init

.gitignore

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+bin/
+obj/
+/packages/
+riderModule.iml
+/_ReSharper.Caches/

Hermeteus.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+    <PropertyGroup>
+        <TargetFramework>net9.0</TargetFramework>
+        <ImplicitUsings>enable</ImplicitUsings>
+        <Nullable>enable</Nullable>
+    </PropertyGroup>
+
+    <ItemGroup>
+      <ProjectReference Include="..\Skeleton\Skeleton.csproj" />
+    </ItemGroup>
+
+</Project>

Hermeteus.sln

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+
+Microsoft Visual Studio Solution File, Format Version 12.00
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Hermeteus", "Hermeteus.csproj", "{65C35817-9FA0-4AC6-B798-4AFBFC66A7C7}"
+EndProject
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Skeleton", "..\Skeleton\Skeleton.csproj", "{D8D5EFCF-16AD-4E1F-ACF6-B47367A5CDB6}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{65C35817-9FA0-4AC6-B798-4AFBFC66A7C7}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{65C35817-9FA0-4AC6-B798-4AFBFC66A7C7}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{65C35817-9FA0-4AC6-B798-4AFBFC66A7C7}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{65C35817-9FA0-4AC6-B798-4AFBFC66A7C7}.Release|Any CPU.Build.0 = Release|Any CPU
+		{D8D5EFCF-16AD-4E1F-ACF6-B47367A5CDB6}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{D8D5EFCF-16AD-4E1F-ACF6-B47367A5CDB6}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{D8D5EFCF-16AD-4E1F-ACF6-B47367A5CDB6}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{D8D5EFCF-16AD-4E1F-ACF6-B47367A5CDB6}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+EndGlobal

src/HomogeneousMixture.cs

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+namespace Hermeteus;
+
+public class HomogeneousMixture
+{
+    public HomogeneousMixture()
+    {
+        Components = new Dictionary<Molecule, double>();
+    }
+
+    internal Dictionary<Molecule, double> Components { get; }
+
+    internal SU3 EigenState => Components.Keys
+        .Select(x => x.EigenState.Log() * Ratio(x))
+        .Aggregate((a, b) => a + b)
+        .Exp();
+
+    public double Amount => Components.Sum(p => p.Value);
+    
+    public double Ratio(Molecule m) => Amount == 0 
+        ? 0 
+        : Components.GetValueOrDefault(m, 0) / Amount;
+    
+    
+}
+

src/Measurements/Basic.cs

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+namespace Hermeteus.Measurements;
+
+public static partial class Measurement
+{
+    private static double MolecularMass(this Molecule m)
+    {
+        H3 w = m.EigenState.ConjugateOn(new DiagR3(Math.PI / 32, Math.PI * 2, Math.PI * 8));
+        double r0 = w.Rayleigh(
+            m.EigenState.Log().ColumnAverageBivariant +
+            m.EigenState.ColumnAverage
+        );
+        return r0 * r0 / 8d;
+    }
+
+    private static double MolecularDensity(this Molecule m)
+    {
+        H3 w = m.EigenState.ConjugateOn(new DiagR3(-Math.PI, 0, Math.PI));
+        double r0 = w.Rayleigh(
+            m.EigenState.ColumnAverageBivariant -
+            m.EigenState.Log().ColumnAverage
+        );
+        return r0 * r0 / 3d;
+    }
+
+    public static double Mass(this HomogeneousMixture h) =>
+        h.Components
+            .Select(p => p.Key.MolecularMass() * p.Value)
+            .Sum();
+
+    public static double Density(this HomogeneousMixture h) =>
+        h.Components.Keys
+            .Select(x => x.MolecularDensity() * h.Ratio(x))
+            .Sum();
+    
+    
+    
+}

