malachite_base/unsigned_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::num::arithmetic::traits::IsUnit;
10use crate::num::basic::unsigneds::PrimitiveUnsigned;
11use crate::unsigned_polynomial::UnsignedPolynomial;
12
13impl<T: PrimitiveUnsigned> IsUnit for UnsignedPolynomial<T> {
14 /// Determines whether an [`UnsignedPolynomial`] is a unit: whether it is the constant
15 /// polynomial 1, the only polynomial with non-negative integer coefficients that has a
16 /// multiplicative inverse.
17 ///
18 /// No modulus is involved, as with [`IsUnit`] for the unsigned primitive types. Modulo $n$,
19 /// every constant coprime to $n$ is also a unit, and so, when $n$ is composite, are some
20 /// polynomials of positive degree.
21 ///
22 /// # Worst-case complexity
23 /// Constant time and additional memory.
24 ///
25 /// # Examples
26 /// ```
27 /// use core::str::FromStr;
28 /// use malachite_base::num::arithmetic::traits::IsUnit;
29 /// use malachite_base::num::basic::traits::Zero;
30 /// use malachite_base::polynomial::Polynomial;
31 /// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
32 ///
33 /// assert_eq!(UnsignedPolynomial::<u64>::one().is_unit(), true);
34 /// assert_eq!(UnsignedPolynomial::<u64>::ZERO.is_unit(), false);
35 /// assert_eq!(UnsignedPolynomial::<u64>::two().is_unit(), false);
36 /// assert_eq!(UnsignedPolynomial::<u8>::x().is_unit(), false);
37 /// assert_eq!(
38 /// UnsignedPolynomial::<u8>::from_str("x+1").unwrap().is_unit(),
39 /// false
40 /// );
41 /// ```
42 #[inline]
43 fn is_unit(&self) -> bool {
44 *self == T::ONE
45 }
46}