Inverse.cs

using System.Numerics;
using Waher.Script.Abstraction.Elements;
using Waher.Script.Functions.Analytic;
using Waher.Script.Model;
using Waher.Script.Objects;
using Waher.Script.Operators.Arithmetics;
 
namespace Waher.Script.Functions.Matrices
{
    public class Inverse : FunctionOneScalarVariable, IDifferentiable
    {
        public Inverse(ScriptNode Argument, int Start, int Length, Expression Expression)
            : base(Argument, Start, Length, Expression)
        {
        }
 
        public override string FunctionName => nameof(Inverse);
 
        public override string[] Aliases
        {
            get { return new string[] { "inv", "invert" }; }
        }
 
        public override IElement Evaluate(IElement Argument, Variables Variables)
        {
            if (Argument is IRingElement E)
            {
                E = E.Invert();
                if (!(E is null))
                    return E;
            }
 
            return base.Evaluate(Argument, Variables);
        }
 
        public ScriptNode Differentiate(string VariableName, Variables Variables)
        {
            if (VariableName == this.DefaultVariableName)
            {
                int Start = this.Start;
                int Len = this.Length;
                Expression Exp = this.Expression;
 
                return this.DifferentiationChainRule(VariableName, Variables, this.Argument,
                    new Negate(
                        new Inverse(
                            new Power(this.Argument, 
                                new ConstantElement(DoubleNumber.TwoElement, Start, Len, Exp), 
                                Start, Len, Exp), 
                            Start, Len, Exp), 
                        Start, Len, Exp));
            }
            else
                return new ConstantElement(DoubleNumber.ZeroElement, this.Start, this.Length, this.Expression);
        }
 
        public override IElement EvaluateScalar(double Argument, Variables Variables)
        {
            return new DoubleNumber(1.0 / Argument);
        }
 
        public override IElement EvaluateScalar(Complex Argument, Variables Variables)
        {
            return new ComplexNumber(Complex.Reciprocal(Argument));
        }
    }
}