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PolynomialGcd

mathhook::prelude

Trait PolynomialGcd 

Source 
pub trait PolynomialGcd {
    // Required methods
    fn gcd(&self, other: &Self) -> Self;
    fn lcm(&self, other: &Self) -> Self;
    fn factor_gcd(&self) -> Self;
    fn cofactors(&self, other: &Self) -> (Expression, Expression, Expression);
    fn div_polynomial(
        &self,
        divisor: &Expression,
        var: &Symbol,
    ) -> (Expression, Expression);
    fn quo_polynomial(&self, divisor: &Expression, var: &Symbol) -> Expression;
    fn rem_polynomial(&self, divisor: &Expression, var: &Symbol) -> Expression;
}
Expand description

Trait for GCD operations on expressions

Required Methods§

Source

fn gcd(&self, other: &Self) -> Self

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fn lcm(&self, other: &Self) -> Self

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fn factor_gcd(&self) -> Self

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fn cofactors(&self, other: &Self) -> (Expression, Expression, Expression)

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

Divides this polynomial by another, returning (quotient, remainder).

Performs polynomial long division with respect to the specified variable. Returns a tuple (quotient, remainder) satisfying the division identity: dividend = divisor * quotient + remainder where degree(remainder) < degree(divisor).

§Arguments
  • divisor - The polynomial to divide by (must be non-zero)
  • var - The variable to treat as the polynomial variable
§Examples
use mathhook_core::{symbol, expr, Expression, algebra::gcd::PolynomialGcd};

let x = symbol!(x);
// Divide (x^2 + 3x + 2) by (x + 1)
// Expected: (x + 1)(x + 2) = x^2 + 3x + 2
let dividend = expr!((x^2) + (3*x) + 2);
let divisor = expr!(x + 1);
let (quotient, remainder) = dividend.div_polynomial(&divisor, &x);
assert_eq!(remainder, Expression::integer(0));
§Returns

Returns (quotient, remainder) tuple where both are expressions

Source

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

Returns the quotient of polynomial division.

Computes only the quotient part of polynomial division, discarding the remainder. Equivalent to div_polynomial(divisor, var).0.

§Arguments
  • divisor - The polynomial to divide by
  • var - The variable to treat as the polynomial variable
§Examples
use mathhook_core::{symbol, expr, algebra::gcd::PolynomialGcd};

let x = symbol!(x);
let dividend = expr!((x^2) - 1);
let divisor = expr!(x - 1);
let quotient = dividend.quo_polynomial(&divisor, &x);
// quotient = x + 1
§Returns

Returns the quotient expression

Source

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

Returns the remainder of polynomial division.

Computes only the remainder part of polynomial division, discarding the quotient. Equivalent to div_polynomial(divisor, var).1.

§Arguments
  • divisor - The polynomial to divide by
  • var - The variable to treat as the polynomial variable
§Examples
use mathhook_core::{symbol, expr, Expression, algebra::gcd::PolynomialGcd};

let x = symbol!(x);
let dividend = expr!((x^2) + 1);
let divisor = expr!(x - 1);
let remainder = dividend.rem_polynomial(&divisor, &x);
assert_eq!(remainder, Expression::integer(2));
§Returns

Returns the remainder expression

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementors§