1math::complexnumbers(n) Tcl Math Library math::complexnumbers(n)
2______________________________________________________________________________
6
8 math::complexnumbers - Straightforward complex number package
9
11 package require Tcl 8.3
12 package require math::complexnumbers ?1.0.2?
14 ::math::complexnumbers::+ z1 z2
16 ::math::complexnumbers::- z1 z2
18 ::math::complexnumbers::* z1 z2
20 ::math::complexnumbers::/ z1 z2
22 ::math::complexnumbers::conj z1
24 ::math::complexnumbers::real z1
26 ::math::complexnumbers::imag z1
28 ::math::complexnumbers::mod z1
30 ::math::complexnumbers::arg z1
32 ::math::complexnumbers::complex real imag
34 ::math::complexnumbers::tostring z1
36 ::math::complexnumbers::exp z1
38 ::math::complexnumbers::sin z1
40 ::math::complexnumbers::cos z1
42 ::math::complexnumbers::tan z1
44 ::math::complexnumbers::log z1
46 ::math::complexnumbers::sqrt z1
48 ::math::complexnumbers::pow z1 z2
50______________________________________________________________________________
52
54 The mathematical module complexnumbers provides a straightforward im‐
55 plementation of complex numbers in pure Tcl. The philosophy is that the
56 user knows he or she is dealing with complex numbers in an abstract way
57 and wants as high a performance as can be had within the limitations of
58 an interpreted language.
59 Therefore the procedures defined in this package assume that the argu‐
61 ments are valid (representations of) "complex numbers", that is, lists
62 of two numbers defining the real and imaginary part of a complex number
63 (though this is a mere detail: rely on the complex command to construct
64 a valid number.)
65 Most procedures implement the basic arithmetic operations or elementary
67 functions whereas several others convert to and from different repre‐
68 sentations:
69 set z [complex 0 1]
71 puts "z = [tostring $z]"
72 puts "z**2 = [* $z $z]
73 would result in:
75 z = i
78 z**2 = -1
79
82 The package implements all or most basic operations and elementary
83 functions.
84 The arithmetic operations are:
86 ::math::complexnumbers::+ z1 z2
88 Add the two arguments and return the resulting complex number
89 complex z1 (in)
91 First argument in the summation
92 complex z2 (in)
94 Second argument in the summation
95 ::math::complexnumbers::- z1 z2
98 Subtract the second argument from the first and return the re‐
99 sulting complex number. If there is only one argument, the oppo‐
100 site of z1 is returned (i.e. -z1)
101 complex z1 (in)
103 First argument in the subtraction
104 complex z2 (in)
106 Second argument in the subtraction (optional)
107 ::math::complexnumbers::* z1 z2
110 Multiply the two arguments and return the resulting complex num‐
111 ber
112 complex z1 (in)
114 First argument in the multiplication
115 complex z2 (in)
117 Second argument in the multiplication
118 ::math::complexnumbers::/ z1 z2
121 Divide the first argument by the second and return the resulting
122 complex number
123 complex z1 (in)
125 First argument (numerator) in the division
126 complex z2 (in)
128 Second argument (denominator) in the division
129 ::math::complexnumbers::conj z1
132 Return the conjugate of the given complex number
133 complex z1 (in)
135 Complex number in question
136 Conversion/inquiry procedures:
139 ::math::complexnumbers::real z1
141 Return the real part of the given complex number
142 complex z1 (in)
144 Complex number in question
145 ::math::complexnumbers::imag z1
148 Return the imaginary part of the given complex number
149 complex z1 (in)
151 Complex number in question
152 ::math::complexnumbers::mod z1
155 Return the modulus of the given complex number
156 complex z1 (in)
158 Complex number in question
159 ::math::complexnumbers::arg z1
162 Return the argument ("angle" in radians) of the given complex
163 number
164 complex z1 (in)
166 Complex number in question
167 ::math::complexnumbers::complex real imag
170 Construct the complex number "real + imag*i" and return it
171 float real (in)
173 The real part of the new complex number
174 float imag (in)
176 The imaginary part of the new complex number
177 ::math::complexnumbers::tostring z1
180 Convert the complex number to the form "real + imag*i" and re‐
181 turn the string
182 float complex (in)
184 The complex number to be converted
185 Elementary functions:
188 ::math::complexnumbers::exp z1
190 Calculate the exponential for the given complex argument and re‐
191 turn the result
192 complex z1 (in)
194 The complex argument for the function
195 ::math::complexnumbers::sin z1
198 Calculate the sine function for the given complex argument and
199 return the result
200 complex z1 (in)
202 The complex argument for the function
203 ::math::complexnumbers::cos z1
206 Calculate the cosine function for the given complex argument and
207 return the result
208 complex z1 (in)
210 The complex argument for the function
211 ::math::complexnumbers::tan z1
214 Calculate the tangent function for the given complex argument
215 and return the result
216 complex z1 (in)
218 The complex argument for the function
219 ::math::complexnumbers::log z1
222 Calculate the (principle value of the) logarithm for the given
223 complex argument and return the result
224 complex z1 (in)
226 The complex argument for the function
227 ::math::complexnumbers::sqrt z1
230 Calculate the (principle value of the) square root for the given
231 complex argument and return the result
232 complex z1 (in)
234 The complex argument for the function
235 ::math::complexnumbers::pow z1 z2
238 Calculate "z1 to the power of z2" and return the result
239 complex z1 (in)
241 The complex number to be raised to a power
242 complex z2 (in)
244 The complex power to be used
245
247 This document, and the package it describes, will undoubtedly contain
248 bugs and other problems. Please report such in the category math ::
249 complexnumbers of the Tcllib Trackers [http://core.tcl.tk/tcllib/re‐
250 portlist]. Please also report any ideas for enhancements you may have
251 for either package and/or documentation.
252 When proposing code changes, please provide unified diffs, i.e the out‐
254 put of diff -u.
255 Note further that attachments are strongly preferred over inlined
257 patches. Attachments can be made by going to the Edit form of the
258 ticket immediately after its creation, and then using the left-most
259 button in the secondary navigation bar.
260
262 complex numbers, math
263
265 Mathematics
266
268 Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
269tcllib 1.0.2 math::complexnumbers(n)