math::complexnumbers - Straightforward complex number package

package require Tcl 8.3 package require math::complexnumbers ?1.0? ::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]

    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

z1 complex (in)

First argument in the summation

z2 complex (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)

z1 complex (in)

First argument in the subtraction

z2 complex (in)

Second argument in the subtraction (optional)

::math::complexnumbers::* z1 z2

Multiply the two arguments and return the resulting complex number

z1 complex (in)

First argument in the multiplication

z2 complex (in)

Second argument in the multiplication

::math::complexnumbers::/ z1 z2

Divide the first argument by the second and return the resulting complex number

z1 complex (in)

First argument (numerator) in the division

z2 complex (in)

Second argument (denominator) in the division

::math::complexnumbers::conj z1

Return the conjugate of the given complex number

z1 complex (in)

Complex number in question

Conversion/inquiry procedures:

::math::complexnumbers::real z1

Return the real part of the given complex number

z1 complex (in)

Complex number in question

::math::complexnumbers::imag z1

Return the imaginary part of the given complex number

z1 complex (in)

Complex number in question

::math::complexnumbers::mod z1

Return the modulus of the given complex number

z1 complex (in)

Complex number in question

::math::complexnumbers::arg z1

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

z1 complex (in)

Complex number in question

::math::complexnumbers::complex real imag

Construct the complex number "real + imag*i" and return it

real float (in)

The real part of the new complex number

imag float (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

complex float (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

z1 complex (in)

The complex argument for the function

::math::complexnumbers::sin z1

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

z1 complex (in)

The complex argument for the function

::math::complexnumbers::cos z1

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

z1 complex (in)

The complex argument for the function

::math::complexnumbers::tan z1

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

z1 complex (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

z1 complex (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

z1 complex (in)

The complex argument for the function

::math::complexnumbers::pow z1 z2

Calculate "z1 to the power of z2" and return the result

z1 complex (in)

The complex number to be raised to a power

z2 complex (in)

The complex power to be used

complex numbers, math

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