DOCSTRING(asin)
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147 @DOCSTRING(acos)
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148 @DOCSTRING(atan)
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149 @DOCSTRING(asec)
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150 @DOCSTRING(acsc)
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151 @DOCSTRING(acot)
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152
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153 @DOCSTRING(sinh)
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154 @DOCSTRING(cosh)
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155 @DOCSTRING(tanh)
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156 @DOCSTRING(sech)
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157 @DOCSTRING(csch)
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158 @DOCSTRING(coth)
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159
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160 @DOCSTRING(asinh)
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161 @DOCSTRING(acosh)
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162 @DOCSTRING(atanh)
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163 @DOCSTRING(asech)
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164 @DOCSTRING(acsch)
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165 @DOCSTRING(acoth)
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166
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167 @DOCSTRING(atan2)
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168
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169 Octave provides the following trigonometric functions where angles are
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170 specified in degrees. These functions produce true zeros at the appropriate
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171 intervals rather than the small round-off error that occurs when using
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172 radians. For example:
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173
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174 @example
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175 @group
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176 cosd (90)
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177 @result{} 0
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178 cos (pi/2)
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179 @result{} 6.1230e-17
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180 @end group
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181 @end example
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182
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183 @DOCSTRING(sind)
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184 @DOCSTRING(cosd)
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185 @DOCSTRING(tand)
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186 @DOCSTRING(secd)
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187 @DOCSTRING(cscd)
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188 @DOCSTRING(cotd)
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189
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190 @DOCSTRING(asind)
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191 @DOCSTRING(acosd)
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192 @DOCSTRING(atand)
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193 @DOCSTRING(atan2d)
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194 @DOCSTRING(asecd)
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195 @DOCSTRING(acscd)
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196 @DOCSTRING(acotd)
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197
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198 @node Sums and Products
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199 @section Sums and Products
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200
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201 @DOCSTRING(sum)
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202
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203 @DOCSTRING(prod)
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204
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205 @DOCSTRING(cumsum)
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206
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207 @DOCSTRING(cumprod)
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208
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209 @DOCSTRING(sumsq)
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210
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211 @node Utility Functions
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212 @section Utility Functions
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213
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214 @DOCSTRING(ceil)
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215
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216 @DOCSTRING(fix)
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217
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218 @DOCSTRING(floor)
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219
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220 @DOCSTRING(round)
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221
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222 @DOCSTRING(roundb)
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223
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224 @DOCSTRING(max)
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225
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226 @DOCSTRING(min)
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227
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228 @DOCSTRING(cummax)
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229
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230 @DOCSTRING(cummin)
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231
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232 @DOCSTRING(hypot)
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233
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234 @DOCSTRING(gradient)
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235
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236 @DOCSTRING(dot)
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237
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238 @DOCSTRING(cross)
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239
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240 @DOCSTRING(divergence)
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241
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242 @DOCSTRING(curl)
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243
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244 @DOCSTRING(del2)
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245
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246 @DOCSTRING(factorial)
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247
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248 @DOCSTRING(factor)
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249
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250 @DOCSTRING(gcd)
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251
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252 @DOCSTRING(lcm)
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253
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254 @DOCSTRING(chop)
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255
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256 @DOCSTRING(rem)
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257
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258 @DOCSTRING(mod)
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259
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260 @DOCSTRING(primes)
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261
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262 @DOCSTRING(list_primes)
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263
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264 @DOCSTRING(sign)
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265
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266 @DOCSTRING(signbit)
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267
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268 @node Special Functions
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269 @section Special Functions
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270
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271 @DOCSTRING(airy)
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272
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273 @DOCSTRING(besselj)
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274
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275 @DOCSTRING(beta)
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276
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277 @DOCSTRING(betainc)
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278
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279 @DOCSTRING(betaincinv)
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280
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281 @DOCSTRING(betaln)
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282
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283 @DOCSTRING(bincoeff)
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284
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285 @DOCSTRING(commutation_matrix)
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286
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287 @DOCSTRING(duplication_matrix)
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288
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289 @DOCSTRING(dawson)
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290
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291 @DOCSTRING(ellipj)
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292
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents: 15698
diff changeset
293 @DOCSTRING(ellipke)
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents: 15698
diff changeset
294
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
295 @DOCSTRING(erf)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
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296
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
297 @DOCSTRING(erfc)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
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298
11529
f98f925d8e5c Add undocumented function erfcx to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
299 @DOCSTRING(erfcx)
f98f925d8e5c Add undocumented function erfcx to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
300
15696
2fac72a256ce Add complex erf,erfc,erfcx,erfi,dawson routines from Faddeeva package.
