public static Polynom <T, R> operator -(Polynom <T, R> Ax)
{
var _minusOne = Ax.FRing.Opposite(Ax.FRing.One);
var _opposite = new Polynom <T, R>(Ax);
_opposite.Mult(_minusOne);
return(_opposite);
}
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);
}
private Polynom <T, R> Div(Polynom <T, R> aDenumerator, List <Polynom <T, R> > aRemainder, bool aIsRight)
{
if (aRemainder == null)
{
aRemainder = new List <Polynom <T, R> >();
}
var quot = new Polynom <T, R>(this.FRing, -1);
if (this.Degree < aDenumerator.Degree)
{
aRemainder.Add(this);
return(quot);
}
int deg_quot = this.Degree - aDenumerator.Degree;
var _rem = new Polynom <T, R>(this);
var _minusOne = this.FRing.Opposite(this.FRing.One);
var c = this.FRing.Reverse(aDenumerator.FCoeffs[aDenumerator.Degree]);
while (_rem.Degree >= aDenumerator.Degree)
{
int p = _rem.Degree - aDenumerator.Degree;
var d = new T[p + 1];
if (aIsRight)
{
d[p] = this.FRing.Prod(_rem.FCoeffs[_rem.Degree], c);
}
else
{
d[p] = this.FRing.Prod(c, _rem.FCoeffs[_rem.Degree]);
}
var dp = new Polynom <T, R>(this.FRing, d);
quot += dp;
var dd = new Polynom <T, R>(this.FRing, -1);
if (aIsRight)
{
dd = dp * aDenumerator;
}
else
{
dd = aDenumerator * dp;
}
aRemainder.Add(new Polynom <T, R>(dd));
dd.Mult(_minusOne);
_rem += dd;
aRemainder.Add(_rem);
}
if (quot.Degree < deg_quot)
{
var _shift = new Polynom <T, R>(this.FRing, deg_quot - quot.Degree);
quot = quot * _shift;
}
return(quot);
}