M2

src/Analysis/AnalyticFunctions/Polynomials/Implements/C2Polynomial.cs

@@ -0,0 +1,74 @@
+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);
+    }
+}