Steven G. Johnson <stevenj@alum.mit.edu>
parents: 15487
diff changeset
301 @DOCSTRING(erfi)
2fac72a256ce Add complex erf,erfc,erfcx,erfi,dawson routines from Faddeeva package.
Steven G. Johnson <stevenj@alum.mit.edu>
parents: 15487
diff changeset
302
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
303 @DOCSTRING(erfinv)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
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304
14770
cb85e836d035 New function: erfcinv (bug #36607)
Axel Mathéi <axel.mathei@gmail.com>
parents: 14138
diff changeset
305 @DOCSTRING(erfcinv)
cb85e836d035 New function: erfcinv (bug #36607)
Axel Mathéi <axel.mathei@gmail.com>
parents: 14138
diff changeset
306
16584
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents: 15698
diff changeset
307 @DOCSTRING(expint)
2f766ceeb03e Add ellipj, ellipke, and expint functions from Octave Forge
Mike Miller <mtmiller@ieee.org>
parents: 15698
diff changeset
308
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
309 @DOCSTRING(gamma)
3294
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jwe
parents:
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310
3444
fa0d84558faa [project @ 2000-01-17 08:40:39 by jwe]
jwe
parents: 3428
diff changeset
311 @DOCSTRING(gammainc)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
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312
6502
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
jwe
parents: 4169
diff changeset
313 @DOCSTRING(legendre)
6ab0a8767780 [project @ 2007-04-06 03:32:06 by jwe]
jwe
parents: 4169
diff changeset
314
17097
e7a059a9a644 doc: Use XREF as anchor prefix in documentation for clearer results in Info viewer.
Rik <rik@octave.org>
parents: 16938
diff changeset
315 @anchor{XREFgammaln}
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
316 @DOCSTRING(lgamma)
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
317
20189
45565ecec019 New function psi to compute the digamma function.
Carnë Draug <carandraug@octave.org>
parents: 19731
diff changeset
318 @DOCSTRING(psi)
45565ecec019 New function psi to compute the digamma function.
Carnë Draug <carandraug@octave.org>
parents: 19731
diff changeset
319
12185
862a8e490445 doc fix for rational approximation functions
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
320 @node Rational Approximations
862a8e490445 doc fix for rational approximation functions
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
321 @section Rational Approximations
862a8e490445 doc fix for rational approximation functions
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
322
862a8e490445 doc fix for rational approximation functions
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
323 @DOCSTRING(rat)
862a8e490445 doc fix for rational approximation functions
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
324
862a8e490445 doc fix for rational approximation functions
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
325 @DOCSTRING(rats)
862a8e490445 doc fix for rational approximation functions
John W. Eaton <jwe@octave.org>
parents: 11532
diff changeset
326
4169
d5667eaf8859 [project @ 2002-11-12 03:13:42 by jwe]
jwe
parents: 4167
diff changeset
327 @node Coordinate Transformations
3803
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
328 @section Coordinate Transformations
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
329
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
330 @DOCSTRING(cart2pol)
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
331
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
332 @DOCSTRING(pol2cart)
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
333
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
334 @DOCSTRING(cart2sph)
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
335
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
336 @DOCSTRING(sph2cart)
63c75bc3db82 [project @ 2001-02-28 08:24:40 by jwe]
jwe
parents: 3459
diff changeset
337
4169
d5667eaf8859 [project @ 2002-11-12 03:13:42 by jwe]
jwe
parents: 4167
diff changeset
338 @node Mathematical Constants
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
diff changeset
339 @section Mathematical Constants
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
diff changeset
340
9155
ad20b967e1c9 Update section 17.3 (Trigonometry) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9154
diff changeset
341 @DOCSTRING(e)
ad20b967e1c9 Update section 17.3 (Trigonometry) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9154
diff changeset
342
ad20b967e1c9 Update section 17.3 (Trigonometry) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9154
diff changeset
343 @DOCSTRING(pi)
ad20b967e1c9 Update section 17.3 (Trigonometry) of arith.txi
Rik <rdrider0-list@yahoo.com>
parents: 9154
diff changeset
344
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
345 @DOCSTRING(I)
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
346
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
347 @DOCSTRING(Inf)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
diff changeset
348
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
349 @DOCSTRING(NaN)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
diff changeset
350
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
351 @DOCSTRING(eps)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
diff changeset
352
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
353 @DOCSTRING(realmax)
3294
bfe1573bd2ae [project @ 1999-10-19 10:06:07 by jwe]
jwe
parents:
diff changeset
354
3321
6923abb04e16 [project @ 1999-10-26 18:15:30 by jwe]
jwe
parents: 3294
diff changeset
355 @DOCSTRING(realmin)