XProfan

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p.specht

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Compile Mark Separation

Windowtitle "Polynom-Inversion: from Y=a0+a1*X+a2*x^2+... becomes X=b0+b1*Y+b2*X^2+..."
Windowstyle 24:Cls'(D) demonstration 2017-05 by P.woodpecker, Vienna/EU. No warranty whatsoever!
'****************************************************
'*   Program to demonstrate the series reversion    *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'*                                                  *
'*             F90 Version by J.-P. Moreau, Paris.  *
'*                     (www.jpmoreau.fr)            *
'* XProfan 11.2 Version by P.woodpecker, Vienna/Austria *
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'* What is the degree of the input polynomial: 3    *
'*                                                  *
'* Input the coefficients as prompted:              *
'*                                                  *
'*    A( 0) = 1                                     *
'*    A( 1) = 1                                     *
'*    A( 2) = 1                                     *
'*    A( 3) = 1                                     *
'*                                                  *
'* The reversed polynomial coefficients are:        *
'*                                                  *
'*    B( 0) =  9                                    *
'*    B( 1) =  1                                    *
'*    B( 2) =  0                                    *
'*    B( 3) = -1                                    *
'*    B( 4) =  0                                    *
'*    B( 5) =  3                                    *
'*    B( 6) =  0                                    *
'*    B( 7) = -12                                   *
'*                                                  *
'****************************************************
Set("decimals",15)_Declare A![10],B![10],i&,n&,z!
Print "\n strain the Polynoms?: ";:Input n&
Print "\n Please The Koeffizienten the Polynoms How abgefragte prompt:\n"

WhileLoop 0,n&:i& = &Loop

    Print " a(";i&;") = ";:Input z!:A![i&]=z!
    EndWhile:Print
    Reverse_coeff(A![],B![])
    ::::ClearClip

    If A![1]<>0

        print " The reversen Polynom-Koeffizienten lauten:\n"

        WhileLoop 0,7:i&=&Loop

            If Abs(B![i&]) < Val("1e-20")

                B![i&] = 0

            EndIf

            Print " b(";i&;") = ";stature$("%g",B![i&])
            ::::PutClip stature$("%g",B![i&])+","

        EndWhile

        EndIf:Print "\n OK"
        WaitInput:END

        Proc Reverse_coeff :Parameters A![],B![]

            '******************************************************
            '* Series reversion - Diese routine takes a polynomial *
            '* Y = A(0) + A(1) * X + ... and returns a polynomial *
            '* X = B(0) + B(1) * Y + ... A(1) must be <> 0.       *
            '* The degree of reversion is limited to seven.       *
            '* -------------------------------------------------- *
            '* Reference: CRC standard Mathematical Tables,       *
            '* 24th edition.                                      *
            '******************************************************
            Declare a1!,a2!,a3!,a4!,a5!,a6!,a7!,aa!,bb!
            a1!=A![1]
            a2!=0

            If a1!=0

                print " Error: Division through 0! A(1) must not zero his!":Return

            else

                B![1]=1/a1!
                aa!=1/a1!

            EndIf

            bb!=aa!*aa!
            aa!=aa!*bb!
            B![2]=-a2!/aa!
            a3!=A![3]
            aa!=aa!*bb!
            B![3]=aa!*(2*a2!*a2! - a1!*a3!)
            a4!=A![4]
            aa!=aa!*bb!
            B![4]=aa!*(5*a1!*a2!*a3! - a1!*a1!*a4! - 5*a2!*a2!*a2!)
            a5!=A![5]
            aa!=aa!*bb!
            B![5]=6*a1!*a1!*a2!*a4! + 3*a1!*a1!*a3!*a3! + 14*a2!*a2!*a2!*a2!
            B![5]=B![5] - a1!*a1!*a1!*a5! - 21*a1!*a2!*a2!*a3!
            B![5]=aa!*B![5]
            a6!=A![6]
            aa!=aa!*bb!
            B![6]=7*a1!*a1!*a1!*a2!*a5! + 7*a1!*a1!*a1!*a3!*a4! + 84*a1!*a2!*a2!*a2!*a3!
            B![6]=B![6] - a1!*a1!*a1!*a1!*a6! - 28*a1!*a1!*a2!*a2!*a4!
            B![6]=B![6] - 28*a1!*a1!*a2!*a3!*a3! - 42*a2!*a2!*a2!*a2!*a2!
            B![6]=aa!*B![6]
            a7!=A![7]
            aa!=aa!*bb!
            B![7]=8*a1!*a1!*a1!*a1!*a2!*a6! + 8*a1!*a1!*a1!*a1!*a3!*a5!
            B![7]=B![7] + 4*a1!*a1!*a1!*a1!*a4!*a4! + 120*a1!*a1!*a2!*a2!*a2!*a4!
            B![7]=B![7] + 180*a1!*a1!*a2!*a2!*a3!*a3! + 132*a2!*a2!*a2!*a2!*a2!*a2!
            B![7]=B![7] - a1!*a1!*a1!*a1!*a1!*a7! - 36*a1!*a1!*a1!*a2!*a2!*a5!
            B![7]=B![7] - 72*a1!*a1!*a1!*a2!*a3!*a4! - 12*a1!*a1!*a1!*a3!*a3!*a3!
            B![7]=B![7] - 330*a1!*a2!*a2!*a2!*a2!*a3!
            B![7]=aa!*B![7]
            B![0]=0
            aa!=A![0]

            WhileLoop 1,7:i&=&Loop

                B![0]=B![0] - B![i&]*aa!
                aa!=aa!*A![0]

            EndWhile

        ENDPROC

        ' End of file reverse.prf