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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::num::arithmetic::traits::IsUnit;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::unsigned_polynomial::UnsignedPolynomial;
impl<T: PrimitiveUnsigned> IsUnit for UnsignedPolynomial<T> {
/// Determines whether an [`UnsignedPolynomial`] is a unit: whether it is the constant
/// polynomial 1, the only polynomial with non-negative integer coefficients that has a
/// multiplicative inverse.
///
/// No modulus is involved, as with [`IsUnit`] for the unsigned primitive types. Modulo $n$,
/// every constant coprime to $n$ is also a unit, and so, when $n$ is composite, are some
/// polynomials of positive degree.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::IsUnit;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::Polynomial;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// assert_eq!(UnsignedPolynomial::<u64>::one().is_unit(), true);
/// assert_eq!(UnsignedPolynomial::<u64>::ZERO.is_unit(), false);
/// assert_eq!(UnsignedPolynomial::<u64>::two().is_unit(), false);
/// assert_eq!(UnsignedPolynomial::<u8>::x().is_unit(), false);
/// assert_eq!(
/// UnsignedPolynomial::<u8>::from_str("x+1").unwrap().is_unit(),
/// false
/// );
/// ```
#[inline]
fn is_unit(&self) -> bool {
*self == T::ONE
}
}