//Written by Reginald Ford

//Horner's method
double polyval(double *a, double t, int order)
{
  double sum = a[order];
  for(int i=order-1;i>=0;i--)
  {
    sum*=t;
    sum+=a[i];
  }
  return sum;
}


//provide the coefficient that goes with t^n
//from the product of power series a and b
double cp(double *a, double *b,int n)
{
  double sum = 0;
  for(int i=0;i<=n;i++)
  {
    sum += a[i]*b[n-i];
  }
  return sum;
}

//provide the coefficient that goes with t^n
//from the product of power series a' and b
double cp2(double *a, double *b,int n)
{
  double sum = 0;
  for(int i=0;i<=n;i++)
  {
    sum += (i+1) * a[i+1]*b[n-i];
  }
  return sum;
}