public Poly add (Poly q) throws NullPointerException {
   //EFFECTS: If q is null throws NullPointerException else
  // returns the Poly this + q.
   Poly la, sm;
   if (deg > q.deg) {la = this; sm = q;} else {la = q; sm = this;}
   int newdeg = la.deg;
   // new degree is the larger degree
   if (deg == q.deg)
       // unless there are trailing zeros
      for (int k = deg; k > 0; k--)
         if (trms[k] + q.trms[k] != 0) break; else newdeg--;
   Poly r = new Poly(newdeg);
   // get a new Poly
   int i;
   for (i = 0; i <= sm.deg && i <= newdeg; i++)
      r.trms[i] = sm.trms[i] + la.trms[i];
   for (int j = i; j <= newdeg; j++) r.trms[j] = la.trms[j];
   return r;
}

public Poly mul (Poly q) throws NullPointerException {
   //EFFECTS: If q is null throws NullPointerException else
  //  returns the Poly this * q.
   if ((q.deg == 0 && q.trms[0] == 0) ||
      (deg == 0 && trms[0] == 0)) return new Poly( );
   Poly r = new Poly(deg+q.deg);
   r.trms[deg+q.deg] = 0;
   // prepare to compute coeffs
   for (int i = 0; i <= deg; i++)
      for (int j = 0; j <= q.deg; j++)
         r.trms[i+j] = r.trms[i+j] + trms[i]*q.trms[j];
   return r;
  }
}