How great is the interest in some extra Math UDF's?

[DexterMorgan]

Oh my God i can't belive i didnt notice this topic before! It is really cool. I will definiatly use all this stuff to cheat in math. HAHa Lol. I was wondering if AutoIt can solve multistep equations Like

3x-23+25=4x-45+54x

And it would solve for the Variable

It would be really cool if it works

Thank you

[martin]

If $a = 0 then in the quadratic formula:

-b +- sqrt( (b^2) - (4*a*c))

2a

Then when you divide by 2a, are you not dividing by zero? thus undefined?

No, that is just blindly applying a formula when the formula doesn't apply.

If a = 0 then you have

0*x^2 + b*x +c = 0

therefore

b*x + c = 0

so, if b is not zero then

x = -c/b

which is what my modified version of your function returns.

You can argue that if a is zero then you haven't got a quadratic, which is true, it's just that if a is zero then anyone could work the answer out and to have a clever function say it hadn't got a clue what to do is a shame.

[crashdemons]

oh lol, I made mine in PHP when I was struggling to figure out some values

- I seriously have never seen anybody else mention it, was starting to wonder if anybody else knew about it.

Edit: I was trying to quote a reply to my post but the quote got garbled with data - eh.

Edited March 20, 2008 by crashdemons

[monoceres]

Do you know what would be really great? I mathematical expression parser, like this: _ParseExpression("58*Sin(90)")

Have been trying to make one myself several times but it just is to complex for me

[Malkey]

Do you know what would be really great? I mathematical expression parser, like this: _ParseExpression("58*Sin(90)")

Have been trying to make one myself several times but it just is to complex for me

You could look at some previous posts :-

http://www.autoitscript.com/forum/index.ph...st&p=374121

and

http://www.autoitscript.com/forum/index.ph...st&p=474934

[Toady]

Do you know what would be really great? I mathematical expression parser, like this: _ParseExpression("58*Sin(90)")

Have been trying to make one myself several times but it just is to complex for me

Execute() in help file.

[crashdemons]

Probably the same thing as the quadratic functions listed but I made it looking at the equation a slightly different way.

If it looks the same or doesnt work any faster, that's okay - I just wanted to try to make one.

For Factoring or solving Trinomials where

ax^2 + bx +c =q

and a,b and c are defined

EDIT: Fixed operations when ($a=0 and $b=0) and when ($a=0 and $b=0 and $c!=$q)

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Func _ComSqr($a=0,$b=0,$c=0,$q=0,$solve_for='x')

    ;$solve_for
    ;x    =  solve for x
    ;0    = solve for 0 (aka factor)
    ;      ^^^NOTICE: this MIGHT NOT produce integers
    ;ans = returns whether you have 0,1 or 2 answers, etc.

    ;    No Solution Returns ''
    ;    Infinite returns 'inf'
    
    Local $qq='',$result='',$sol1='',$sol2='', $ans=0,$z=0, $xinf=false
    If $a=0 Then
        ;bx+c=q  or  c=q
        $q-=$c
        If $b=0 Then
            $xinf=true ; 0x+c=0  X is infinite but you can still solve for 0 (0=0)
            If $q<>0 Then return '';  if  c=q then q-c=0
        Else
            If $b<>0 Then $q/=$b
        EndIf
        
    Else
        ;ax^2+bx+c=q
        $q-=$c
        $q/=$a
        $b/=$a
        $z=$b/2
        $q+=$z^2
        $c=$z
        If $q<0 then return $result
        
        $q=Sqrt($q)
        $qq=(-1*$q)-$c
        $q-=$c
    EndIf
    Switch $solve_for
        Case 'ans'
            If $xinf Then Return 'inf'
            If StringLen($q )>0 Then $ans+=1
            If StringLen($qq)>0 Then $ans+=1
            $result=$ans
        Case 'x'
            If $xinf Then Return 'inf'
            $result=$q&','&$qq
            If $q=$qq Then $result=$q
            If $q=='' Or $qq=='' Then $result=$q&$qq
        Case '0'
            If $xinf Then Return $q ; q, which is 0 :D
            $sol1='(x+'&(-1*$q)&')'
            $sol2='(x+'&(-1*$qq)&')'
            If $q=='' Then $sol1=''
            If $qq=='' Then $sol2=''
            $result=$sol1&$sol2
            If $sol1==$sol2 and StringLen($result)>0 Then $result=$sol1&'^2'
            $result=StringReplace(StringReplace(StringReplace($result,'+-','-'),'(x+0)','(x)'),'(x-0)','(x)')
    EndSwitch
    Return $result
EndFunc

Edited March 21, 2008 by crashdemons

[crashdemons]

Need some operations ABOVE exponentiation (really big / really small numbers?)

I wrote the following based upon the Wikipedia article on Iterated Powers of Tetration

_MultExp(2, 4) should solve for: (see image)

and

_IterExp(2, 2, 3) should solve for: (see image)

Func _MultExp($a, $n)
    ;Multilevel exponentiation
    ;- Example:  _MultExp(2, 4)==(2^(2^(2^(2))))
    If $n<0 Then
        $a=1/$a
        $n*=-1
    EndIf
    $b=1
    Select
        Case $n=1
            $b=$a
        Case $n>1
            $b=$a
            $exp=1
            For $i=1 To $n
                $b=$a^$exp
                $exp=$b
            Next
    EndSelect
    Return $b
EndFunc
Func _IterExp($a, $b, $n)
    ;Iterated Exponentiation
    ;- Examples:  _IterExp(1, 2, 3)==((((1)^2)^2)^2)==1^(2^3)
    ;             _IterExp(2, 2, 3)==((((2)^2)^2)^2)==2^(2^3)
    Return $a^($b^($n))
EndFunc

