Trait PolynomialProperties 

pub trait PolynomialProperties: PolynomialClassification {
    // Required methods
    fn degree(&self, var: &Symbol) -> Option<i64>;
    fn total_degree(&self) -> Option<i64>;
    fn leading_coefficient(&self, var: &Symbol) -> Expression;
    fn content(&self) -> Expression;
    fn primitive_part(&self) -> Expression;
}

Trait for polynomial properties

Provides methods for computing polynomial properties such as degree, leading coefficient, content, and primitive part. Results are cached using thread-local LRU caching for performance.

Examples

use mathhook_core::core::polynomial::{PolynomialClassification, PolynomialProperties};
use mathhook_core::{expr, symbol};

let x = symbol!(x);
let poly = expr!(x ^ 3);

assert_eq!(poly.degree(&x), Some(3));

Required Methods

fn degree(&self, var: &Symbol) -> Option<i64>

Compute degree with respect to a variable

Returns the highest power of the variable in the polynomial.

Arguments

• var - The variable to compute degree for

Returns

Some(degree) if the expression is a polynomial in the variable, None if not a polynomial.

Examples

use mathhook_core::core::polynomial::PolynomialProperties;
use mathhook_core::{expr, symbol};

let x = symbol!(x);

assert_eq!(expr!(x ^ 3).degree(&x), Some(3));
assert_eq!(expr!(5).degree(&x), Some(0));

fn total_degree(&self) -> Option<i64>

Compute total degree (sum of degrees in all variables)

For multivariate polynomials, returns the maximum sum of exponents across all terms.

Examples

use mathhook_core::core::polynomial::PolynomialProperties;
use mathhook_core::{expr, symbol};

let x = symbol!(x);
let y = symbol!(y);
let poly = expr!(x * y);  // x*y has total degree 2

assert_eq!(poly.total_degree(), Some(2));

fn leading_coefficient(&self, var: &Symbol) -> Expression

Get leading coefficient with respect to a variable

Returns the coefficient of the highest degree term.

Arguments

• var - The variable to find leading coefficient for

Examples

use mathhook_core::core::polynomial::PolynomialProperties;
use mathhook_core::{expr, symbol};

let x = symbol!(x);
let poly = expr!((5 * (x ^ 2)) + (3 * x) + 1);

// Leading coefficient of 5x^2 + 3x + 1 is 5
let lc = poly.leading_coefficient(&x);

fn content(&self) -> Expression

Extract content (GCD of all coefficients)

The content is the GCD of all numeric coefficients in the polynomial.

Examples

use mathhook_core::core::polynomial::PolynomialProperties;
use mathhook_core::{expr, symbol};

let x = symbol!(x);
let poly = expr!((6 * (x ^ 2)) + (9 * x) + 3);

// Content of 6x^2 + 9x + 3 is 3
let content = poly.content();

fn primitive_part(&self) -> Expression

Extract primitive part (polynomial divided by content)

The primitive part is the polynomial with content factored out.

Examples

use mathhook_core::core::polynomial::PolynomialProperties;
use mathhook_core::{expr, symbol};

let x = symbol!(x);
let poly = expr!((6 * (x ^ 2)) + (9 * x) + 3);

// Primitive part of 6x^2 + 9x + 3 is 2x^2 + 3x + 1
let pp = poly.primitive_part();

Implementors

impl PolynomialProperties for Expression