Struct PolynomialProperties 

pub struct PolynomialProperties {
    pub family: PolynomialFamily,
    pub recurrence: ThreeTermRecurrence,
    pub orthogonality: Option<OrthogonalityData>,
    pub rodrigues_formula: Option<RodriguesFormula>,
    pub generating_function: Option<GeneratingFunction>,
    pub special_values: Vec<SpecialValue>,
    pub evaluation_method: EvaluationMethod,
    pub symbolic_expander: Option<SymbolicExpander>,
    pub antiderivative_rule: AntiderivativeRule,
    pub wolfram_name: Option<&'static str>,
}

Polynomial function properties (legendre, hermite, laguerre, etc.)

Comprehensive properties for orthogonal polynomials and polynomial families with focus on computational efficiency and mathematical correctness.

Note: Evaluation is handled by direct dispatch through Expression::evaluate_function_dispatch() for performance. This struct stores only mathematical properties, not evaluation logic.

Fields

family: PolynomialFamily

Polynomial family classification

recurrence: ThreeTermRecurrence

Three-term recurrence relation Examples: P_{n+1} = ((2n+1)x P_n - n P_{n-1})/(n+1)

orthogonality: Option<OrthogonalityData>

Orthogonality properties (if applicable)

rodrigues_formula: Option<RodriguesFormula>

Rodrigues’ formula (if available) Examples: P_n(x) = (1/2^n n!) d^n/dx^n (x²-1)^n

generating_function: Option<GeneratingFunction>

Generating function Examples: 1/√(1-2xt+t²) = Σ P_n(x) t^n

special_values: Vec<SpecialValue>

Special values and boundary conditions

evaluation_method: EvaluationMethod

Computational method for evaluation

symbolic_expander: Option<SymbolicExpander>

Symbolic expansion method for intelligence-driven computation

Converts polynomial from recurrence-based representation to explicit symbolic expression. This enables algebraic manipulation and simplification of polynomial expressions in the Expression system.

antiderivative_rule: AntiderivativeRule

Antiderivative rule (for polynomial integration) All polynomials are integrable, so this is always Some(…)

wolfram_name: Option<&'static str>

Wolfram Language function name Used for Wolfram formatting without hardcoded matches Example: “legendre_p” → “LegendreP”, “hermite_h” → “HermiteH”

Trait Implementations

impl Clone for PolynomialProperties

fn clone(&self) -> PolynomialProperties

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for PolynomialProperties

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.