private static void test()
{
Poly2 poly = new Poly2(
new Complex(2, 3),
new Complex(1, -2),
new Complex(-1, 4));
poly.solve();
poly.print();
}
//Neumark - Solution Of Cubic & Quartic Equations
public void solve()
{
x = new Complex[4];
if (B.abs() < 1e-12 && D.abs() < 1e-12)
{
Poly2 poly2 = new Poly2(A, C, E);
poly2.solve();
x[0] = poly2.x[0].sqrt();
x[1] = x[0].negate();
x[2] = poly2.x[1].sqrt();
x[3] = x[2].negate();
}
else
{
Poly3 subpoly = new Poly3(Complex.ONE,
C * (-2),
C * C + B * D - A * E * 4,
-(B * C * D - B * B * E - A * D * D));
subpoly.solve();
Complex y = findMaxDelta(subpoly.x);
Complex DeltaRoot = (B * B - A * y * 4).sqrt();
Complex G, g, H, h;
if (DeltaRoot.abs() < 1e-12)
{
G = B * 0.5;
g = G;
H = (C - y) * 0.5;
h = H;
}
else
{
G = (B + DeltaRoot) * 0.5;
g = (B - DeltaRoot) * 0.5;
Complex part = (B * (C - y) - A * D * 2) / (DeltaRoot * 2);
H = (C - y) * 0.5 + part;
h = (C - y) * 0.5 - part;
}
Poly2 poly2a = new Poly2(A, G, H);
poly2a.solve();
Poly2 poly2b = new Poly2(A, g, h);
poly2b.solve();
x[0] = poly2a.x[0];
x[1] = poly2a.x[1];
x[2] = poly2b.x[0];
x[3] = poly2b.x[1];
}
}