/// <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;
}
