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‎CSharpClassLibrary/Algebra/AntimatroidModified/D8/D8Symmetry.cs

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namespace CSharpClassLibrary.Algebra.One.D8
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.D8
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{
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public enum D8Symmetry { Rot000, Rot090, Rot180, Rot270, RefVer, RefDes, RefHoz, RefAsc }
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/D8/D8SymmetryGroup.cs

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namespace CSharpClassLibrary.Algebra.One.D8
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.D8
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{
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public class D8SymmetryGroup : D8SymmetryMonoid, IGroup<D8Symmetry>

‎CSharpClassLibrary/Algebra/AntimatroidModified/D8/D8SymmetryGroupoid.cs

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namespace CSharpClassLibrary.Algebra.One.D8
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.D8
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{
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public class D8SymmetryGroupoid : IGroupoid<D8Symmetry>

‎CSharpClassLibrary/Algebra/AntimatroidModified/D8/D8SymmetryMonoid.cs

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namespace CSharpClassLibrary.Algebra.One.D8
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.D8
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{
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public class D8SymmetryMonoid : D8SymmetryGroupoid,IMonoid<D8Symmetry>

‎CSharpClassLibrary/Algebra/AntimatroidModified/D8/D8SymmetrySemigroup.cs

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namespace CSharpClassLibrary.Algebra.One.D8
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.D8
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{
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public class D8SymmetrySemigroup : D8SymmetryGroupoid, ISemigroup<D8Symmetry>
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{

‎CSharpClassLibrary/Algebra/AntimatroidModified/IAbelianGroup.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IAbelianGroup<T> : IGroup<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IDivisionRing.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IDivisionRing<T, A, M> : IRingWithUnity<T, A, M>
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where A : IGroup<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IField.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IField<T, A, M> : IDivisionRing<T, A, M>
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where A : IAbelianGroup<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IGroup.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IGroup<T>: IMonoid<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IGroupoid.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IGroupoid<T>
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{

‎CSharpClassLibrary/Algebra/AntimatroidModified/IModule.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IModule<
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TScalar,

‎CSharpClassLibrary/Algebra/AntimatroidModified/IMonoid.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IMonoid<T>: ISemigroup<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IRing.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IRing<T, A, M> : ISemiring<T, A, M>
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where A : IGroup<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IRingWithUnity.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IRingWithUnity<T, A, M> : IRing<T, A, M>
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where A : IGroup<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IRingoid.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IRingoid<T, A, M>

‎CSharpClassLibrary/Algebra/AntimatroidModified/ISemigroup.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface ISemigroup<T> : IGroupoid<T>
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{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ISemiring.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface ISemiring<T, A, M> : IRingoid<T, A, M>
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where A : IMonoid<T>

‎CSharpClassLibrary/Algebra/AntimatroidModified/IUnitaryModule.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IUnitaryModule<
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TScalar,

‎CSharpClassLibrary/Algebra/AntimatroidModified/IVectorSpace.cs

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namespace CSharpClassLibrary.Algebra.One
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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public interface IVectorSpace<
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TScalar,

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/AdditiveRealAbelianGroup.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class AdditiveRealAbelianGroup : AdditiveRealGroup, IAbelianGroup<double>
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{
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/AdditiveRealGroup.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class AdditiveRealGroup : AdditiverRealMonoid, IGroup<double>
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{
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public double Inverse(double a) => -a;
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/AdditiveRealGroupoid.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class AdditiveRealGroupoid : IGroupoid<double>
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{
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public double Operation(double a, double b) => a + b;
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/AdditiveRealSemigroup.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class AdditiveRealSemigroup : AdditiveRealGroupoid, ISemigroup<double>
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{
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/AdditiverRealMonoid.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class AdditiverRealMonoid : AdditiveRealSemigroup, IMonoid<double>
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{
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public double Identity => 0L;
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/MultiplicativeRealGroupoid.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class MultiplicativeRealGroupoid : IGroupoid<double>
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{
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public double Operation(double a, double b) => a * b;
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/MultiplicativeRealMonoid.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class MultiplicativeRealMonoid : MultiplicativeRealSemigroup, IMonoid<double>
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{
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public double Identity => 1.0;
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/MultiplicativeRealSemigroup.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class MultiplicativeRealSemigroup : MultiplicativeRealGroupoid, ISemigroup<double>
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{
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/RealRing.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class RealRing : RealSemiring, IRing<double, AdditiveRealGroup, MultiplicativeRealMonoid>
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{
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public new AdditiveRealGroup Addition { get; init; }
6+
7+
public RealRing()
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{
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Addition = new();
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}
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/RealRingoid.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class RealRingoid : IRingoid<double, AdditiveRealGroupoid, MultiplicativeRealGroupoid>
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{
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public AdditiveRealGroupoid Addition { get; init; }
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public MultiplicativeRealGroupoid Multiplication { get; init; }
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8+
public RealRingoid()
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{
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Addition = new();
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Multiplication = new();
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}
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public double Distribute(double a, double b) => Multiplication.Operation(a, b);
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/RealSemiring.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class RealSemiring : RealRingoid, ISemiring<double, AdditiverRealMonoid, MultiplicativeRealMonoid>
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{
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public new AdditiverRealMonoid Addition { get; init; }
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public new MultiplicativeRealMonoid Multiplication { get; init; }
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public RealSemiring()
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{
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Addition = new();
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Multiplication = new();
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}
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/RealVectorModule.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class RealVectorModule : IModule<double,
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Vector<double>,
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RealRing,
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AdditiveRealGroup,
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MultiplicativeRealMonoid,
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VectorAbelianGroup<double>>
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{
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public RealRing Scalar
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{
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get;
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private set;
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}
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16+
public VectorAbelianGroup<double> Vector
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{
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get;
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private set;
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}
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public RealVectorModule()
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{
24+
Scalar = new RealRing();
25+
Vector = new VectorAbelianGroup<double>(/*new AdditiveRealAbelianGroup()*/);
26+
}
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28+
public Vector<double> Distribute(double t, Vector<double> r)
29+
{
30+
Vector<double> c = new Vector<double>();
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for (int i = 0; i < c.Dimension; i++)
32+
c[i] = Scalar.Multiplication.Operation(t, r[i]);
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return c;
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}
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/RealNumber/VectorAbelianGroup.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified.RealNumber
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{
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public class VectorAbelianGroup<T> : IAbelianGroup<Vector<T>>
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{
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//public IAbelianGroup<T> AbelianGroup { get; init; }
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////public VectorAbelianGroup(IAbelianGroup<T> abelianGroup)
7+
////{
8+
//// AbelianGroup = abelianGroup;
9+
////}
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11+
public Vector<T> Identity => throw new System.NotImplementedException();
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13+
public Vector<T> Inverse(Vector<T> t)
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{
15+
throw new System.NotImplementedException();
16+
}
17+
18+
public Vector<T> Operation(Vector<T> a, Vector<T> b)
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{
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throw new System.NotImplementedException();
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}
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/String/StringGroupoid.cs

