/****************************************************
*  This program calculates R(x) = a*P(x) + b*Q(x),  *
*  P(x), Q(x) and R(x) being polynomials.           *
* ------------------------------------------------- *
* Ref.: "Mathématiques en Turbo-Pascal By M. Ducamp *
* and A. Reverchon (vol 2), Eyrolles, Paris, 1988"  *
* [BIBLI 05].                                       *
* ------------------------------------------------- *
* SAMPLE RUN:                                       *
*                                                   *
* LINEAR COMBINATION OF TWO POLYNOMIALS:            *
*                                                   *
* P(X) = x3 +5/4x2 -8                               *
* Q(x) = 2x2 -1/7                                   *
*                                                   *
*  a = 1/2                                          *
*  b = -1/3                                         *
*                                                   *
* +1/2 X3 -1/24 X2 -83/21                           *
*                                                   *
* ------------------------------------------------- *
* Functions used (of module Polynoms):              *
*                                                   *
*  AddNumber(), EnterPolynom(), DisplayPolynom(),   *
*  MultNumber() and SetNumber().                    *
*                                                   *
*                      C++ version by J-P Moreau.   *
*                  (To be linked with polynoms.cpp).*
*                         (www.jpmoreau.fr)         *
****************************************************/
#include <stdio.h>
#include <malloc.h>
#include <math.h>

#include "polynoms.h"


ar_polynom *P, *Q, *R;
ar_number  a,  b;


// a P(X) + b Q(X) = R(X)
bool CombiPolynom(ar_polynom *P, ar_polynom *Q, ar_number a, ar_number b, ar_polynom *R) {
  int i; ar_number u,v;
  if (Q->degree > P->degree)  R->degree=Q->degree;
  else R->degree=P->degree;
  if (R->degree > AR_MAXPOL) return FALSE;   // degree of R is too big
  for (i=0; i<=R->degree; i++) {
    if (!SetNumber(&u,"0")) return FALSE;
    if (!SetNumber(&v,"0")) return FALSE;
    if (i<=P->degree)
      if (!MultNumber(a,P->coeff[i], &u)) return FALSE;
    if (i<=Q->degree)
      if (!MultNumber(b,Q->coeff[i], &v)) return FALSE;
	  if (!AddNumber(u,v,&R->coeff[i])) return FALSE;
  }
  while (R->degree>0 && fabs(R->coeff[R->degree].value)<AR_SMALL)
      R->degree--;
  return TRUE;
}


void main()  {
  //dynamic memory allocation of polynomials
  P = (ar_polynom *) calloc(1,sizeof(ar_polynom));
  Q = (ar_polynom *) calloc(1,sizeof(ar_polynom));
  R = (ar_polynom *) calloc(1,sizeof(ar_polynom));
  printf("\n LINEAR COMBINATION OF TWO POLYNOMIALS:\n\n");
  if (!EnterPolynom(" P(X) = ", P)) return;
  if (!EnterPolynom(" Q(X) = ", Q)) return;
  printf("\n");
  ReadNumber(" a = ", &a);
  ReadNumber(" b = ", &b);
  if (CombiPolynom(P,Q,a,b,R))
    DisplayPolynom(R);
  else
    printf(" Error in linear combination.");
  printf("\n\n");
  free(P); free(Q); free(R);
}

//end of file combipol.cpp