public FunctionPolynomialLagrange(IAlgebraInteger <SymbolType> algebra, IList <Tuple <SymbolType, SymbolType> > points)
{
this.algebra = algebra;
this.domain = new SymbolType[points.Count];
this.range = new SymbolType[points.Count];
for (int point_index = 0; point_index < points.Count; point_index++)
{
domain[point_index] = points[point_index].Item1;
range[point_index] = points[point_index].Item2;
}
}
public AlgebraFiniteFieldGenericPrime(IAlgebraInteger <IntegerType> algebra, IntegerType prime)
{
if (!ToolsMathBigIntegerPrime.IsPrime(algebra.ToBigInteger(prime)))
{
throw new Exception("Number " + prime.ToString() + " is not prime");
}
Prime = prime;
Algebra = algebra;
ElementCount = Algebra.ToBigInteger(prime);
AddIdentity = new FiniteFieldElement <IntegerType>(this, Algebra.AddIdentity);
MultiplyIdentity = new FiniteFieldElement <IntegerType>(this, Algebra.MultiplyIdentity);
}
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 Polynomial(IAlgebraInteger <DomainType> algebra, DomainType [] coeffecients)
{
this.algebra = algebra;
this.coeffecients = ToolsCollection.Copy(coeffecients);
}
public Polynomial(IAlgebraInteger <DomainType> algebra)
{
this.algebra = algebra;
coeffecients = new DomainType[0];
}