SymSharp/AddOperator.cs at main · GreatCoder1000/SymSharp · GitHub

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namespace SymSharp;

/// <summary>
/// Represents the binary addition operator between two expressions.
/// </summary>
public class AddOperator : IBinaryOperator
{
    /// <summary>
    /// The left operand.
    /// </summary>
    private readonly IMathExpression left;

    /// <summary>
    /// The right operand.
    /// </summary>
    private readonly IMathExpression right;

    /// <summary>
    /// Gets the left operand.
    /// </summary>
    public IMathExpression Left => left;

    /// <summary>
    /// Gets the right operand.
    /// </summary>
    public IMathExpression Right => right;

    /// <summary>
    /// Constructs an addition operator with the specified operands.
    /// </summary>
    /// <param name="left">Left operand.</param>
    /// <param name="right">Right operand.</param>
    public AddOperator(IMathExpression left, IMathExpression right)
    {
        this.left = left;
        this.right = right;
    }

    /// <summary>
    /// Returns a textual representation of the addition.
    /// </summary>
    public override string ToString()
    {
        return $"({Left} + {Right})";
    }

    /// <summary>
    /// Simplifies the addition expression by applying algebraic and constant-folding rules.
    /// </summary>
    public IMathExpression Simplified()
    {
        IMathExpression simplifiedLeft = Left.Simplified();
        IMathExpression simplifiedRight = Right.Simplified();

        // Case: both scalars → collapse into one scalar
        if (simplifiedLeft is Scalar leftScalar && simplifiedRight is Scalar rightScalar)
        {
            return new Scalar(leftScalar.ToDouble() + rightScalar.ToDouble());
        }

        // Case: x + 0 → x
        if (simplifiedRight is Scalar zeroRight && zeroRight.ToDouble() == 0.0)
        {
            return simplifiedLeft;
        }
        if (simplifiedLeft is Scalar zeroLeft && zeroLeft.ToDouble() == 0.0)
        {
            return simplifiedRight;
        }

        // Case: x + x → 2 * x
        if (simplifiedLeft.ToString() == simplifiedRight.ToString())
        {
            return new MultiplyOperator(new Scalar(2), simplifiedLeft).Simplified();
        }

        // Case: (a * x) + (b * x) → (a+b) * x
        if (simplifiedLeft is MultiplyOperator ml && simplifiedRight is MultiplyOperator mr)
        {
            if (ml.Left is Scalar sl && mr.Left is Scalar sr &&
                ml.Right.ToString() == mr.Right.ToString())
            {
                return new MultiplyOperator(new Scalar(sl.ToDouble() + sr.ToDouble()), ml.Right).Simplified();
            }
            if (ml.Right is Scalar slr && mr.Right is Scalar srr &&
                ml.Left.ToString() == mr.Left.ToString())
            {
                return new MultiplyOperator(new Scalar(slr.ToDouble() + srr.ToDouble()), ml.Left).Simplified();
            }
        }

        // Case: (a * x) + x → (a+1) * x
        if (simplifiedLeft is MultiplyOperator ml2 && simplifiedRight is Variable vr &&
            ml2.Right.ToString() == vr.ToString() && ml2.Left is Scalar sl2)
        {
            return new MultiplyOperator(new Scalar(sl2.ToDouble() + 1), vr).Simplified();
        }
        if (simplifiedRight is MultiplyOperator mr2 && simplifiedLeft is Variable vl &&
            mr2.Right.ToString() == vl.ToString() && mr2.Left is Scalar sr2)
        {
            return new MultiplyOperator(new Scalar(sr2.ToDouble() + 1), vl).Simplified();
        }

        // Case: reorder Scalar + Variable → Variable + Scalar
        if (simplifiedLeft is Scalar && simplifiedRight is Variable)
        {
            return new AddOperator(simplifiedRight, simplifiedLeft);
        }

        // Default: keep as is
        return new AddOperator(simplifiedLeft, simplifiedRight);
    }

    /// <summary>
    /// The derivative of a sum is the sum of derivatives.
    /// </summary>
    /// <param name="varname">The variable name to differentiate with respect to.</param>
    public IMathExpression Derivative(string varname)
    {
        return new AddOperator(Left.Derivative(varname), Right.Derivative(varname)).Simplified();
    }
}