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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::gaussian_rational::GaussianRational;
use malachite_base::num::arithmetic::traits::IsUnit;
impl IsUnit for GaussianRational {
/// Determines whether a [`GaussianRational`] is a unit: nonzero. $\mathbb{Q}(i)$ is a field, so
/// every nonzero element has a multiplicative inverse and the only non-unit is zero. This
/// differs from the four units of $\mathbb{Z}\[i\]$, which are the only
/// [`GaussianInteger`](malachite_nz::gaussian_integer::GaussianInteger) units.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::IsUnit;
/// use malachite_base::num::basic::traits::{I, NegativeI, NegativeOne, One, Zero};
/// use malachite_q::gaussian_rational::GaussianRational;
/// use std::str::FromStr;
///
/// assert_eq!(GaussianRational::ONE.is_unit(), true);
/// assert_eq!(GaussianRational::NEGATIVE_ONE.is_unit(), true);
/// assert_eq!(GaussianRational::I.is_unit(), true);
/// assert_eq!(GaussianRational::NEGATIVE_I.is_unit(), true);
/// assert_eq!(GaussianRational::from_str("1/2+i").unwrap().is_unit(), true);
/// assert_eq!(GaussianRational::ZERO.is_unit(), false);
/// ```
fn is_unit(&self) -> bool {
self.real != 0u32 || self.imaginary != 0u32
}
}