1math::complexnumbers(n) Tcl Math Library math::complexnumbers(n)
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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
55 implementation of complex numbers in pure Tcl. The philosophy is that
56 the user knows he or she is dealing with complex numbers in an abstract
57 way and wants as high a performance as can be had within the limita‐
58 tions of 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
77 z**2 = -1
78
81 The package implements all or most basic operations and elementary
82 functions.
83 The arithmetic operations are:
85 ::math::complexnumbers::+ z1 z2
87 Add the two arguments and return the resulting complex number
88 z1 complex (in)
90 First argument in the summation
91 z2 complex (in)
93 Second argument in the summation
94 ::math::complexnumbers::- z1 z2
97 Subtract the second argument from the first and return the
98 resulting complex number. If there is only one argument, the
99 opposite of z1 is returned (i.e. -z1)
100 z1 complex (in)
102 First argument in the subtraction
103 z2 complex (in)
105 Second argument in the subtraction (optional)
106 ::math::complexnumbers::* z1 z2
109 Multiply the two arguments and return the resulting complex num‐
110 ber
111 z1 complex (in)
113 First argument in the multiplication
114 z2 complex (in)
116 Second argument in the multiplication
117 ::math::complexnumbers::/ z1 z2
120 Divide the first argument by the second and return the resulting
121 complex number
122 z1 complex (in)
124 First argument (numerator) in the division
125 z2 complex (in)
127 Second argument (denominator) in the division
128 ::math::complexnumbers::conj z1
131 Return the conjugate of the given complex number
132 z1 complex (in)
134 Complex number in question
135 Conversion/inquiry procedures:
138 ::math::complexnumbers::real z1
140 Return the real part of the given complex number
141 z1 complex (in)
143 Complex number in question
144 ::math::complexnumbers::imag z1
147 Return the imaginary part of the given complex number
148 z1 complex (in)
150 Complex number in question
151 ::math::complexnumbers::mod z1
154 Return the modulus of the given complex number
155 z1 complex (in)
157 Complex number in question
158 ::math::complexnumbers::arg z1
161 Return the argument ("angle" in radians) of the given complex
162 number
163 z1 complex (in)
165 Complex number in question
166 ::math::complexnumbers::complex real imag
169 Construct the complex number "real + imag*i" and return it
170 real float (in)
172 The real part of the new complex number
173 imag float (in)
175 The imaginary part of the new complex number
176 ::math::complexnumbers::tostring z1
179 Convert the complex number to the form "real + imag*i" and
180 return the string
181 complex float (in)
183 The complex number to be converted
184 Elementary functions:
187 ::math::complexnumbers::exp z1
189 Calculate the exponential for the given complex argument and
190 return the result
191 z1 complex (in)
193 The complex argument for the function
194 ::math::complexnumbers::sin z1
197 Calculate the sine function for the given complex argument and
198 return the result
199 z1 complex (in)
201 The complex argument for the function
202 ::math::complexnumbers::cos z1
205 Calculate the cosine function for the given complex argument and
206 return the result
207 z1 complex (in)
209 The complex argument for the function
210 ::math::complexnumbers::tan z1
213 Calculate the tangent function for the given complex argument
214 and return the result
215 z1 complex (in)
217 The complex argument for the function
218 ::math::complexnumbers::log z1
221 Calculate the (principle value of the) logarithm for the given
222 complex argument and return the result
223 z1 complex (in)
225 The complex argument for the function
226 ::math::complexnumbers::sqrt z1
229 Calculate the (principle value of the) square root for the given
230 complex argument and return the result
231 z1 complex (in)
233 The complex argument for the function
234 ::math::complexnumbers::pow z1 z2
237 Calculate "z1 to the power of z2" and return the result
238 z1 complex (in)
240 The complex number to be raised to a power
241 z2 complex (in)
243 The complex power to be used
244
246 complex numbers, math
247
249 Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
250math 1.0.2 math::complexnumbers(n)