!*****************************************************
!*       Nth Derivative of a polynomial P(x)         *
!* ------------------------------------------------- *
!* Ref.: "Mathématiques 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                         *
!*                                                   *
!* ------------------------------------------------- *
!* Functions used (of module Polynoms):              *
!*                                                   *
!*  EnterPolynom(), DisplayPolynom(), MultNumber(),  *
!*  SetNumber().                                     *
!*                                                   *
!*                       F90 version by J-P Moreau.  *
!*                           (www.jpmoreau.fr)       *
!*****************************************************
Program DerivPol
Use Polynoms                  !see module polynoms.f90

type(ar_polynom)  P, R        !polynomial type
integer n                     !order of derivative
integer res, DerivPolynom

  print *,''
  print *,' Nth DERIVATIVE OF A POLYNOMIAL:'
  print *,''
  if (EnterPolynom('  P(X) = ', P).eq.0)  stop
  print *,''
  write(*,10,advance='no'); read *, n

  res = DerivPolynom(P,n,R)
  if (res.ne.0) then
    call Displaypolynom(R)
  else
    print *,' Error in calculating derivative.'
  end if
  print *,''
  print *,''
  stop

10 format('  Order of derivative: ')

END


integer Function DerivPolynom(P,n,R)
  USE POLYNOMS
  type(ar_polynom) P, R
  type(ar_number)  u, v
  integer*4 ii,jj
  R%degree=P%degree-n
  if (R%degree<0) then
    R%degree=0; 
    if (SetNumber(R%coeff(0), '0').eq.0) then
      DerivPolynom=0
      return
  end if
  else
    do i=0, R%degree
      R%coeff(i)=P%coeff(i+n)
      ii=i;
      do j=1, n
        !put ii+jj in u (as integer)
	jj=j
	u%is_real=0; u%p=ii+jj; u%q=1; u%value=0.d0
        if (MultNumber(R%coeff(i),u,v).eq.0) then
          DerivPolynom=0
	  return
        end if
	R%coeff(i)=v
      end do
    end do
  end if	       
  DerivPolynom=1
End      


!end of file derivpol.f90