/// <summary>
/// Creates a new triangle
/// </summary>
/// <param name="sideA">First side</param>
/// <param name="sideB">Second side</param>
/// <param name="sideC">Third side</param>
public Triangle (Complex sideA, Complex sideB, Complex sideC)
{
SideA = sideA;
SideB = sideB;
SideC = sideC;
AngleAB = Functions.ArcCos((sideA.Square() + sideB.Square() - sideC.Square()) / (2 * sideA * sideB));
AngleBC = Functions.ArcCos((sideC.Square() + sideB.Square() - sideA.Square()) / (2 * sideC * sideB));
AngleAC = Functions.ArcCos((sideA.Square() + sideC.Square() - sideB.Square()) / (2 * sideA * sideC));
}
public HComplex()
{
Value = new Complex(0, 0);
Attributes.Add("real", new HassiumProperty("real", x => Real, (self, x) => Real = x[0].HDouble().Value));
Attributes.Add("imaginary", new HassiumProperty("imaginary", x => Imaginary, (self, x) => Imaginary = x[0].HDouble().Value));
Attributes.Add("imag", new HassiumProperty("imag", x => Imaginary, (self, x) => Imaginary = x[0].HDouble().Value));
Attributes.Add("module", new HassiumProperty("module", x => (double)Value.Module, null, true));
Attributes.Add("argument", new HassiumProperty("argument", x => (double)Value.Argument, null, true));
Attributes.Add("conjugate", new HassiumProperty("conjugate", x => (double)Value.Conjugate, null, true));
Attributes.Add("__add", new InternalFunction(Add, -1));
Attributes.Add("__substract", new InternalFunction(Substract, -1));
Attributes.Add("__multiply", new InternalFunction(Multiply, -1));
Attributes.Add("__divide", new InternalFunction(Divide, -1));
Attributes.Add("__compare", new InternalFunction(x =>
{
var v = x[0].HComplex().Value;
if (v > Value) return 1;
if (v < Value) return -1;
return 0;
}, 1));
Attributes.Add("__pow", new InternalFunction(x => new HComplex(Functions.Pow(Value, x[0].HComplex().Value)), 1));
Attributes.Add("__root", new InternalFunction(x => new HComplex(Functions.NthRoot(Value, x[0].HComplex().Value)), 1));
Attributes.Add("negate", new InternalFunction(Negate, 0));
Attributes.Add("square", new InternalFunction(x => new HComplex(Value.Square()), 0));
}
public static Complex ArcCos(Complex value)
{
if (value.IsReal()) return Math.Acos(value.Real);
/*if (value.Imaginary < 0 || value.Imaginary == 0d && value.Real > 0)
{
return Constant.Pi - Acos(-value);
}
*/
return -Complex.ImaginaryOne * Ln(value + Complex.ImaginaryOne * Sqrt(1 - value.Square()));
//return (Constant.Pi / 2.0) + Constant.I * Ln(Constant.I * value + Sqrt(1 - value.Square()));
}
public static Complex ArcSin(Complex value)
{
if (value.IsReal()) return Math.Asin(value.Real);
if (value.IsImaginary() || value.Imaginary == 0d && value.Real < 0)
{
return -ArcSin(-value);
}
return -Complex.ImaginaryOne * Sqrt(Ln((1 - value.Square())) + (Complex.ImaginaryOne * value));
}
public static Complex HermiteHFunc(Complex nu, Complex z)
{
return Pow(2.0, nu) * Sqrt(Constants.Pi) *
(1.0 / Gamma((1.0 - nu) / 2) * Hypergeometric1F1(-nu / 2.0, 0.5, z.Square()) -
(2.0 * z) / Gamma(-nu / 2.0) * Hypergeometric1F1((1.0 - nu) / 2.0, 1.5, z.Square()));
}
public static Complex FibonacciFunc(Complex nu, Complex z)
{
return (Pow(2.0, -nu) * Pow(z + Sqrt(z.Square() + 4.0), nu) -
Cos(nu * Constants.Pi) * Pow(2.0, nu) * Pow(z + Sqrt(z.Square() + 4.0), -nu)) /
Sqrt(z.Square() + 4.0);
}
public static Complex ChebyshevUFunc(Complex nu, Complex z)
{
return Sin((nu + 1.0) * ArcCos(z)) / Sqrt(1.0 - z.Square());
}
public static Complex AreaCylinder(Complex radius, Complex height)
{
return 2 * Constants.Pi * radius.Square() + 2 * Constants.Pi * radius * height;
}
public static Complex AreaCube(Complex side)
{
return 6.0 * side.Square();
}
public static Complex AreaSphere(Complex radius)
{
return 4 * Constants.Pi * radius.Square();
}
public static Complex AreaPolygon(Complex sides, Complex length)
{
return (sides * length.Square()) / (4 * Tan(Constants.Pi / sides));
}
public static Complex AreaSector(Complex radius, Complex angle)
{
return (radius.Square() / 2.0) * Angle(angle);
}
public static Complex AreaCircle(Complex radius)
{
return Constants.Pi * radius.Square();
}
public static Complex AreaSquare(Complex cote)
{
return cote.Square();
}
public static Complex ArcTan(Complex x, Complex y)
{
return 2.0 * ArcTan(y / (Sqrt(x.Square() + y.Square()) + x));
}
public void CanComputeSquare()
{
var complex = new Complex(1.19209289550780998537e-7, 1.19209289550780998537e-7);
AssertHelpers.AlmostEqual(new Complex(0, 2.8421709430403888e-14), complex.Square(), 15);
complex = new Complex(0.0, 1.19209289550780998537e-7);
AssertHelpers.AlmostEqual(new Complex(-1.4210854715201944e-14, 0.0), complex.Square(), 15);
complex = new Complex(0.0, -1.19209289550780998537e-7);
AssertHelpers.AlmostEqual(new Complex(-1.4210854715201944e-14, 0.0), complex.Square(), 15);
complex = new Complex(0.0, 0.5);
AssertHelpers.AlmostEqual(new Complex(-0.25, 0.0), complex.Square(), 15);
complex = new Complex(0.0, -0.5);
AssertHelpers.AlmostEqual(new Complex(-0.25, 0.0), complex.Square(), 15);
complex = new Complex(0.0, -8.388608e6);
AssertHelpers.AlmostEqual(new Complex(-70368744177664.0, 0.0), complex.Square(), 15);
}
