/// <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;
}