src/Measurements/Color.cs

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+using Skeleton.Constants;
+
+namespace Hermeteus.Measurements;
+
+public static partial class Measurement
+{
+    private static readonly U3 RedFilter = new LieU3
+    (
+        I, 0, -1,
+        0, I, 0,
+        1, 0, -I
+    ).Exp();
+
+    private static readonly U3 GreenFilter = new LieU3
+    (
+        0, -I, 0,
+        -I, 0, -1,
+        0, 1, 0
+    ).Exp();
+
+    private static readonly U3 BlueFilter = new LieU3
+    (
+        0, 0, -I,
+        0, 0, -1,
+        -I, 1, 0
+    ).Exp();
+
+    private static readonly U3 OpacityFilter = new LieU3(
+        I, -I, -I,
+        -I, I, -1,
+        -I, 1, -I
+    ).Exp();
+
+
+    private static readonly H3 RedDefinite = RedFilter.ConjugateOn(AlgebraConstant.UniformSpectrum3);
+
+    private static readonly H3 GreenDefinite = GreenFilter.ConjugateOn(AlgebraConstant.UniformSpectrum3);
+
+    private static readonly H3 BlueDefinite = BlueFilter.ConjugateOn(AlgebraConstant.UniformSpectrum3);
+
+    private static readonly H3 OpacityDefinite = OpacityFilter.ConjugateOn(new DiagR3(0.05d, 0.74d, 1d));
+
+    public static Byte Red(HomogeneousMixture m) => (Byte)
+    (
+        m.EigenState
+            .ConjugateOn(RedDefinite)
+            .Rayleigh(Ita(m)) * 255
+    );
+
+    public static Byte Green(HomogeneousMixture m) => (Byte)
+    (
+        m.EigenState
+            .ConjugateOn(GreenDefinite)
+            .Rayleigh(Ita(m)) * 255
+    );
+
+    public static Byte Blue(HomogeneousMixture m) => (Byte)
+    (
+        m.EigenState
+            .ConjugateOn(BlueDefinite)
+            .Rayleigh(Ita(m)) * 255
+    );
+
+    public static Byte Alpha(HomogeneousMixture m) => (Byte)
+    (
+        m.EigenState
+            .ConjugateOn(OpacityDefinite)
+            .Rayleigh(Ita(m)) * 255
+    );
+}

src/Measurements/Measurement.cs

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+using System.Numerics;
+
+namespace Hermeteus.Measurements;
+
+public static partial class Measurement
+{
+    private static Complex I => Complex.ImaginaryOne;
+    public static C3 Ita(this HomogeneousMixture h) => h.Components.Keys
+        .Select(x => x.EigenState.ColumnAverageBivariant * h.Ratio(x))
+        .Aggregate((a, b) => a + b);
+}

src/Measurements/Reaction.cs

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+namespace Hermeteus.Measurements;
+
+public static partial class Measurement
+{
+    public static double[] Negativity(this Molecule m) =>
+        m.EigenState.EigenValues()
+            .Select(eiv => eiv.Phase/Math.PI)
+            .ToArray();
+    
+    
+
+}

src/Molecule.cs

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+
+namespace Hermeteus;
+
+public class Molecule
+{
+    internal SU3 EigenState { get; set; }
+
+    public Molecule(SU3 eigenState)
+    {
+        EigenState = eigenState;
+    }
+    
+}

src/Using.cs

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+global using C3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.OnField<System.Numerics.Complex>.FVector;
+
+global using R3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.OnField<double>.FVector;
+
+global using C33 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.OnField<System.Numerics.Complex>.FMatrix;
+
+global using R33 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.OnField<double>.FMatrix;
+
+global using U3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.FUnitaryMatrix;
+
+global using SU3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.FSpecialUnitaryMatrix;
+
+global using LieU3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.FLieUnitaryMatrix;
+
+global using LieSU3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.FSpecialLieUnitaryMatrix;
+
+global using C3Space = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.OnField<System.Numerics.Complex>.FVectorSpace;
+
+global using R3Space = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.OnField<double>.FVectorSpace;
+
+global using DiagR3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.OnField<double>.FDiagonalMatrix;
+
+global using H3 = Skeleton.Algebra.CategoryOf<Skeleton.Algebra.DimensionProviders.IDim3>.FHermitianMatrix;