public Polynomial <T, TField> Divide(Polynomial <T, TField> t1, Polynomial <T, TField> t2, out Polynomial <T, TField> r)
{
return(Polynomial <T, TField> .Divide(t1, t2, out r));
}
public Polynomial <T, TField> Gcd(Polynomial <T, TField> t1, Polynomial <T, TField> t2)
{
return(Polynomial <T, TField> .Gcd(t1, t2));
}
public Polynomial <T, TField> Pow(Polynomial <T, TField> t, int n)
{
return(t.Pow(n));
}
public BigInteger Euclidean(Polynomial <T, TField> t)
{
return(t.Degree);
}
public static Polynomial <T, TField> Divide(Polynomial <T, TField> p1, Polynomial <T, TField> p2)
{
Polynomial <T, TField> rem;
return(Divide(p1, p2, out rem));
}
public Polynomial <T, TField> Multiply(Polynomial <T, TField> t, int n)
{
return(t * _field.Multiply(_field.One, n));
}
public Polynomial <T, TField> Negate(Polynomial <T, TField> t)
{
return(-t);
}
public bool IsApproxZero(Polynomial <T, TField> t)
{
return(t.Degree == 0 && _field.IsApproxZero(t.CoefficientAt(0)));
}
public static Polynomial <T, TField> Spread(int n, Polynomial <T, TField> x)
{
return((x.Field.One - ChebyshevT(n, x.Field.One - x * 2)) / 2);
}
public Polynomial <T, TField> Add(Polynomial <T, TField> t1, Polynomial <T, TField> t2)
{
return(t1 + t2);
}
public static Polynomial <T, TField> Lcm(Polynomial <T, TField> p1, Polynomial <T, TField> p2)
{
return((p1 / Gcd(p1, p2)) * p2);
}
public static Polynomial <T, TField> FromPolynomial <U, UField>(Polynomial <U, UField> p, Func <U, T> f) where U : IEquatable <U> where UField : IField <U>, new()
{
return(new Polynomial <T, TField>(p.Select(term => new Term <T>(term.Deg, f(term.Coeff)))));
}
public static Polynomial <T, TField> FromPolynomial <UField>(Polynomial <T, UField> p) where UField : IField <T>, new()
{
return(new Polynomial <T, TField>(p.CloneArray()));
}
public Polynomial <T, TField> Lcm(Polynomial <T, TField> t1, Polynomial <T, TField> t2)
{
return(Polynomial <T, TField> .Lcm(t1, t2));
}
public Polynomial <T, TField> Subtract(Polynomial <T, TField> t1, Polynomial <T, TField> t2)
{
return(t1 - t2);
}
public Polynomial <T, TField> Divide(Polynomial <T, TField> t, int n)
{
return(t / _field.Multiply(_field.One, n));
}
public Polynomial <T, TField> Multiply(Polynomial <T, TField> t1, Polynomial <T, TField> t2)
{
return(t1 * t2);
}
public bool IsUnit(Polynomial <T, TField> t)
{
return(t.Degree == 0 && _field.IsUnit(t.CoefficientAt(0)));
}
public static Polynomial <T, TField> Divide(Polynomial <T, TField> p1, Polynomial <T, TField> p2, out Polynomial <T, TField> rem)
{
IField <T> field = p1.Field;
T leadingCoeff;
T[] dividList;
T[] divisList;
T[] quotList;
T[] workList;
if (p2.Degree > p1.Degree)
{
rem = p1;
return(Polynomial <T, TField> .Zero);
}
if (p2.Degree == 0)
{
rem = new Polynomial <T, TField>();
return(Divide(p1, p2[0].Coeff));
}
dividList = p1.ToCoefficientList();
divisList = p2.ToCoefficientListForDivisor(out leadingCoeff);
quotList = new T[p1.Degree - p2.Degree + 1];
workList = new T[divisList.Length];
if (!field.IsOne(leadingCoeff))
{
// Fix the dividend.
for (int i = 0; i < dividList.Length; i++)
{
dividList[i] = field.Divide(dividList[i], leadingCoeff);
}
}
// Initialize the work list.
Array.Copy(dividList, workList, workList.Length);
for (int i = 0; i < quotList.Length; i++)
{
// Save the quotient cofficient.
quotList[i] = workList[0];
// Shift left, take in from dividend.
Array.Copy(workList, 1, workList, 0, workList.Length - 1);
workList[workList.Length - 1] = dividList[i + workList.Length];
// Copy the divisor and multiply with the last quotient
// coefficient. Add this to the work list. Note that this
// is all done in one step.
for (int j = 0; j < workList.Length; j++)
{
workList[j] = field.Add(workList[j], field.Multiply(divisList[j], quotList[i]));
}
}
if (!field.IsOne(leadingCoeff))
{
// Fix the remainder.
for (int i = 0; i < workList.Length; i++)
{
workList[i] = field.Multiply(workList[i], leadingCoeff);
}
}
rem = FromCoefficientList(workList);
return(FromCoefficientList(quotList));
}