public static Polynom <T, R> GetGcd(Polynom <T, R> a, Polynom <T, R> b)
{
var _alocal = new Polynom <T, R>(a);
var _zero = new Polynom <T, R>(_alocal.FRing, -1);
var _one = new Polynom <T, R>(_alocal.FRing, 0);
var gcd = _zero;
if (_alocal.Degree < 0)
{
gcd = b;
}
else if (b.Degree < 0)
{
gcd = _alocal;
}
else
{
var r1 = b;
var r2 = new List <Polynom <T, R> >();
var _quot = _alocal.Div(b, r2);
gcd = b;
var q = _zero;
var temp = new List <Polynom <T, R> >();
var temp1 = _zero;
while (r2.Last().Degree >= 0)
{
gcd = r2.Last();
q = r1.Div(r2.Last(), temp);
//r1 = r2.Last();
r1 = gcd;
r2 = temp;
}
}
var _major = gcd.FCoeffs[gcd.Degree];
if (!_alocal.FRing.Equals(_major, _alocal.FRing.One))
{
var _major_1 = _alocal.FRing.Reverse(_major);
gcd.Mult(_major_1);
}
return(gcd);
}
private List <Polynom <T, R> > Factorisation(Polynom <T, R> aPolynom)
{
if (!(aPolynom.FRing is IEnumerable <T>))
{
throw new ArgumentException("Polinom's ring mast be enumerable.");
}
var p = (int)aPolynom.FRing.Size;
var _res = new List <Polynom <T, R> >();
if (aPolynom.Degree < 2)
{
return(_res);
}
var _pring = new Rx <T, R>(aPolynom.FRing);
var _derivative = aPolynom.Derivative;
var _gcd = Polynom <T, R> .GetGcd(aPolynom, _derivative);
if (_gcd.Degree > 0)
{
if (_derivative != _pring.Zero)
{
_res.Add(_gcd);
_res.Add(aPolynom.Div(_gcd, null));
}
else
{
p = (int)aPolynom.FRing.SimpleSubfieldSize;
var c = aPolynom.Degree / p;
var _pol = new Polynom <T, R>(aPolynom.FRing, c);
for (var i = 0; i <= c; i++)
{
_pol.FCoeffs[i] = aPolynom.FRing.Pow(
aPolynom.FCoeffs[p * i], this.FRing.Size / p);
}
for (var i = 0; i < p; i++)
{
_res.Add(new Polynom <T, R>(_pol));
}
}
return(_res);
}
var _aij_vals = new T[aPolynom.Degree, aPolynom.Degree];
for (var i = 1; i < aPolynom.Degree; i++)
{
var _pol = new Polynom <T, R>(aPolynom.FRing, i * p);
_pol.FCoeffs[i] = aPolynom.FRing.Opposite(aPolynom.FRing.One);
var _rem = new List <Polynom <T, R> >();
_pol.Div(aPolynom, _rem);
var _ai = _rem.Last();
for (var j = 0; j <= _ai.Degree; j++)
{
_aij_vals[j, i - 1] = _ai.FCoeffs[j];
}
}
var _aij = new Matrix <T, R>(aPolynom.FRing, _aij_vals);
var _matrix = Matrix <T, R> .SolveLs(_aij);
var _solvation = new T[_matrix.RowCount + 1];
_solvation[0] = aPolynom.FRing.Zero;
bool IsResEmpty = true;
var _matrixValues = _matrix.Values;
for (var i = 0; i < _matrix.RowCount; i++)
{
if (_solvation[i + 1] == null)
{
_solvation[i + 1] = aPolynom.FRing.Zero;
}
for (var j = 0; j < _matrix.ColumnCount; j++)
{
_solvation[i + 1] = aPolynom.FRing.Sum(_solvation[i + 1], _matrixValues[i, j]);
}
IsResEmpty = _solvation[i + 1].Equals(aPolynom.FRing.Zero);
}
if (!IsResEmpty)
{
var _pp = new Polynom <T, R>(aPolynom.FRing, _solvation);
var _gcd1 = _pring.One;
var _enumerable = (IEnumerable <T>) this.FRing;
foreach (var _item in _enumerable)
{
var _ppp = new Polynom <T, R>(_pp);
_ppp.FCoeffs[0] = _ppp.FRing.Sum(_item, _ppp.FCoeffs[0]);
_gcd1 = Polynom <T, R> .GetGcd(aPolynom, _ppp);
if (!_gcd1.Equals(_pring.One))
{
_res.Add(_gcd1);
var _rem = new List <Polynom <T, R> >();
var _quot = aPolynom.Div(_gcd1, _rem);
_res.Add(_quot);
break;
}
}
}
return(_res);
}
public static Polynom <T, R> GetGcdEx(Polynom <T, R> a, Polynom <T, R> b,
out Polynom <T, R> u, out Polynom <T, R> v)
{
var _alocal = new Polynom <T, R>(a);
var _zero = new Polynom <T, R>(_alocal.FRing, -1);
var _one = new Polynom <T, R>(_alocal.FRing, 0);
var gcd = _zero;
if (_alocal.Degree < 0)
{
u = _zero;
v = (b.Degree < 0 ? _zero : _one);
gcd = b;
}
else if (b.Degree < 0)
{
v = _zero;
u = (_alocal.Degree < 0 ? _zero : _one);
gcd = _alocal;
}
else
{
var r1 = b;
var r2 = new List <Polynom <T, R> >();
var _quot = _alocal.Div(b, r2);
gcd = b;
var u1 = _one;
var u2 = _zero;
var v1 = _one;
var v2 = _one;
var q = _zero;
if (r2.Last().Degree < 0)
{
u1 = _zero;
}
else
{
v1 = -_quot;
}
var temp = new List <Polynom <T, R> >();
var temp1 = _zero;
while (r2.Last().Degree >= 0)
{
gcd = r2.Last();
q = r1.Div(r2.Last(), temp);
//r1 = r2.Last();
r1 = gcd;
r2 = temp;
temp1 = u1;
u1 = u2 - u1 * q;
u2 = temp1;
temp1 = v1;
v1 = v2 - v1 * q;
v2 = temp1;
}
u = u2;
v = v2;
}
var _major = gcd.FCoeffs[gcd.Degree];
if (!_alocal.FRing.Equals(_major, _alocal.FRing.One))
{
var _major_1 = _alocal.FRing.Reverse(_major);
gcd.Mult(_major_1);
}
var _sum = u * a + v * b;
_major = _sum.FCoeffs[_sum.Degree];
if (!_alocal.FRing.Equals(_major, _alocal.FRing.One))
{
var _major_1 = _alocal.FRing.Reverse(_major);
u.Mult(_major_1);
v.Mult(_major_1);
}
return(gcd);
}