AComplex

[ValeryVal]

This sample is an example of AutoItObject using. It allows to have complex Math Lib and calculate something like this:

Log[(3-4i)/(4-7i)]

The results of tests are very much appreciated.

Fixed: 20 July 2010

Added: 22 July 2010

Enjoy

AComplex.au3

Edited July 22, 2010 by Valery

[jaberwacky]

CLn(): undefined function.

CDiv(): undefined function.

CPow(): undefined function.

CMul(): undefined function.

CRt(): undefined function.

OOps, are there any other UDFs I need to have?

Edited July 19, 2010 by jaberwocky6669

[ValeryVal]

CLn(): undefined function.

CDiv(): undefined function.

CPow(): undefined function.

CMul(): undefined function.

CRt(): undefined function.

Fixed. See first message.

are there any other UDFs I need to have?

New version has the following:

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;===========================
; Complex Number Math Lib
;===========================
;New complex is equal to negative of $oA
Func _CMin($oA)
;New complex is equal to $oA + $oB
Func _CAdd($oA,$oB)
;New complex is equal to $oA - $oB
Func _CSub($oA,$oB)
;New complex is equal to $oA * $oB
Func _CMul($oA,$oB)
;New complex is equal to $oA / $oB
Func _CDiv($oA,$oB)
;New complex is equal to exp($oA)
Func _CExp($oA)
;New complex is equal to natural logarithm of $oA
Func _CLog($oA)
;New complex is equal to result of raising comples to the complex power
Func _CPow($oA,$oB)
;New complex is equal to complex squared
Func _CSqr($oA)
;New complex is equal to logarithmic base $oA of $oB
Func _CLogB($oA,$oB)
;New complex is equal to $oAth root of $oB
Func _CRt($oA,$oB)
;New complex is equal to square root of $oA
Func _CSqrt($oA)
;New complex is equal to sine of $oA
Func _CSin($oA)
;New complex is equal to cosine of $oA
Func _CCos($oA)
;New complex is equal to tangent of $oA
Func _CTan($oA)
;New complex is equal to tangent of $oA
Func _CCot($oA)
;New complex is equal to secant of $oA
Func _CSec($oA)
;New complex is equal to cosecant of $oA
Func _CCsc($oA)
;New complex is equal to arcsine of $oA
Func _CASin($oA)
;New complex is equal to arccosine of $oA
Func _CACos($oA)
;New complex is equal to arctangent of $oA
Func _CATan($oA)
;New complex is equal to arccotangent of $oA
Func _CACot($oA)
;New complex is equal to arcsecant of $oA
Func _CASec($oA)
;New complex is equal to arccosecant of $oA
Func _CACsc($oA)
;New complex is equal to hyperbolic sine of $oA
Func _CSinh($oA)
;New complex is equal to hyperbolic cosine of $oA
Func _CCosh($oA)
;New complex is equal to hyperbolic tangent of $oA
Func _CTanh($oA)
;New complex is equal to hyperbolic cotangent of $oA
Func _CCoth($oA)
;New complex is equal to hyperbolic secant of $oA
Func _CSech($oA)
;New complex is equal to hyperbolic cosecant of $oA
Func _CCSch($oA)

Any test is very much appreciated.

Enjoy,

[ValeryVal]

Added new functions:

;New complex is equal to arcsine hyperbolic of $oA
Func _CASinh($oA)
;New complex is equal to arccosine hyperbolic of $oA
Func _CACosh($oA)
;New complex is equal to arctangent hyperbolic of $oA
Func _CATanh($oA)
;New complex is equal to arccotangent hyperbolic of $oA
;New complex is equal to arcsecant hyperbolic of $oA
Func _CASech($oA)
;New complex is equal to arcsecant hyperbolic of $oA
Func _CACsch($oA)

Now AComplex.au3 (see first message) has the following funcs:

