math::complexnumbers - Straightforward complex number package
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 limitations of an interpreted language.
Therefore the procedures defined in this package assume that the arguments 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 representations:
set z [complex 0 1]
puts "z = [tostring $z]"
puts "z**2 = [* $z $z]
would result in:
z = i
z**2 = -1
The package implements all or most basic operations and elementary functions.
The arithmetic operations are:
Add the two arguments and return the resulting complex number
First argument in the summation
Second argument in the summation
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)
First argument in the subtraction
Second argument in the subtraction (optional)
Multiply the two arguments and return the resulting complex number
First argument in the multiplication
Second argument in the multiplication
Divide the first argument by the second and return the resulting complex number
First argument (numerator) in the division
Second argument (denominator) in the division
Return the conjugate of the given complex number
Complex number in question
Conversion/inquiry procedures:
Return the real part of the given complex number
Complex number in question
Return the imaginary part of the given complex number
Complex number in question
Return the modulus of the given complex number
Complex number in question
Return the argument ("angle" in radians) of the given complex number
Complex number in question
Construct the complex number "real + imag*i" and return it
The real part of the new complex number
The imaginary part of the new complex number
Convert the complex number to the form "real + imag*i" and return the string
The complex number to be converted
Elementary functions:
Calculate the exponential for the given complex argument and return the result
The complex argument for the function
Calculate the sine function for the given complex argument and return the result
The complex argument for the function
Calculate the cosine function for the given complex argument and return the result
The complex argument for the function
Calculate the tangent function for the given complex argument and return the result
The complex argument for the function
Calculate the (principle value of the) logarithm for the given complex argument and return the result
The complex argument for the function
Calculate the (principle value of the) square root for the given complex argument and return the result
The complex argument for the function
Calculate "z1 to the power of z2" and return the result
The complex number to be raised to a power
The complex power to be used
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 Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.
Mathematics
Copyright © 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>