math::complexnumbers(n)        Tcl Math Library        math::complexnumbers(n)



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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

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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 SF Trackers
       [http://sourceforge.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)
