/
complex_numbers.ahk
161 lines (127 loc) · 4.04 KB
/
complex_numbers.ahk
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; Link: https://www.autohotkey.com/boards/viewtopic.php?f=6&t=35809
; Author: jeeswg
; Date: 14.08.2017
; for: AHK_L
/*
;note: this script puts a list of complex numbers onto the clipboard
;note: the comments (algebra) can be pasted into (used with) wolframalpha.com
;note: complex exponentiation is multi-valued (JEE_CPow only returns a single value)
vPi := 3.141592653589793
MsgBox, % JEE_CDisp(JEE_CAdd([1,2],[3,4])) ;(1+2i)+(3+4i)
MsgBox, % JEE_CDisp(JEE_CSub([1,2],[3,4])) ;(1+2i)-(3+4i)
MsgBox, % JEE_CDisp(JEE_CMul([1,2],[3,4])) ;(1+2i)*(3+4i)
MsgBox, % JEE_CDisp(JEE_CDiv([1,2],[3,4])) ;(1+2i)/(3+4i)
MsgBox, % JEE_CDisp(JEE_CPow([1,2],[3,4])) ;(1+2i)^(3+4i)
MsgBox, % JEE_CDisp(JEE_CPow([Exp(1),0],[0,vPi])) ;e^((pi)i)
MsgBox, % JEE_CDisp(JEE_CPow([0,1],[0,1])) ;i^i
MsgBox, % JEE_CDisp(JEE_CConj([1,2])) ;conj(1+2i)
MsgBox, % JEE_CDisp(JEE_CConj([3,4])) ;conj(3+4i)
MsgBox, % JEE_CAbs([1,2]) " " JEE_CAbs([3,4]) ;abs(1+2i) abs(3+4i)
MsgBox, % JEE_CArg([1,2]) " " JEE_CArg([3,4]) ;arg(1+2i) arg(3+4i)
;test the JEE_CDisp function:
vR := -5
Loop, 21
{
vI := -5
Loop, 21
{
vOutput .= JEE_CDisp([vR,vI]) "`r`n"
vI += 0.5
}
vR += 0.5
}
Clipboard := vOutput
MsgBox, % vOutput
*/
;==================================================
;key possibilities for JEE_CDisp to consider:
;if real part is 0/nonzero (e.g. real part: 3 or 0)
;if imag part is positive/negative/1/-1 (e.g. imag part: 3 or 1 or -3 or -1)
;[3]+[3]i [3]i
;[3]+[]i []i
;[3][-3]i [-3]i
;[3][-]i [-]i
JEE_CDisp(obj2)
{
local obj := obj2.Clone()
;crop trailing zeros after decimal point (remove decimal point if required)
if InStr(obj.1, ".")
obj.1 := RegExReplace(obj.1, "\.0+$|\..*?\K0+$")
if InStr(obj.2, ".")
obj.2 := RegExReplace(obj.2, "\.0+$|\..*?\K0+$")
if !obj.1 && !obj.2
return 0
else if !obj.2
return obj.1
else if !obj.1
obj.1 := ""
else if (obj.2 > 0)
obj.1 .= "+"
if (obj.2 = 1)
return obj.1 "i"
else if (obj.2 = -1)
return obj.1 "-i"
else
return obj.1 obj.2 "i"
}
;==================================================
JEE_CAdd(obj1, obj2)
{
return [obj1.1+obj2.1, obj1.2+obj2.2]
}
;==================================================
JEE_CSub(obj1, obj2)
{
return [obj1.1-obj2.1, obj1.2-obj2.2]
}
;==================================================
JEE_CMul(obj1, obj2)
{
;(a+bi)(c+di) = (ac-bd) + i(ad+bc)
return [(obj1.1*obj2.1)-(obj1.2*obj2.2), (obj1.1*obj2.2)+(obj1.2*obj2.1)]
}
;==================================================
;Complex Division -- from Wolfram MathWorld
;http://mathworld.wolfram.com/ComplexDivision.html
JEE_CDiv(obj1, obj2)
{
;real part: (ac+bd) / (c^2+d^2)
;imag part: (-ad+bc) / (c^2+d^2)
return [((obj1.1*obj2.1)+(obj1.2*obj2.2))/(obj2.1**2+obj2.2**2), ((-obj1.1*obj2.2)+(obj1.2*obj2.1))/(obj2.1**2+obj2.2**2)]
}
;==================================================
;Complex Exponentiation -- from Wolfram MathWorld
;http://mathworld.wolfram.com/ComplexExponentiation.html
;Complex number - Wikipedia
;https://en.wikipedia.org/wiki/Complex_number#Exponentiation
;note: complex exponentiation is multi-valued (JEE_CPow only returns a single value)
JEE_CPow(obj1, obj2)
{
local a := obj1.1, b := obj1.2, c := obj2.1, d := obj2.2, vTemp, vR, vI
vTemp := ((a**2+b**2)**(c/2))*Exp(-d*JEE_CArg(obj1))
vR := vTemp * Cos(c*JEE_CArg(obj1)+0.5*d*Ln(a**2+b**2))
vI := vTemp * Sin(c*JEE_CArg(obj1)+0.5*d*Ln(a**2+b**2))
return [vR,vI]
}
;==================================================
;Complex Modulus -- from Wolfram MathWorld
;http://mathworld.wolfram.com/ComplexModulus.html
JEE_CAbs(obj)
{
return Sqrt(obj.1**2+obj.2**2)
}
;==================================================
;Complex Argument -- from Wolfram MathWorld
;http://mathworld.wolfram.com/ComplexArgument.html
JEE_CArg(obj)
{
return DllCall("msvcrt\atan2", "Double",obj.2, "Double",obj.1, "Cdecl Double")
}
;==================================================
;Complex Conjugate -- from Wolfram MathWorld
;http://mathworld.wolfram.com/ComplexConjugate.html
JEE_CConj(obj)
{
return [obj.1,-obj.2]
}
;==================================================