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  limita-
       tions 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  con-
       struct a valid number.)

       Most procedures implement the basic arithmetic operations or elementary functions whereas several others convert to and from different rep-
       resentations:

	   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)