protected override GCDResult PolyGCD(Polynomial g, out Polynomial gcd)
{
Polynomial f = this;
GCDResult A = new GCDResult(new Polynomial {
1
}, new Polynomial {
0
});
GCDResult B = new GCDResult(new Polynomial {
0
}, new Polynomial {
1
});
GCDResult Temp;
Polynomial a, b;
if (f.degree > g.degree)
{
a = new Polynomial(f);
b = new Polynomial(g);
}
else
{
a = new Polynomial(g);
b = new Polynomial(f);
}
while (!b.IsNull())
{
DividionResult divres = a / b;
a = b;
b = divres.Item2;
Temp = new GCDResult(A - new GCDResult(B.Item1 * divres.Quotient, B.Item2 * divres.Quotient));
A = B;
B = Temp;
}
gcd = a;
if (f.degree <= g.degree)
{
A = new GCDResult(A.Coef2, A.Coef1);
}
if (gcd[gcd.degree] < 0)
{
gcd = -gcd;
return(new GCDResult(-A.Item1, -A.Item2));
}
return(new GCDResult(A.Item1, A.Item2));
}
protected override GCDResult PolyGCD(IntPolynomial g, out IntPolynomial gcd)
{
IntPolynomial f = this;
GCDResult A = new GCDResult(new IntPolynomial {
1
}, new IntPolynomial {
0
});
GCDResult B = new GCDResult(new IntPolynomial {
0
}, new IntPolynomial {
1
});
IntPolynomial a, b;
if (f.degree > g.degree)
{
a = new IntPolynomial(f);
b = new IntPolynomial(g);
}
else
{
a = new IntPolynomial(g);
b = new IntPolynomial(f);
}
BigInteger CoeffReminder;
while (!b.IsNull())
{
BigInteger CurrentMultiplyCoeff = BigInteger.Pow(b[b.size - 1], (a.size - 1) - (b.size - 1) + 1);
DividionResult divres = (a * CurrentMultiplyCoeff) / b;
a = b;
CoeffReminder = divres.Item2.CoeffGCD();
b = divres.Item2 / CoeffReminder;
}
CoeffReminder = a.CoeffGCD();
gcd = a / CoeffReminder;
if (gcd[gcd.size - 1] < 0)
{
gcd *= -1;
}
return(new GCDResult(A.Item1, A.Item2));
}
public static FullSolution SolveEquation(Polynomial f, Polynomial g, Polynomial c)
{
FullSolution solution = new FullSolution();
//f=0; g=0; c=0 | c!=0
if (f.IsNull() && g.IsNull())
{
if (c.IsNull())
{
solution.zeroSolution = new Solution(new Polynomial(), new Polynomial());
solution.solutionStep = new Solution(null, null);
solution.areCoefsIndependent = true;
}
else
{
solution.isDefined = false;
}
return(solution);
}
if (c.IsNull() && f.IsNull() != g.IsNull())
{
solution.zeroSolution = new Solution(new Polynomial(), new Polynomial());
if (f.IsNull() && !g.IsNull())
{
solution.solutionStep = new Solution(null, new Polynomial());
}
else if (!f.IsNull() && g.IsNull())
{
solution.solutionStep = new Solution(new Polynomial(), null);
}
return(solution);
}
else if (f.IsNull() != g.IsNull())
{
if (f.IsNull())
{
DividionResult divres = c / g;
if (!divres.Reminder.IsNull())
{
solution.isDefined = false;
return(solution);
}
solution.solutionStep = new Solution(null, new Polynomial {
0
});
solution.zeroSolution = new Solution(new Polynomial {
0
}, divres.Quotient);
}
else
{
DividionResult divres = c / f;
if (!divres.Reminder.IsNull())
{
solution.isDefined = false;
return(solution);
}
solution.solutionStep = new Solution(new Polynomial {
0
}, null);
solution.zeroSolution = new Solution(divres.Quotient, new Polynomial {
0
});
}
return(solution);
}
Polynomial gcd = new Polynomial();
GCDResult expCoefs = GCD(f, g, out gcd);
DividionResult tempX0 = (expCoefs.Coef1 * c / gcd);
DividionResult tempY0 = (expCoefs.Coef2 * c / gcd);
// К этому моменту f и g не нулевые (ветвление для c)
if (c.IsNull())
{
solution.zeroSolution = new Solution(new Polynomial(), new Polynomial());
solution.solutionStep = new Solution((g / gcd).Quotient, -(f / gcd).Quotient);
}
else
{
if (tempX0.Reminder.IsNull() && tempY0.Reminder.IsNull())
{
solution.zeroSolution = new Solution(tempX0.Quotient, tempY0.Quotient);
solution.solutionStep = new Solution((g / gcd).Quotient, -(f / gcd).Quotient);
}
else
{
return(new FullSolution()
{
isDefined = false
});
}
}
return(solution);
}