public static Tuple <IntegerType, IntegerType, IntegerType> ExtendedEuclideanAlgorithm <IntegerType>(IAlgebraInteger <IntegerType> algebra, IntegerType a, IntegerType b)
{
if (algebra.Compare(algebra.Abs(a), algebra.Abs(b)) == -1)
{
Tuple <IntegerType, IntegerType, IntegerType> xyd = ExtendedEuclideanAlgorithm(algebra, b, a);
return(new Tuple <IntegerType, IntegerType, IntegerType>(xyd.Item2, xyd.Item1, xyd.Item3));
}
if (algebra.Abs(b).Equals(algebra.AddIdentity))
{
return(new Tuple <IntegerType, IntegerType, IntegerType>(algebra.MultiplyIdentity, algebra.AddIdentity, a));
}
IntegerType x1 = algebra.AddIdentity;
IntegerType x2 = algebra.MultiplyIdentity;
IntegerType y1 = algebra.MultiplyIdentity;
IntegerType y2 = algebra.AddIdentity;
while (algebra.Compare(algebra.AddIdentity, algebra.Abs(b)) == -1)
{
IntegerType q = algebra.Divide(a, b);
IntegerType r = algebra.Modulo(a, b);
IntegerType x = algebra.Subtract(x2, algebra.Multiply(q, x1));
IntegerType y = algebra.Subtract(y2, algebra.Multiply(q, y1));
a = b;
b = r;
x2 = x1;
x1 = x;
y2 = y1;
y1 = y;
}
return(new Tuple <IntegerType, IntegerType, IntegerType>(x2, y2, a));
}
public Tuple <Polynomial <DomainType>, Polynomial <DomainType> > DivideRemainder(Polynomial <DomainType> divisor_poly)
{
Debug.Assert(algebra.Equals(divisor_poly.algebra));
// if divisor is too big
if (coeffecients.Length < divisor_poly.coeffecients.Length)
{
return(new Tuple <Polynomial <DomainType>, Polynomial <DomainType> >(new Polynomial <DomainType>(algebra), new Polynomial <DomainType>(algebra, coeffecients)));
}
// if divisor is too big
if ((coeffecients.Length == divisor_poly.coeffecients.Length) && (algebra.Compare(coeffecients[coeffecients.Length - 1], coeffecients[coeffecients.Length - 1]) == -1))
{
return(new Tuple <Polynomial <DomainType>, Polynomial <DomainType> >(new Polynomial <DomainType>(algebra), new Polynomial <DomainType>(algebra, coeffecients)));
}
//Else do long division
DomainType[] remainder = ToolsCollection.Copy(coeffecients);
DomainType[] results = new DomainType[coeffecients.Length];
DomainType[] divisor = divisor_poly.coeffecients;
for (int index = 0; index < results.Length; index++)
{
results[index] = algebra.AddIdentity;
}
int max_shift = remainder.Length - divisor.Length;
for (int shift = max_shift; 0 <= shift; shift--)
{
DomainType multiplier = algebra.Divide(remainder[shift], divisor[divisor.Length - 1]);
for (int index = shift; index < coeffecients.Length; index++)
{
remainder[index] = algebra.Subtract(remainder[index], algebra.Multiply(divisor[index + shift], multiplier));
}
results[shift] = multiplier;
}
return(new Tuple <Polynomial <DomainType>, Polynomial <DomainType> >(new Polynomial <DomainType>(algebra, results), new Polynomial <DomainType>(algebra, remainder)));
}