[james3mg]

Script Function:
    Tests if a number is even or odd.
    Returns 1 - If the number is even.
    Returns 2 - If the number is odd.
#ce ----------------------------------------------------------------------------
Func _IsEven($eVal)
    Local $a = $eVal / 2
    Select
        Case Round($a, 0) = $a
            Return 1
        Case Round($a, 0) <> $a
            Return 0
    EndSelect
EndFunc

It looks to me like it returns 0 if it's odd, and 1 if it's even, not 1 and 2 for even and odd...

and it would be simpler to use:

Func _IsEven($eVal)
  Return Not BitAND($eVal,1)
EndFunc

this returns false (0) if it's odd, and true (1) if it's even, just like yours appears to

Also, this will work with decimal numbers; if I'm not mistaken, 5280.3 is considered even (though not whole), but your function would return that it's odd.

[crashdemons]

Anyone post something like this yet?

ConsoleWrite( 'Pi = ' & SumPi( 0, 9 ) & @LF ); only 14 decimal places anyway...

Func SumPi( $iMin, $iMax)
    Local $Sum = 0
    For $k = $iMin To $iMax
        $Sum += 1/16^$k * ( 4/(8*$k+1) - 2/(8*$k+4) - 1/(8*$k+5) - 1/(8*$k+6) )
    Next
    Return $Sum
EndFunc

From:

EDIT: it is also said you can use part of it to extract binary/hexadecimal digits from Pi (not decimal,) but I can't figure it out.

Edited November 2, 2008 by crashdemons

[clarinetmeister]

Dunno if this will help any of you, but here's a formula that solves a quadratic given the values for a, b, c, and the array in which to put the two solutions. Always returns 1, but changes values in input array into the solution values. It also works for quadratics with imaginary roots! (form a + bi)

CODE

Func QuadraticFormula($a, $b, $c, ByRef $Array)

If $b ^ 2 - 4 * $a * $c < 0 Then ; Negative discriminant

$disc = -1 * ($b ^ 2 - 4 * $a * $c)

$imaginary_part = $disc / (2 * $a)

$imaginary_coefficient = $imaginary_part & "i"

$real_coefficient = (-1 * $ / (2 * $a)

$ans_1 = $real_coefficient & " + " & $imaginary_coefficient

$ans_2 = $real_coefficient & " - " & $imaginary_coefficient

Else

$disc = $b ^ 2 - 4 * $a * $c ; Positive discriminant

$ans_1 = (-1 * $b + Sqrt($disc)) / (2 * $a)

$ans_2 = (-1 * $b - Sqrt($disc)) / (2 * $a)

EndIf

If $ans_1 = $ans_2 Then

$stat = 1 ; number of distinct solutions

Else

$stat = 2 ; number of distinct solutions

EndIf

$Array[0] = $stat

$Array[1] = $ans_1

$Array[2] = $ans_2

Return (1)

EndFunc ;==>QuadraticFormula

[Malkey]

Dunno if this will help any of you, but here's a formula that solves a quadratic given the values for a, b, c, and the array in which to put the two solutions. Always returns 1, but changes values in input array into the solution values. It also works for quadratics with imaginary roots! (form a + bi)

This is pretty good, clarinetmeister. It does return a complex number solution when called for.

Here is a working example with your QuadraticFormula() function to save people time checking it out.

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#include <array.au3>

Local $Array[3] ; for results

;quadratic equation  2x^2 + 3x + 7 = 0
QuadraticFormula(2, 3, 7, $Array)
_ArrayDisplay($Array, "2x^2 + 3x + 7 = 0") ; Display results

Local $Array[3] ; for results
;quadratic equation  x^2 - 8x + 16 = 0
QuadraticFormula(1, -8, 16, $Array)
_ArrayDisplay($Array, "x^2 - 8x + 16 = 0") ; Display results


Func QuadraticFormula($a, $b, $c, ByRef $Array)
    Local $stat
    If $b ^ 2 - 4 * $a * $c < 0 Then ; Negative discriminant
        $disc = -1 * ($b ^ 2 - 4 * $a * $c)
        $imaginary_part = $disc / (2 * $a)
        $imaginary_coefficient = $imaginary_part & "i"
        $real_coefficient = (-1 * $b) / (2 * $a)
        $ans_1 = $real_coefficient & " + " & $imaginary_coefficient
        $ans_2 = $real_coefficient & " - " & $imaginary_coefficient
    Else
        $disc = $b ^ 2 - 4 * $a * $c ; Positive discriminant
        $ans_1 = (-1 * $b + Sqrt($disc)) / (2 * $a)
        $ans_2 = (-1 * $b - Sqrt($disc)) / (2 * $a)
    EndIf

    If $ans_1 = $ans_2 Then
        $stat = 1 ; number of distinct solutions
    Else
        $stat = 2 ; number of distinct solutions
    EndIf

    $Array[0] = $stat
    $Array[1] = $ans_1
    $Array[2] = $ans_2

    Return (1)

EndFunc   ;==>QuadraticFormula

[jennico]

_LCM (lowest common multiple)

_HCF (highest common factor)

_IsPrime

well, as for that and lots of other math functions please try my _Primes.au3 UDF.

i made them with highest precision and best optimization.

cheers j.

as for LCM and HCF, there is an ancient algorithm called Euclidean Algorithm (though probably invented before Euclid). its efficiency is unbeatable.

Edited December 30, 2008 by jennico