using System;
using System.Linq;
using System.Numerics;
using Skeleton.Algebra.Extensions;
using Skeleton.Analysis.AnalyticFunctions.Polynomials.Implements;

namespace SkeletonTest.tests;

public static class AlgebraMiscTest
{

	private static readonly Complex ii = new Complex(0, 1);
	[Test]
	public static void SolverTest()
	{
		var fff = new C2Polynomial(ii, ii, 1);
		var qrs = fff.Roots.ToArray();
		Assert.IsTrue(qrs.LSum().IsEqualApprox(-ii));
		Assert.IsTrue(qrs.LProd().IsEqualApprox(ii));

		GeneralExt.SetTol(1E-7f);
		qrs = new C3Polynomial(ii, ii, 1, 1).Roots.ToArray();
		Assert.IsTrue(qrs.LSum().IsEqualApprox(-1));
		Assert.IsTrue(qrs.LProd().IsEqualApprox(-ii));
		Assert.IsTrue(qrs.ApproxContains(-1));
		Assert.IsTrue(qrs.ApproxContains((1 - ii) / Complex.Sqrt(2)));
		Assert.IsTrue(qrs.ApproxContains(-(1 - ii) / Complex.Sqrt(2)));
		
		qrs = new C4Polynomial(ii, ii, 1, -ii, 1).Roots.ToArray();
		Assert.IsTrue(qrs.LSum().IsEqualApprox(ii));
		Assert.IsTrue(qrs.LProd().IsEqualApprox(ii));
		GeneralExt.ResetTol();
	}
	[Test]
	public static void KernelTest()
	{
		C22 mc22 = new C22(
			1 + ii, 2,
			0, 0
		);
		C2Space c2ks = mc22.Ker;
		Assert.IsTrue(c2ks.Rank == 1);
		Console.WriteLine((mc22 * c2ks[0]).Representation);
		Assert.IsTrue((mc22 * c2ks[0]).IsEqualApprox(C2.Zero));
		R22 mr22 = new R22(
			1, 3,
			0, 0
		);
		R2Space r2ks = mr22.Ker;
		Assert.IsTrue(r2ks.Rank == 1);
		Console.WriteLine((mr22 * r2ks[0]).Representation);
		Assert.IsTrue((mr22 * r2ks[0]).IsEqualApprox(R2.Zero));

		C33 mc33 = new C33(
			3 + ii, 0, 1 - ii,
			0, 0, 0,
			0, 0, 0
		);
		C3Space c3ks = mc33.Ker;
		Assert.IsTrue(c3ks.Rank == 2);

		Assert.IsTrue((mc33 * ((3.2 + 1.7 * ii) * c3ks[0] + (1.1 - 0.8 * ii) * c3ks[1])).IsEqualApprox(C3.Zero));
		Assert.IsTrue((mc33 * ((1.2 + 3.7 * ii) * c3ks[0] + (3.1 + 1.2 * ii) * c3ks[1])).IsEqualApprox(C3.Zero));
		R33 mr33 = new R33(
			3, 5, 1,
			3, 0, 1,
			0, 5, 0
		);
		R3Space r3ks = mr33.Ker;
		Assert.IsTrue(r3ks.Rank == 1);
		Assert.IsTrue((mr33 * r3ks[0]).IsEqualApprox(R3.Zero));
		C44 mc44 = new C44(
			1 + ii, 2 - ii, 0, 0,
			1 + ii, 0, 0, 0,
			0, 1, 0, 0,
			0, 0, 0, 0
		);
		C4Space c4ks = mc44.Ker;
		Assert.IsTrue(c4ks.Rank == 2);
		Assert.IsTrue((mc44 * (1.2 * c4ks[0] + 3.1 * c4ks[1])).IsEqualApprox(C4.Zero));
		
	}

	[Test]
	public static void TransposeTest()
	{
		C22 a = new C22(
			1, 2,
			3, 4
		);
		C22 at = new C22(
			1, 3,
			2, 4
		);
		Assert.IsTrue(a.Transpose().IsEqualApprox(at));
	}
}