C++ Polynomial Multplication

Question

I'm trying to multiply two polynomials together in C++. I'd like to keep the overal structure of this code as-is if possible. I understand there may be a "faster way." Here is my code for polynomial addition:

    Polynomial Add(Polynomial &poly1, Polynomial &poly2)
    {
      vector<int> temp1;
      if( poly1.Degree() > poly2.Degree() )
      {
        for( int i = 0 ; i<poly2.Degree() ; i++ )
        {
          temp1[i]=poly1.Coefficient(i)+poly2.Coefficient(i);
        }
        Polynomial temp0(temp1);
        return temp0;
      }
      else if ( poly1.Degree() < poly2.Degree() )
      {
        for( int i = 0 ; i<poly1.Degree() ; i++ )
        {
          temp1[i]=poly1.Coefficient(i)+poly2.Coefficient(i);
        }
        Polynomial temp0(temp1);
        return temp0;
      }
    }

Here is my Degree() member function definition:

      int Polynomial::Degree() const
    {

      for(int i = 0; i < coefficient.size(); i++)

      {
        int last=0;
        if(coefficient[i] != 0)
        {
          last = i;
        }
        return last;
      }
    }

Here is my Polynomial class declaration:

    class Polynomial {
    public:
      Polynomial();
      Polynomial(vector<int> &coeffs);
      int Degree() const;
      int Coefficient(int k) const;
      void print() const;
      void constantMultiply(int x);
      void Transform();
      int nonzero() const;
    private:
      vector<int> coefficient;
    };

Now, what I'm trying to do is multiply two input polynomials using this addition function, and I feel that I could use the below literature from Cohn's Classic Algebra to do the trick with some sufficient thought.

COHN'S CLASSIC ALGEBRA REFERENCE

Answer 1

I think this should do what you're looking for. If poly1 has a coefficient for degree i then we iterate over poly2's coeffecients. Each coefficient of poly2 is multiplied and the result will be degree i+j, like x^1*x^2=x^(1+2)=x^3.

Polynomial Mul(Polynomial &poly1, Polynomial &poly2)
{
  vector<int> temp1;
  for( int i = 0; i<poly1.Degree() ; i++ ){
    if(poly1.Coefficient[i] != 0){
      for( int j = 0; j<poly2.Degree() ; j++ ){
        if(poly2.Coefficient[j] != 0){
          temp1[i+j] = poly1.Coefficient(i)*poly2.Coefficient(j);
        }
      }
    }
  }
  Polynomial temp0(temp1);
  return temp0;
}

Please let me know if I'm missing the question, or if this doesn't solve it for you!

Answer 2

Your temp[i] won't work. I checked. You'll need to do push_back or some such operation to fill it. It will work if you already know the size of the larger polynomial.

Something like this:

int how_big;

if(poly1.Degree()>poly2.Degree())
{
    how_big = poly1.Degree()+1;
}
else
{
    how_big = poly2.Degree()+1;
}