Struct ShortlexIntegerPolynomial 

pub struct ShortlexIntegerPolynomial(pub IntegerPolynomial);

ShortlexIntegerPolynomial is a wrapper around an IntegerPolynomial, taking the IntegerPolynomial by value.

IntegerPolynomial is ordered by how its polynomials behave for large arguments, which is the order that respects their arithmetic. Sometimes a different order is wanted: one that puts the smaller polynomials first, whatever their signs, so that a list of them is enumerated from the simplest upward. Wrapping an IntegerPolynomial in a ShortlexIntegerPolynomial provides one: polynomials are compared first by degree and then, in case of a tie, by their coefficients from highest to lowest. This is a total order whose equality agrees with IntegerPolynomial equality; it is FLINT’s order for polynomials, the one fmpq_poly_cmp implements.

The difference from the Ord implementation on IntegerPolynomial is what happens when the degrees differ. There, a polynomial of higher degree dominates, so it is the greater one only if its leading coefficient is positive, and $-x^3 < x^2$. Here, degree decides outright, so $-x^3 > x^2$.

Neither order is a well-order. Ordering by degree first does not make one: $x > x - 1 > x - 2 > \ldots$ all have degree 1, so the chain descends forever under either order. No order that restricts to the usual order on the constant polynomials can be a well-order, since the Integers are not well-ordered.

ShortlexIntegerPolynomial owns its value. This is useful in many cases, for example if you want to use IntegerPolynomials as keys in a map. In other situations, it is better to use ShortlexIntegerPolynomialRef, which only has a reference to its value.

Tuple Fields

0: IntegerPolynomial

Implementations

impl ShortlexIntegerPolynomial

pub const fn as_ref(&self) -> ShortlexIntegerPolynomialRef<'_>

Borrows a ShortlexIntegerPolynomial as a ShortlexIntegerPolynomialRef.

Worst-case complexity

Constant time and additional memory.

Examples

use core::str::FromStr;
use malachite_nz::integer_polynomial::{
    IntegerPolynomial, ShortlexIntegerPolynomial, ShortlexIntegerPolynomialRef,
};

let p = IntegerPolynomial::from_str("x^2-3*x+2").unwrap();
let x = ShortlexIntegerPolynomial(p.clone());
assert_eq!(x.as_ref(), ShortlexIntegerPolynomialRef(&p));

Methods from Deref<Target = IntegerPolynomial>

pub fn coefficients_asc(&self) -> &[Integer]

Returns a reference to an IntegerPolynomial’s coefficients, in ascending order.

The first is the constant term and the last is the leading coefficient, so the slice is what from_coefficients_asc would take back. It holds no trailing zeros, and for the zero polynomial it is empty.

Worst-case complexity

Constant time and additional memory.

Examples

use core::str::FromStr;
use malachite_base::num::basic::traits::Zero;
use malachite_base::strings::ToDebugString;
use malachite_nz::integer_polynomial::IntegerPolynomial;

let p = IntegerPolynomial::from_str("x^2+3*x+2").unwrap();
assert_eq!(p.coefficients_asc().to_debug_string(), "[2, 3, 1]");
assert_eq!(
    IntegerPolynomial::ZERO.coefficients_asc().to_debug_string(),
    "[]"
);

Trait Implementations

impl Clone for ShortlexIntegerPolynomial

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for ShortlexIntegerPolynomial

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

Formats the value using the given formatter.

impl Default for ShortlexIntegerPolynomial

fn default() -> Self

Returns the “default value” for a type.

impl Deref for ShortlexIntegerPolynomial

fn deref(&self) -> &IntegerPolynomial

Allows a ShortlexIntegerPolynomial to dereference to an IntegerPolynomial.

use core::str::FromStr;
use malachite_nz::integer_polynomial::{IntegerPolynomial, ShortlexIntegerPolynomial};

let p = IntegerPolynomial::from_str("x^2-3*x+2").unwrap();
let x = ShortlexIntegerPolynomial(p.clone());
assert_eq!(*x, p);

type Target = IntegerPolynomial

The resulting type after dereferencing.

impl Eq for ShortlexIntegerPolynomial

impl Hash for ShortlexIntegerPolynomial

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Ord for ShortlexIntegerPolynomial

fn cmp(&self, other: &Self) -> Ordering

Compares two ShortlexIntegerPolynomials.

The order is shortlex: the polynomials are compared first by degree, and then, in case of a tie, by their coefficients from highest to lowest. See the Ord implementation for ShortlexIntegerPolynomialRef for details.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is the smaller of the two polynomials’ total number of bits, summed over their coefficients. Polynomials of different degrees are compared in constant time.

Examples

use core::str::FromStr;
use malachite_nz::integer_polynomial::{IntegerPolynomial, ShortlexIntegerPolynomial};

let x_squared = IntegerPolynomial::from_str("x^2").unwrap();
let negative_x_cubed = IntegerPolynomial::from_str("-x^3").unwrap();

// Degree decides, whatever the sign of the leading coefficient.
assert!(ShortlexIntegerPolynomial(x_squared) < ShortlexIntegerPolynomial(negative_x_cubed));

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

fn clamp_to<R>(self, range: R) -> Self

where Self: Sized, R: ClampBounds<Self>,

🔬This is a nightly-only experimental API. (clamp_to)

Restrict a value to a certain range.

impl PartialEq for ShortlexIntegerPolynomial

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl PartialOrd for ShortlexIntegerPolynomial

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

Compares two ShortlexIntegerPolynomials.

See the documentation for the Ord implementation.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl StructuralPartialEq for ShortlexIntegerPolynomial