'*****************************************************
'*       Nth Derivative of a polynomial P(x)         *
'* ------------------------------------------------- *
'* Ref.: "Mathematiques en Turbo-Pascal By M. Ducamp *
'* and A. Reverchon (vol 2), Eyrolles, Paris, 1988"  *
'* [BIBLI 05].                                       *
'* ------------------------------------------------- *
'* SAMPLE RUN:                                       *
'*                                                   *
'* Nth DERIVATIVE OF A POLYNOMIAL:                   *
'*                                                   *
'* P(X) = 4x5 -3/5x3 + x2 -7/2x +11                  *
'* Order of derivative: 1                            *
'*                                                   *
'*                                                   *
'* 20 X4  - 9 / 5 X2  + 2 X - 7 / 2                  *
'*                                                   *
'*                                                   *
'* Nth DERIVATIVE OF A POLYNOMIAL:                   *
'*                                                   *
'* P(X) = 4x5 -3/5x3 + x2 -7/2x +11                  *
'* Order of derivative: 3                            *
'*                                                   *
'*                                                   *
'* 240 X2  - 18 / 5                                  *
'*                                                   *
'*                                                   *
'*                     BASIC version by J-P Moreau.  *
'*                          (www.jpmoreau.fr)        *
'*****************************************************
defdbl a-h,o-z
defint i-n

MAXINT = 32767  'Maximum integer number
MAXPOL = 20     'Maximum degree for a polynomial
SMALL  = 1e-20  'small real number

' number zz (real, integer or fractional)
' isrzz=1: zz is real (double precision)
' isrzz=0: zz is integer or fractional
' zzv:  value of zz if real
' ipzz: integer value of zz if integer (or numerator value if fractional)
' iqzz: denominator value if fractional (=1 if integer)

'a polynomial P is defined by:
'integer ipdeg (degree of polynomial)
'number  cp(MAXPOL) (coefficients of polynomial, real, integer or fractional)

'predefine 2 polynomials P,R
DIM isrcp(MAXPOL),cpv(MAXPOL),ipcp(MAXPOL),iqcp(MAXPOL)
DIM isrcr(MAXPOL),crv(MAXPOL),ipcr(MAXPOL),iqcr(MAXPOL)

  cls
  print
  print " Nth DERIVATIVE OF A POLYNOMIAL:"
  print
  tx$=" P(x) = ": gosub 4000  'Enter P(x)
  print
  input " Order of derivative: ", n
  print

  gosub 500  'call Derivative(P,n,R)

  if IERROR<>0 then
    print " Error in calculating derivative."
  else
    'copy R(x) in P(x) for printing
    ipdeg=irdeg
    for i=0 to ipdeg
      isrcp(i)=isrcr(i):cpv(i)=crv(i):ipcp(i)=ipcr(i):iqcp(i)=iqcr(i)
    next i
    gosub 5000  'Display P(x)
  end if

END

'Nth derivative of a polynomial P(x)
'DerivPolynom(P,n,R)
'NUMBER: u
500 IERROR=1
  irdeg=ipdeg-n
  if irdeg<0 then
    irdeg=0
    isrcr(0)=0:crv(0)=0#:ipcr(0)=0:iqcr(0)=1
  else
    for ii=0 to irdeg
      'R coeff(ii)=P coeff(ii+n)
      isrcr(ii)=isrcp(ii+n):crv(ii)=cpv(ii+n)
      ipcr(ii)=ipcp(ii+n):iqcr(ii)=iqcp(ii+n)
      for jj=1 to n
        isru=0:uv=ii+jj:ipu=ii+jj:iqu=1                          'u=ii+jj
        'MultNumber(R coeff(ii), u, R coeff(ii))
        isrxx=isrcr(ii):xxv=crv(ii):ipxx=ipcr(ii):iqxx=iqcr(ii)  'xx=cr(ii)
        isryy=isru:yyv=uv:ipyy=ipu:iqyy=iqu                      'yy=u
        gosub 3100                                               'zz=xx*yy
        isrcr(ii)=isrzz:crv(ii)=zzv:ipcr(ii)=ipzz:iqcr(ii)=iqzz  'cr(ii)=zz
      next jj
    next ii
  end if
  IERROR=0
return


$INCLUDE "numeric\polynoms\polynoms.bas"

'end of file derivpol.bas