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math::complexnumbers(3tcl)     Tcl Math Library	    math::complexnumbers(3tcl)

______________________________________________________________________________

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(3tcl)
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