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
| Type | Name | Mode |
| 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)
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| complex | z1 | in |
| |
Complex number in question
|
Conversion/inquiry procedures:
-
::math::complexnumbers::real z1
-
Return the real part of the given complex number
| Type | Name | Mode |
| complex | z1 | in |
| |
Complex number in question
|
-
::math::complexnumbers::imag z1
-
Return the imaginary part of the given complex number
| Type | Name | Mode |
| complex | z1 | in |
| |
Complex number in question
|
-
::math::complexnumbers::mod z1
-
Return the modulus of the given complex number
| Type | Name | Mode |
| complex | z1 | in |
| |
Complex number in question
|
-
::math::complexnumbers::arg z1
-
Return the argument ("angle" in radians) of the given complex number
| Type | Name | Mode |
| complex | z1 | in |
| |
Complex number in question
|
-
::math::complexnumbers::complex real imag
-
Construct the complex number "real + imag*i" and return it
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| 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
| Type | Name | Mode |
| complex | z1 | in |
| |
The complex number to be raised to a power
|
| complex | z2 | in |
| |
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
http://sourceforge.net/tracker/?group_id=12883.
Please also report any ideas for enhancements you may have for either
package and/or documentation.
math, complex numbers