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







math::complexnumbers - Straightforward complex number package








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












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:



  
::math::complexnumbers::+ z1 z2

  
Add the two arguments and return the resulting complex number







  

  
First argument in the summation

  

  
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)







  

  
First argument in the subtraction

  

  
Second argument in the subtraction (optional)









  
::math::complexnumbers::* z1 z2

  
Multiply the two arguments and return the resulting complex number







  

  
First argument in the multiplication

  

  
Second argument in the multiplication









  
::math::complexnumbers::/ z1 z2

  
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









  
::math::complexnumbers::conj z1

  
Return the conjugate of the given complex number







  

  
Complex number in question








Conversion/inquiry procedures:



  
::math::complexnumbers::real z1

  
Return the real part of the given complex number







  

  
Complex number in question









  
::math::complexnumbers::imag z1

  
Return the imaginary part of the given complex number







  

  
Complex number in question









  
::math::complexnumbers::mod z1

  
Return the modulus of the given complex number







  

  
Complex number in question









  
::math::complexnumbers::arg z1

  
Return the argument ("angle" in radians) of the given complex
      number







  

  
Complex number in question









  
::math::complexnumbers::complex real imag

  
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









  
::math::complexnumbers::tostring z1

  
Convert the complex number to the form "real + imag*i" and
      return the string







  

  
The complex number to be converted








Elementary functions:



  
::math::complexnumbers::exp z1

  
Calculate the exponential for the given complex argument and return the
      result







  

  
The complex argument for the function









  
::math::complexnumbers::sin z1

  
Calculate the sine function for the given complex argument and return the
      result







  

  
The complex argument for the function









  
::math::complexnumbers::cos z1

  
Calculate the cosine function for the given complex argument and return
      the result







  

  
The complex argument for the function









  
::math::complexnumbers::tan z1

  
Calculate the tangent function for the given complex argument and return
      the result







  

  
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







  

  
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







  

  
The complex argument for the function









  
::math::complexnumbers::pow z1 z2

  
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 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.








complex numbers, math








Mathematics








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








  

    1.0.2
    math