M2

src/Algebra/ScalarFieldStructure/ComplexFieldStructure.cs

@@ -0,0 +1,121 @@
+using System.Numerics;
+
+namespace Skeleton.Algebra.ScalarFieldStructure;
+
+/// <inheritdoc />
+public class ComplexFieldStructure : FieldStructure<Complex>
+{
+    /// <summary>
+    /// 
+    /// </summary>
+    public static readonly ComplexFieldStructure Structure = new();
+
+    /// <inheritdoc />
+    public override Complex Addition(Complex self, Complex other) => self + other;
+
+    /// <inheritdoc />
+    public override Complex AdditionUnit => 0d;
+
+    /// <inheritdoc />
+    public override Complex Multiplication(Complex self, Complex other) => self * other;
+
+    /// <inheritdoc />
+    public override Complex MultiplicationUnit => 1d;
+
+    /// <inheritdoc />
+    public override Complex AdditionInverse(Complex self) => -self;
+
+    /// <inheritdoc />
+    public override Complex MultiplicationInverse(Complex self) => 1d / self;
+
+    /// <inheritdoc />
+    public override Complex Subtraction(Complex self, Complex other) => self - other;
+
+    /// <inheritdoc />
+    public override Complex Division(Complex self, Complex other) => self / other;
+
+    /// <inheritdoc />
+    public override bool IsEqualApprox(Complex self, Complex other, double? absTol = null, double? relTol = null)
+
+        => RealFieldStructure.Structure.IsEqualApprox(self.Real, other.Real, absTol, relTol) &&
+           RealFieldStructure.Structure.IsEqualApprox(self.Imaginary, other.Imaginary, absTol, relTol);
+
+    /// <inheritdoc />
+    public override Complex Fix(Complex x)
+        => base.Fix(new Complex(
+            RealFieldStructure.Structure.Fix(x.Real),
+            RealFieldStructure.Structure.Fix(x.Imaginary)
+        ));
+
+    /// <inheritdoc />
+    public override Complex Conj(Complex self) => Complex.Conjugate(self);
+
+    /// <inheritdoc />
+    public override double AsReal(Complex x) => x.Real;
+
+    /// <inheritdoc />
+    public override Complex FromReal(double x) => x;
+
+    private const string PlusSign = "+";
+    private const string EmptyString = "";
+
+    /// <inheritdoc />
+    public override string RawRepresentation(Complex x)
+        => RealFieldStructure.Structure.IsEqualApprox(x.Imaginary, 0d)
+            ? RealFieldStructure.Structure.Representation(x.Real)
+            : $"{x.Real}{(x.Imaginary > 0 ? PlusSign : EmptyString)}{x.Imaginary}i";
+
+    /// <inheritdoc />
+    public override string RawPythonRepresentation(Complex x)
+        => RealFieldStructure.Structure.IsEqualApprox(x.Imaginary, 0d)
+            ? RealFieldStructure.Structure.Representation(x.Real)
+            : $"{x.Real}{(x.Imaginary > 0 ? PlusSign : EmptyString)}{x.Imaginary}j";
+
+    /// <inheritdoc />
+    public override string RawCSharpRepresentation(Complex x)
+        => RealFieldStructure.Structure.IsEqualApprox(x.Imaginary, 0d)
+            ? RealFieldStructure.Structure.Representation(x.Real)
+            : $"{x.Real}{(x.Imaginary >= 0 ? PlusSign : EmptyString)}{x.Imaginary}*AlgebraConstant.I";
+
+    /// <inheritdoc />
+    public override string DumpString(Complex x)
+        => "<C>" +
+           RealFieldStructure.Structure.DumpString(x.Real) +
+           "<CSPLIT/>" +
+           RealFieldStructure.Structure.DumpString(x.Imaginary) +
+           "</C>";
+
+    /// <inheritdoc />
+    public override Complex Resolve(string dumpString)
+    {
+        double[] restored = dumpString
+            .Replace("<C>", "")
+            .Replace("</C>", "")
+            .Split("<CSPLIT/>")
+            .Select(x => RealFieldStructure.Structure.Resolve(x))
+            .ToArray();
+        return new Complex(restored[0], restored[1]);
+    }
+
+    /// <inheritdoc />
+    public override double MaxError(Complex a) 
+        => Math.Max(Math.Abs(a.Real), Math.Abs(a.Imaginary));
+
+    /// <inheritdoc />
+    public override Complex ComplexCast(Complex a) => a;
+
+    /// <inheritdoc />
+    public override Complex RealMul(Complex a, double b) => a * b;
+
+    /// <inheritdoc />
+    public override Complex SquareRoot(Complex a) => Complex.Sqrt(a);
+
+    /// <inheritdoc />
+    public override Complex FromComplex(Complex a) => a;
+
+    /// <inheritdoc />
+    public override Complex Log(Complex x) => Complex.Log(x);
+
+    /// <inheritdoc />
+    public override Complex Exp(Complex x) => Complex.Exp(x);
+}