using System.Numerics;
using Skeleton.Algebra.Extensions;
using Skeleton.Analysis.BivariantFunctions.Real.Implements;
using Skeleton.Analysis.BivariantFunctions.Real.PolynomialHelpers;
using Skeleton.Utils.Helpers;

namespace Skeleton.Analysis.AnalyticFunctions.Polynomials.Implements;

/// <summary>
/// </summary>
public class C2Polynomial : Polynomial
{
    /// <inheritdoc />
    public C2Polynomial()
    {
        Coefficients = new Complex[3];
        Fix();
    }

    /// <inheritdoc />
    public C2Polynomial(Complex a0, Complex a1, Complex a2)
    {
        Coefficients = new[] { a0, a1, a2 };
        Fix();
    }

    /// <summary>
    /// </summary>
    public Complex A0 => Coefficients[0];

    /// <summary>
    /// </summary>
    public Complex A1 => Coefficients[1];

    /// <summary>
    /// </summary>
    public Complex A2 => Coefficients[2];

    /// <inheritdoc />
    public override string Representation =>
        $"{A0.Real} + {A0.Imaginary}i + ({A1.Real} + {A1.Imaginary}i)x + ({A2.Real} + {A2.Imaginary}i)x2";

    /// <inheritdoc />
    public override int Dim => 2;

    /// <inheritdoc />
    public override Polynomial Derivative => new C1Polynomial(A1, A2 * 2);

    /// <inheritdoc />
    public override IEnumerable<Complex> Roots => Decorators.WithTol(1E-20, 
        () =>
        {
            if (A2.IsEqualApprox(0))
                return new C1Polynomial(A0, A1).Roots;
            if (A0.IsEqualApprox(0))
                return new C1Polynomial(A1, A2).Roots.Concat(new[] { Complex.Zero });
            Complex x1 = (-A1 + Complex.Sqrt(A1 * A1 - 4 * A2 * A0)) / (2 * A2);
            Complex x2 = (-A1 - Complex.Sqrt(A1 * A1 - 4 * A2 * A0)) / (2 * A2);
            return new[] { x1, x2 };
        }
    );

    /// <inheritdoc />
    public override BivariantContinuous Re => new PolyCHelper.PolyC2Re(A0, A1, A2);

    /// <inheritdoc />
    public override BivariantContinuous Im => new PolyCHelper.PolyC2Im(A0, A1, A2);

    /// <inheritdoc />
    public override Complex Evaluate(Complex x)
    {
        return A0 + x * (A1 + x * A2);
    }
}