/// <summary>
        /// Returns the remainder of <c>this</c> divided by <c>G</c> in a new GF2Polynomial
        /// </summary>
        /// 
        /// <param name="G">A GF2Polynomial != 0</param>
        /// 
        /// <returns>Returns a new GF2Polynomial (<c>this</c> % <c>G</c>)</returns>
        public GF2Polynomial Remainder(GF2Polynomial G)
        {
            // a div b = q / r
            GF2Polynomial a = new GF2Polynomial(this);
            GF2Polynomial b = new GF2Polynomial(G);
            GF2Polynomial j;
            int i;

            if (b.IsZero())
                throw new Exception();

            a.ReduceN();
            b.ReduceN();

            if (a._length < b._length)
                return a;

            i = a._length - b._length;
            while (i >= 0)
            {
                j = b.ShiftLeft(i);
                a.SubtractFromThis(j);
                a.ReduceN();
                i = a._length - b._length;
            }

            return a;
        }
        /// <summary>
        /// Returns the greatest common divisor of <c>this</c> and <c>G</c> in a new GF2Polynomial
        /// </summary>
        /// 
        /// <param name="G">A GF2Polynomial != 0</param>
        /// 
        /// <returns>Returns a new GF2Polynomial gcd(<c>this</c>,<c>g</c>)</returns>
        public GF2Polynomial Gcd(GF2Polynomial G)
        {
            if (IsZero() && G.IsZero())
                throw new ArithmeticException("Both operands of gcd equal zero.");

            if (IsZero())
                return new GF2Polynomial(G);
            if (G.IsZero())
                return new GF2Polynomial(this);

            GF2Polynomial a = new GF2Polynomial(this);
            GF2Polynomial b = new GF2Polynomial(G);
            GF2Polynomial c;

            while (!b.IsZero())
            {
                c = a.Remainder(b);
                a = b;
                b = c;
            }

            return a;
        }
        /// <summary>
        /// Returns the absolute quotient of <c>this</c> divided by <c>G</c> in a new GF2Polynomial
        /// </summary>
        /// 
        /// <param name="G">A GF2Polynomial != 0</param>
        /// 
        /// <returns>Returns a new GF2Polynomial |_ <c>this</c> / <c>G</c></returns>
        public GF2Polynomial Quotient(GF2Polynomial G)
        {
            // a div b = q / r
            GF2Polynomial q = new GF2Polynomial(_length);
            GF2Polynomial a = new GF2Polynomial(this);
            GF2Polynomial b = new GF2Polynomial(G);
            GF2Polynomial j;
            int i;

            if (b.IsZero())
                throw new Exception();

            a.ReduceN();
            b.ReduceN();
            if (a._length < b._length)
                return new GF2Polynomial(0);

            i = a._length - b._length;
            q.ExpandN(i + 1);

            while (i >= 0)
            {
                j = b.ShiftLeft(i);
                a.SubtractFromThis(j);
                a.ReduceN();
                q.XorBit(i);
                i = a._length - b._length;
            }

            return q;
        }
        /// <summary>
        /// Divides <c>this</c> by <c>G</c> and returns the quotient and remainder in a new GF2Polynomial[2], quotient in [0], remainder in [1]
        /// </summary>
        /// 
        /// <param name="G">A GF2Polynomial != 0</param>
        /// 
        /// <returns>Returns a new GF2Polynomial[2] containing quotient and remainder</returns>
        public GF2Polynomial[] Divide(GF2Polynomial G)
        {
            // a div b = q / r
            GF2Polynomial[] result = new GF2Polynomial[2];
            GF2Polynomial q = new GF2Polynomial(_length);
            GF2Polynomial a = new GF2Polynomial(this);
            GF2Polynomial b = new GF2Polynomial(G);
            GF2Polynomial j;
            int i;

            if (b.IsZero())
                throw new Exception();

            a.ReduceN();
            b.ReduceN();

            if (a._length < b._length)
            {
                result[0] = new GF2Polynomial(0);
                result[1] = a;
                return result;
            }

            i = a._length - b._length;
            q.ExpandN(i + 1);

            while (i >= 0)
            {
                j = b.ShiftLeft(i);
                a.SubtractFromThis(j);
                a.ReduceN();
                q.XorBit(i);
                i = a._length - b._length;
            }

            result[0] = q;
            result[1] = a;

            return result;
        }