'****************************************************
'*         Test program for Horner's rule           *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'*                                                  *
'* Input the five coefficients:                     *
'*                                                  *
'*    A( 0) = ? 1                                   *
'*    A( 1) = ? 4                                   *
'*    A( 2) = ? 6                                   *
'*    A( 3) = ? 4                                   *
'*    A( 4) = ? 1                                   *
'*                                                  *
'* What is the expansion point: 1                   *
'*                                                  *
'* The shifted coefficients are:                    *
'*                                                  *
'*    B( 0) =  16                                   *
'*    B( 1) =  32                                   *
'*    B( 2) =  24                                   *
'*    B( 3) =  8                                    *
'*    B( 4) =  1                                    *
'*                                                  *
'****************************************************
defint i-n
defdbl a-h,o-z
dim C(4,5)
cls
print
print " Input the five coefficients:"
print
for i=0 to 4
  print "  A(";i;") = ";:input A(i)
next
print
input " What is the expansion point: ",x0
print
gosub 1000
print
print " The shifted coefficients are:"
print
for i=0 to 4
  print "  B(";i;") = ";B(i)
next
print
end

'***************************************************
'*       Horner's shifting rule subroutine         *
'* ----------------------------------------------- *
'* This routine takes a given quartic polynomial   *
'* and converts it to a Taylor expansion.          *
'* The input series coefficients are A(i), the     *
'* expansion point is x0. The shifted coefficients *
'* are returned in B(i).                           *
'***************************************************
1000 for j=0 to 4
       C(j,0)=A(4-j)
     next
     for i=0 to 4
       C(0,i+1)=C(0,i)
       j=1
1100   if j > 4-i then goto 1200
       C(j,i+1)=x0*C(j-1,i+1)+C(j,i)
       j=j+1
       goto 1100
1200 next
     for i=0 to 4
       B(4-i)=C(i,4-i+1)
     next
return


'End of file Horner.bas