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namespace CSharpClassLibrary.Algebra.One.String
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.String
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{
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public record StringGroupoid : IGroupoid<string>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/String/StringMonoid.cs

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namespace CSharpClassLibrary.Algebra.One.String
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.String
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{
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public record StringMonoid : StringSemigroup, IMonoid<string>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/String/StringSemigroup.cs

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namespace CSharpClassLibrary.Algebra.One.String
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.String
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{
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public record StringSemigroup : StringGroupoid, ISemigroup<string>

‎CSharpClassLibrary/Algebra/AntimatroidModified/Vector.cs

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namespace CSharpClassLibrary.Algebra.AntimatroidModified
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{
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public class Vector<T>
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{
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private T[] vector;
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public int Dimension
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{
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get { return vector.Length; }
10+
}
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12+
public T this[int n]
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{
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get { return vector[n]; }
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set { vector[n] = value; }
16+
}
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public Vector()
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{
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vector = new T[2];
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}
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}
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}

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/AdditiveIntegerAbelianGroup.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public class AdditiveIntegerAbelianGroup : AdditiveIntegerGroup, IAbelianGroup<long>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/AdditiveIntegerGroup.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public class AdditiveIntegerGroup : AdditiveIntegerMonoid, IGroup<long>
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{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/AdditiveIntegerGroupoid.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public class AdditiveIntegerGroupoid : IGroupoid<long>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/AdditiveIntegerMonoid.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public class AdditiveIntegerMonoid : AdditiveIntegerSemigroup, IMonoid<long>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/AdditiveIntegerSemigroup.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public class AdditiveIntegerSemigroup : AdditiveIntegerGroupoid, ISemigroup<long>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/IntegerRing.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public record IntegerRing : IntegerSemiring, IRing<long, AdditiveIntegerGroup, MultiplicativeIntegerMonoid>

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/IntegerRingWithUnity.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public record IntegerRingWithUnity : IntegerRing, IRingWithUnity<long, AdditiveIntegerGroup, MultiplicativeIntegerMonoid>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/IntegerRingoid.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public record IntegerRingoid : IRingoid<long, AdditiveIntegerGroupoid, MultiplicativeIntegerGroupoid>

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/IntegerSemiring.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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44
public record IntegerSemiring : IntegerRingoid, ISemiring<long, AdditiveIntegerMonoid, MultiplicativeIntegerMonoid>

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/MultiplicativeIntegerGroupoid.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public class MultiplicativeIntegerGroupoid : IGroupoid<long>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/MultiplicativeIntegerMonoid.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
33
public class MultiplicativeIntegerMonoid : MultiplicativeIntegerSemigroup, IMonoid<long>
44
{

‎CSharpClassLibrary/Algebra/AntimatroidModified/ZnZ/MultiplicativeIntegerSemigroup.cs

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namespace CSharpClassLibrary.Algebra.One.ZnZ
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namespace CSharpClassLibrary.Algebra.AntimatroidModified.ZnZ
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{
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public class MultiplicativeIntegerSemigroup : MultiplicativeIntegerGroupoid, ISemigroup<long>
44
{

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