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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::natural_polynomial::NaturalPolynomial;
use malachite_base::polynomial::{ExponentGcd, slice_exponent_gcd};
impl ExponentGcd for NaturalPolynomial {
/// Computes the greatest common divisor of the exponents at which a [`NaturalPolynomial`] has
/// nonzero coefficients.
///
/// $$
/// f(p) = \gcd \\{i : p_i \neq 0\\}.
/// $$
///
/// When the polynomial is not constant, this is the largest $k$ such that $p(x) = q(x^k)$ for
/// some polynomial $q$, and
/// [`compose_power_of_x`](malachite_base::polynomial::ComposePowerOfX::compose_power_of_x) with
/// $k$ recovers $p$ from $q$. A constant polynomial, including zero, gives 0.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::ExponentGcd;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// NaturalPolynomial::from_str("x^6+2*x^3+1")
/// .unwrap()
/// .exponent_gcd(),
/// 3
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("x^4+x").unwrap().exponent_gcd(),
/// 1
/// );
/// assert_eq!(
/// NaturalPolynomial::from_str("x^4").unwrap().exponent_gcd(),
/// 4
/// );
/// assert_eq!(NaturalPolynomial::from_str("5").unwrap().exponent_gcd(), 0);
/// assert_eq!(NaturalPolynomial::ZERO.exponent_gcd(), 0);
/// ```
///
/// This is equivalent to `fmpz_poly_deflation` from `fmpz_poly/deflation.c`, FLINT 3.6.0,
/// except that a constant gives 0 rather than 1.
#[inline]
fn exponent_gcd(&self) -> u64 {
slice_exponent_gcd(&self.coefficients, |c| *c == 0u32)
}
}