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;===========================
; Complex Number Math Lib
;===========================
;New complex is equal to negative of $oA
Func _CMin($oA)
;New complex is equal to $oA + $oB
Func _CAdd($oA,$oB)
;New complex is equal to $oA - $oB
Func _CSub($oA,$oB)
;New complex is equal to $oA * $oB
Func _CMul($oA,$oB)
;New complex is equal to $oA / $oB
Func _CDiv($oA,$oB)
;New complex is equal to exp($oA)
Func _CExp($oA)
;New complex is equal to natural logarithm of $oA
Func _CLog($oA)
;New complex is equal to result of raising comples to the complex power
Func _CPow($oA,$oB)
;New complex is equal to complex squared
Func _CSqr($oA)
;New complex is equal to logarithmic base $oA of $oB
Func _CLogB($oA,$oB)
;New complex is equal to $oAth root of $oB
Func _CRt($oA,$oB)
;New complex is equal to square root of $oA
Func _CSqrt($oA)
;New complex is equal to sine of $oA
Func _CSin($oA)
;New complex is equal to cosine of $oA
Func _CCos($oA)
;New complex is equal to tangent of $oA
Func _CTan($oA)
;New complex is equal to tangent of $oA
Func _CCot($oA)
;New complex is equal to secant of $oA
Func _CSec($oA)
;New complex is equal to cosecant of $oA
Func _CCsc($oA)
;New complex is equal to arcsine of $oA
Func _CASin($oA)
;New complex is equal to arccosine of $oA
Func _CACos($oA)
;New complex is equal to arctangent of $oA
Func _CATan($oA)
;New complex is equal to arccotangent of $oA
Func _CACot($oA)
;New complex is equal to arcsecant of $oA
Func _CASec($oA)
;New complex is equal to arccosecant of $oA
Func _CACsc($oA)
;New complex is equal to hyperbolic sine of $oA
Func _CSinh($oA)
;New complex is equal to hyperbolic cosine of $oA
Func _CCosh($oA)
;New complex is equal to hyperbolic tangent of $oA
Func _CTanh($oA)
;New complex is equal to hyperbolic cotangent of $oA
Func _CCoth($oA)
;New complex is equal to hyperbolic secant of $oA
Func _CSech($oA)
;New complex is equal to hyperbolic cosecant of $oA
Func _CCSch($oA)
;New complex is equal to arcsine hyperbolic of $oA
Func _CASinh($oA)
;New complex is equal to arccosine hyperbolic of $oA
Func _CACosh($oA)
;New complex is equal to arctangent hyperbolic of $oA
Func _CATanh($oA)
;New complex is equal to arccotangent hyperbolic of $oA
;New complex is equal to arcsecant hyperbolic of $oA
Func _CASech($oA)
;New complex is equal to arcsecant hyperbolic of $oA
Func _CACsch($oA)

Short sample for it AComplex_Example_1.au3:

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;=====================================================
; AComplex - 20 July 2010 by Valery Ivanov
; The sample of AutoItObject using for Complex Number Math Lib
; 20 July 2010 by Valery Ivanov
;------------------------------
#include <AutoItObject.au3>
#include "AComplex.au3"

; Calculate value of
; Log[(3-4i)/(4-7i)]
Global $oA = _ComplexCreator(3,-4)
Global $oB = _ComplexCreator(4,-7)
Global $oC = 0

$oC = _CDiv($oA, $oB)

Global $oD = _CLog($oC)
MsgBox(0,"","Re(Log[(3-4i)/(4-7i)]) = " & $oD.Re & @CrLf & "Im(Log[(3-4i)/(4-7i)]) = " & $oD.Im)

; Calculate value of
; Log[(3-4i)*(4-7i)]
;Release object $oC returned from _CMul!
$oC = 0
$oC = _CMul($oA, $oB)

;Release object $oD returned from _CLog!
$oD = 0
$oD = _CLog($oC)
MsgBox(0,"","Re(Log[(3-4i)*(4-7i)]) = " & $oD.Re & @CrLf & "Im(Log[(3-4i)*(4-7i)]) = " & $oD.Im)


Global $oE = _ComplexCreator(6.5,4.7)
Global $oF = _ComplexCreator(4.7,-6.5)

With $oE
   MsgBox(0,"","_CAbs(6.5 + i*4.7) = " & .CAbs() & @CrLf & "_CAbsSqr(6.5 + i*4.7) = " & .CAbsSqr())
   MsgBox(0,"","_CArg(6.5 + i*4.7) = " & .CArg())
EndWith

With $oF
   MsgBox(0,"","_CAbs(4.7 - i*6.5) = " & .CAbs() & @CrLf & "_CAbsSqr(4.7 - i*6.5) = " & .CAbsSqr())
   MsgBox(0,"","_CArg(4.7 - i*6.5) = " & .CArg())
EndWith

[ValeryVal]

The next AQuaternion.au3 is an example of AutoItObject using for Quaternion's Math Lib.

It has the following functions:

;New quaternion is equal to opposite quaternion of $oA
Func _HOpp($oA)
;New quaternion is equal to reciprocal quaternion of $oA
Func _HRec($oA)
;New quaternion is equal to $oA + $oB
Func _HAdd($oA, $oB)
;New quaternion is equal to $oA - $oB
Func _HSub($oA, $oB)
;New quaternion is equal to $oA * $oB
Func _HMul($oA, $oB)
;New quaternion is equal to quaternion squared
Func _HSqr($oA)
;New quaternion is equal to $oA / $oB

Enjoy,

AQuaternion.au3