malachite_nz/integer_polynomial/arithmetic/is_unit.rs
1// Copyright © 2026 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::integer_polynomial::IntegerPolynomial;
10use malachite_base::num::arithmetic::traits::IsUnit;
11
12impl IsUnit for IntegerPolynomial {
13 /// Determines whether an [`IntegerPolynomial`] is a unit: whether it is the constant polynomial
14 /// 1 or $-1$, the only polynomials with integer coefficients that have a multiplicative
15 /// inverse.
16 ///
17 /// # Worst-case complexity
18 /// Constant time and additional memory.
19 ///
20 /// # Examples
21 /// ```
22 /// use core::str::FromStr;
23 /// use malachite_base::num::arithmetic::traits::IsUnit;
24 /// use malachite_base::num::basic::traits::Zero;
25 /// use malachite_base::polynomial::Polynomial;
26 /// use malachite_nz::integer_polynomial::IntegerPolynomial;
27 ///
28 /// assert_eq!(IntegerPolynomial::one().is_unit(), true);
29 /// assert_eq!(IntegerPolynomial::negative_one().is_unit(), true);
30 /// assert_eq!(IntegerPolynomial::ZERO.is_unit(), false);
31 /// assert_eq!(IntegerPolynomial::two().is_unit(), false);
32 /// assert_eq!(IntegerPolynomial::x().is_unit(), false);
33 /// assert_eq!(
34 /// IntegerPolynomial::from_str("-x-1").unwrap().is_unit(),
35 /// false
36 /// );
37 /// ```
38 fn is_unit(&self) -> bool {
39 match self.coefficients.as_slice() {
40 [c] => c.is_unit(),
41 _ => false,
42 }
43 }
44}