XProfan

'Var Koeff$="1,10"
'Var Koeff$="10,0,-1000"
'Var Koeff$="1,-10,0,100,0,10,0,1,0,-1000"
Var Koeff$="10,0,-20.2,1.8,-40,300,-1,0"
Window Title "Nullstellen of Polynomen - Bairstow-Verfahren"
' fountain: https://www.rhirte.de/vb/home2.htm
' Umsetzung the VB-Program of Prof.em. Dr.Rolf Hirte, technical college Wildau
' to XProfan 11.2a; only to demonstration gedacht; No warranty! Demoware only!
' accompanying text: The Solution of Polynomausdrücken (Nullstellensuche) becomes uncomfortably, if the
' Polynom about of Grade 5 or z,B. 25 is. Bairstow verfährt thereby folgendermaßen:
' it split in a Iteration ongoing The quadratischen factors ex, The then in known point
' (set of Vieta) resolved go - the such a long time, To the Restpolynom of Grade 0 or 1 is.
' The users must LEDIGLICH each Koeffizienten the on Normalform "Polynom = 0" brought Polynoms
' in fallender Potenz provide (Text in starker Anlehnung on The named fountain).
'
' WIR HIER pack The Koeffizienten as well as the Absolutglied to fallendem Exponenten in a
' comma-separierten String, z.B. Var Koeff$="10,20,-2.2,1.8,-40,300,1.1111111,0", see 1. row.
' thereafter GEHTS go:
Cls
Font 2
AppendMenuBar 253,"Run Bairstow"
AppendMenuBar 252,"Finish"
print
Declare Grad&,A$[],A![],W!
A$[]=Explode(Koeff$,","):Grad&=SizeOf(A $[])-1
SetSize A![],Grad&

WhileLoop 0,Grad&

    A![&Loop]=val(A $[Grad&-&Loop])

EndWhile

WhileLoop Grad&,0,-1

    Set("NumWidth",1) :set("Decimals",0)

    if &Loop<Grad&:print " +";:else:print "  ";:endif

        Print "X^";&Loop,
        Set("NumWidth",26):set("Decimals",15):Print " time ";A![&Loop]

    EndWhile

    Print:Print " for Berechnungsstart Please Button pressing!"
    WaitInput
    CLS
    Set("NumWidth",1) :set("Decimals",0)
    Print "Das given Polynom of strain ";Grad&;" has following Nullstellen:":Print
    Bairstow(A![])
    WaitInput
    End'Main

    Proc Bairstow

        Parameters A![]
        Var Grad& = SizeOf(A![])-1
        Declare i&,R!,P!,P1!,Q!,Q1!,Ce!,s!,t!
        Declare B![Grad&],C![Grad&]
        set("NumWidth",20):set("Decimals",15)

        While Grad& > 2

            R! = 0
            P1! = 1
            Q1! = -1
            B![Grad&] = A![Grad&]
            C![Grad&] = A![Grad&]

            Repeat

                P! = P1!
                Q! = Q1!
                B![Grad&-1] = B![Grad&] * P! + A![Grad& - 1]
                C![Grad&-1] = B![Grad&-1] + B![Grad&] * P!

                Whileloop Grad& - 2 , 0 , -1 : i& = &Loop'For

                    B![i&] = B![i& + 2] * Q! + B![i& + 1] * P! + A![i&]
                    C![i&] = C![i& + 2] * Q! + C![i& + 1] * P! + B![i&]

                EndWhile' Next

                Ce! = C![2] * C![2] - C![1] * C![3]
                case Ce! = 0 : Print " others Startwerte necessary!"
                P1! = P! - (B![1] * C![2] - B![0] * C![3]) / Ce!
                Q1! = Q! - (B![0] * C![2] - B![1] * C![1]) / Ce!
                R! = R! + 1

                If R! > 4000

                    Print:Print:Print "   Sorry, to 4000 rounds no (further) Konvergenz!"
                    WaitInput
                    End

                EndIf

            Until Abs(B![0]) + Abs(B![1]) < 10^-12' inside loop

            ' Nullstelle the quad. Faktors
            s! = P1! / 2
            t! = P1!*P1! + 4 * Q1!

            If t! < 0

                Print s!;"   + ";0.5 * Sqrt(-t!);"*i "; : comment
                Print s!;"   - ";0.5 * Sqrt(-t!);"*i "; : comment

            Else

                Print s! + 0.5 * Sqrt(t!)
                Print s! - 0.5 * Sqrt(t!)

            EndIf

            whileloop 2,Grad&

                i& = &Loop
                A![i& - 2] = B![i&]

            endwhile

            Grad& = Grad& - 2

        EndWhile' Outer Loop

        If Grad& = 1

            Print -A![0]/A![1]

        Else

            s! = -0.5 * A![1] / A![2]
            t! = A![1] * A![1] - 4 * A![2] * A![0]

            If t! < 0

                Print s!;"   + ";0.5 * Sqrt(-t!) / A![2];"*i "; : comment
                Print s!;"   - ";0.5 * Sqrt(-t!) / A![2];"*i "; : comment

            Else

                Print s! + 0.5 * Sqrt(t!) / A![2]
                Print s! - 0.5 * Sqrt(t!) / A![2]

            EndIf

        EndIf

    ENDPROC

    Proc comment

        if nearly(s!,0,9)

            print "(Imaginär)"

        else

            print "(Komplex)"

        endif

    endproc