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# math::complexnumbers(n) 1.0.2 tcllib "Tcl Math Library"

## 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. Please also report any ideas for enhancements you may have for either package and/or documentation.

## Keywords

complex numbers, math

## Category

Mathematics

## Copyright

Copyright © 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>