Struct ShortlexIntegerPolynomialRef 

pub struct ShortlexIntegerPolynomialRef<'a>(pub &'a IntegerPolynomial);

ShortlexIntegerPolynomialRef is a wrapper around an IntegerPolynomial, taking the IntegerPolynomial by reference.

See the ShortlexIntegerPolynomial documentation for details.

Tuple Fields

0: &'a IntegerPolynomial

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<'a> Clone for ShortlexIntegerPolynomialRef<'a>

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<'a> Debug for ShortlexIntegerPolynomialRef<'a>

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

Formats the value using the given formatter.

impl Deref for ShortlexIntegerPolynomialRef<'_>

fn deref(&self) -> &IntegerPolynomial

Allows a ShortlexIntegerPolynomialRef to dereference to an IntegerPolynomial.

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

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

type Target = IntegerPolynomial

The resulting type after dereferencing.

impl<'a> Eq for ShortlexIntegerPolynomialRef<'a>

impl<'a> Hash for ShortlexIntegerPolynomialRef<'a>

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 ShortlexIntegerPolynomialRef<'_>

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

Compares two ShortlexIntegerPolynomialRefs.

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. The zero polynomial, having no degree at all, comes first. This is a total order, and its equality agrees with IntegerPolynomial equality. It is the order FLINT uses for polynomials, the one fmpq_poly_cmp implements.

Where the degrees differ this parts company with IntegerPolynomial’s own Ord, which compares polynomials by how they behave for large arguments and so lets a negative leading coefficient send a high-degree polynomial to the bottom. Here degree decides outright, so $-x^3 > x^2$ where the asymptotic order has $-x^3 < x^2$.

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, ShortlexIntegerPolynomialRef};

let zero = IntegerPolynomial::from_str("0").unwrap();
let x_squared = IntegerPolynomial::from_str("x^2").unwrap();
let negative_x_cubed = IntegerPolynomial::from_str("-x^3").unwrap();

// The zero polynomial comes first.
assert!(ShortlexIntegerPolynomialRef(&zero) < ShortlexIntegerPolynomialRef(&x_squared));
// Degree decides, whatever the sign of the leading coefficient.
assert!(
    ShortlexIntegerPolynomialRef(&x_squared)
        < ShortlexIntegerPolynomialRef(&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<'a> PartialEq for ShortlexIntegerPolynomialRef<'a>

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

Equality operator ==.

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

Inequality operator !=.

impl PartialOrd for ShortlexIntegerPolynomialRef<'_>

fn partial_cmp( &self, other: &ShortlexIntegerPolynomialRef<'_>, ) -> Option<Ordering>

Compares two ShortlexIntegerPolynomialRefs.

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<'a> StructuralPartialEq for ShortlexIntegerPolynomialRef<'a>