Sqrt.cs

using System;
using System.Numerics;
using Waher.Script.Abstraction.Elements;
using Waher.Script.Model;
using Waher.Script.Objects;
using Waher.Script.Operators.Arithmetics;
 
namespace Waher.Script.Functions.Analytic
{
    public class Sqrt : FunctionOneScalarVariable, IDifferentiable
    {
        public Sqrt(ScriptNode Argument, int Start, int Length, Expression Expression)
            : base(Argument, Start, Length, Expression)
        {
        }
 
        public override string FunctionName => nameof(Sqrt);
 
        public override string[] Aliases => new string[] { "√" };
 
        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 Invert(
                        new Multiply(
                            new ConstantElement(DoubleNumber.TwoElement, Start, Len, Exp),
                            this,
                            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)
        {
            if (Argument < 0)
                return new ComplexNumber(0, Math.Sqrt(-Argument));
            else
                return new DoubleNumber(Math.Sqrt(Argument));
        }
 
        public override IElement EvaluateScalar(Complex Argument, Variables Variables)
        {
            return new ComplexNumber(Complex.Sqrt(Argument));
        }
    }
}