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 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

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 number

              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
       Trackers   [http://core.tcl.tk/tcllib/reportlist].   Please  also  report  any  ideas  for
       enhancements you may have for either package and/or documentation.

       When proposing code changes, please provide unified diffs, i.e the output of diff -u.

       Note further that attachments are strongly preferred over inlined patches. Attachments can
       be  made  by going to the Edit form of the ticket immediately after its creation, and then
       using the left-most button in the secondary navigation bar.

KEYWORDS

       complex numbers, math

CATEGORY

       Mathematics

COPYRIGHT

       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>