math

    Run mathematical operations (unified Mathematica-style tool)

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    SymKit's core tool — supports ~25 mathematical operations.
    One tool handles derivation, calculation, solving, and transformation.
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    **Supported operations (operation):**

    | Category | Operation | Description |
    |------|------|------|
    | Parse | `parse` | Parse expression and extract symbols |
    | Simplify | `simplify` | General simplification |
    | | `expand` | Expand polynomial |
    | | `factor` | Factorization |
    | | `collect` | Collect like terms (requires variable) |
    | | `cancel` | Cancel rational function |
    | | `apart` | Partial fraction expansion (requires variable) |
    | | `together` | Combine over common denominator |
    | | `trigsimp` | Trigonometric simplification |
    | | `powsimp` | Power simplification |
    | | `radsimp` | Radical simplification |
    | | `combsimp` | Combinatorial simplification |
    | Solve | `solve` | Solve for variable (requires variable) |
    | Substitute | `substitute` | Substitute variables (requires substitution dict) |
    | Calculus | `diff` | Differentiate (requires variable; order optional) |
    | | `integrate` | Integrate (variable, lower/upper optional) |
    | | `limit` | Limit (variable, point, direction) |
    | | `series` | Series expansion (variable, point, order) |
    | ODE | `dsolve` | Solve ODE (variable=function name, with_respect_to=independent variable) |
    | Vector | `gradient` | Gradient (variable="x,y,z" comma-separated coordinates) |
    | | `divergence` | Divergence |
    | | `curl` | Curl |
    | | `laplacian` | Laplacian |
    | Matrix | `det` | Determinant |
    | | `inv` | Inverse matrix |
    | | `eigenvals` | Eigenvalues |
    | | `eigenvects` | Eigenvectors |
    | Transform | `laplace` | Laplace transform (variable=time, with_respect_to=s) |
    | | `ilaplace` | Inverse Laplace transform (variable=s, with_respect_to=t) |
    | | `fourier` | Fourier transform |
    | | `ifourier` | Inverse Fourier transform |

    Args:
        operation: Operation name (see table above)
        expression: Mathematical expression (SymPy or LaTeX format)
        variable: Differentiation/integration/solving variable (for vector operations can be comma-separated like "x,y,z")
        with_respect_to: Second variable (independent variable for ODE, target variable for transforms)
        substitution: Substitution mapping {"var": "replacement", ...}
        point: Limit point / series expansion point (default "0")
        direction: Limit direction "+-", "+", "-"
        order: Differentiation order / number of series terms (default 1)
        lower: Definite integral lower bound
        upper: Definite integral upper bound
        assumptions: Symbolic assumptions ["x is positive", "t is real"]
        method: Simplification method "auto", "trig", "radical", "expand_then_simplify"
        session: True=record to derivation session, False=stateless computation
        description: Description of this step (used when recording to session)
        notes: Human insight (used when recording to session)

    Returns:
        Result dict containing expression, latex, operation

    Examples:
        # Stateless quick calculation
        math("diff", "x**3", variable="x")
        → {"expression": "3*x**2", "latex": "3 x^{2}"}

        # Substitute
        math("substitute", "m*a", substitution={"m": "2", "a": "9.8"})
        → {"expression": "19.6", ...}

        # Laplace transform
        math("laplace", "exp(-k*t)", variable="t", with_respect_to="s")
        → {"expression": "1/(k + s)", ...}

        # Vector calculus
        math("gradient", "x**2 + y**2 + z**2", variable="x,y,z")
        → gradient in vector form

        # Solve ODE
        math("dsolve", "diff(y,t) - k*y", variable="y", with_respect_to="t")