math::complexnumbers(n) Tcl Math Library math::complexnumbers(n) ______________________________________________________________________________
NAME
math::complexnumbers - Straightforward complex number package
SYNOPSIS
package require Tcl 8.3
package require math::complexnumbers ?1.0.2?
::math::complexnumbers::+ z1 z2
::math::complexnumbers::- z1 z2
::math::complexnumbers::* z1 z2
::math::complexnumbers::/ z1 z2
::math::complexnumbers::conj z1
::math::complexnumbers::real z1
::math::complexnumbers::imag z1
::math::complexnumbers::mod z1
::math::complexnumbers::arg z1
::math::complexnumbers::complex real imag
::math::complexnumbers::tostring z1
::math::complexnumbers::exp z1
::math::complexnumbers::sin z1
::math::complexnumbers::cos z1
::math::complexnumbers::tan z1
::math::complexnumbers::log z1
::math::complexnumbers::sqrt z1
::math::complexnumbers::pow z1 z2
_________________________________________________________________
DESCRIPTION
The mathematical module complexnumbers provides a straightforward
implementation of complex numbers in pure Tcl. The philosophy is that
the user knows he or she is dealing with complex numbers in an abstract
way and wants as high a performance as can be had within the limita-
tions of an interpreted language.
Therefore the procedures defined in this package assume that the argu-
ments are valid (representations of) "complex numbers", that is, lists
of two numbers defining the real and imaginary part of a complex number
(though this is a mere detail: rely on the complex command to construct
a valid number.)
Most procedures implement the basic arithmetic operations or elementary
functions whereas several others convert to and from different repre-
sentations:
set z [complex 0 1]
puts "z = [tostring $z]"
puts "z**2 = [* $z $z]
would result in:
z = i
z**2 = -1
AVAILABLE PROCEDURES
The package implements all or most basic operations and elementary
functions.
The arithmetic operations are:
::math::complexnumbers::+ z1 z2
Add the two arguments and return the resulting complex number
complex z1 (in)
First argument in the summation
complex z2 (in)
Second argument in the summation
::math::complexnumbers::- z1 z2
Subtract the second argument from the first and return the
resulting complex number. If there is only one argument, the
opposite of z1 is returned (i.e. -z1)
complex z1 (in)
First argument in the subtraction
complex z2 (in)
Second argument in the subtraction (optional)
::math::complexnumbers::* z1 z2
Multiply the two arguments and return the resulting complex num-
ber
complex z1 (in)
First argument in the multiplication
complex z2 (in)
Second argument in the multiplication
::math::complexnumbers::/ z1 z2
Divide the first argument by the second and return the resulting
complex number
complex z1 (in)
First argument (numerator) in the division
complex z2 (in)
Second argument (denominator) in the division
::math::complexnumbers::conj z1
Return the conjugate of the given complex number
complex z1 (in)
Complex number in question
Conversion/inquiry procedures:
::math::complexnumbers::real z1
Return the real part of the given complex number
complex z1 (in)
Complex number in question
::math::complexnumbers::imag z1
Return the imaginary part of the given complex number
complex z1 (in)
Complex number in question
::math::complexnumbers::mod z1
Return the modulus of the given complex number
complex z1 (in)
Complex number in question
::math::complexnumbers::arg z1
Return the argument ("angle" in radians) of the given complex
number
complex z1 (in)
Complex number in question
::math::complexnumbers::complex real imag
Construct the complex number "real + imag*i" and return it
float real (in)
The real part of the new complex number
float imag (in)
The imaginary part of the new complex number
::math::complexnumbers::tostring z1
Convert the complex number to the form "real + imag*i" and
return the string
float complex (in)
The complex number to be converted
Elementary functions:
::math::complexnumbers::exp z1
Calculate the exponential for the given complex argument and
return the result
complex z1 (in)
The complex argument for the function
::math::complexnumbers::sin z1
Calculate the sine function for the given complex argument and
return the result
complex z1 (in)
The complex argument for the function
::math::complexnumbers::cos z1
Calculate the cosine function for the given complex argument and
return the result
complex z1 (in)
The complex argument for the function
::math::complexnumbers::tan z1
Calculate the tangent function for the given complex argument
and return the result
complex z1 (in)
The complex argument for the function
::math::complexnumbers::log z1
Calculate the (principle value of the) logarithm for the given
complex argument and return the result
complex z1 (in)
The complex argument for the function
::math::complexnumbers::sqrt z1
Calculate the (principle value of the) square root for the given
complex argument and return the result
complex z1 (in)
The complex argument for the function
::math::complexnumbers::pow z1 z2
Calculate "z1 to the power of z2" and return the result
complex z1 (in)
The complex number to be raised to a power
complex z2 (in)
The complex power to be used
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain
bugs and other problems. Please report such in the category math ::
complexnumbers of the Tcllib SF Trackers [http://source-
forge.net/tracker/?group_id=12883]. Please also report any ideas for
enhancements you may have for either package and/or documentation.
KEYWORDS
complex numbers, math
CATEGORY
Mathematics
COPYRIGHT
Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
math 1.0.2 math::complexnumbers(n)
Mac OS X 10.8 - Generated Wed Sep 12 14:29:18 CDT 2012