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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::integer_polynomial::IntegerPolynomial;
use crate::natural::Natural;
use crate::natural_polynomial::NaturalPolynomial;
use alloc::vec::Vec;
use malachite_base::num::arithmetic::traits::BalancedMod;
use malachite_base::polynomial::Polynomial;
impl BalancedMod<Natural> for NaturalPolynomial {
type Output = IntegerPolynomial;
/// Reduces every coefficient of a [`NaturalPolynomial`] modulo a [`Natural`] to the
/// representative closest to zero, returning an [`IntegerPolynomial`], taking the polynomial by
/// value and the modulus by value.
///
/// Each coefficient $r_i$ of the result satisfies $-m/2 < r_i \leq m/2$ and $r_i \equiv p_i
/// \bmod m$, which determine it uniquely, as with [`BalancedMod`] for [`Natural`]s. A remainder
/// of exactly $m/2$ is positive. Remainders above $m/2$ become negative, which is why the
/// result is an [`IntegerPolynomial`].
///
/// Reducing can lower the degree, and can even give the zero polynomial: a leading coefficient
/// that is a multiple of $m$ becomes zero, and a polynomial does not hold trailing zero
/// coefficients. So $10x^2 + 7x + 5$ modulo $10$ is $-3x + 5$.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// polynomial's coefficients.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// // Each coefficient goes to the representative closest to zero.
/// let p = NaturalPolynomial::from_str("x^2+27*x+23").unwrap();
/// assert_eq!(
/// p.clone().balanced_mod(Natural::from(10u32)).to_string(),
/// "x^2-3*x+3"
/// );
///
/// // Half the modulus stays positive, and reducing the leading coefficient to zero lowers the
/// // degree.
/// let p = NaturalPolynomial::from_str("10*x^2+7*x+5").unwrap();
/// assert_eq!(
/// p.clone().balanced_mod(Natural::from(10u32)).to_string(),
/// "-3*x+5"
/// );
/// ```
#[inline]
fn balanced_mod(self, m: Natural) -> IntegerPolynomial {
(&self).balanced_mod(m)
}
}
impl<'a> BalancedMod<&'a Natural> for NaturalPolynomial {
type Output = IntegerPolynomial;
/// Reduces every coefficient of a [`NaturalPolynomial`] modulo a [`Natural`] to the
/// representative closest to zero, returning an [`IntegerPolynomial`], taking the polynomial by
/// value and the modulus by reference.
///
/// See the documentation for the [`BalancedMod`] implementation on [`NaturalPolynomial`] that
/// takes both arguments by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// polynomial's coefficients.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// // Each coefficient goes to the representative closest to zero.
/// let p = NaturalPolynomial::from_str("x^2+27*x+23").unwrap();
/// assert_eq!(
/// p.clone().balanced_mod(&Natural::from(10u32)).to_string(),
/// "x^2-3*x+3"
/// );
///
/// // Half the modulus stays positive, and reducing the leading coefficient to zero lowers the
/// // degree.
/// let p = NaturalPolynomial::from_str("10*x^2+7*x+5").unwrap();
/// assert_eq!(
/// p.clone().balanced_mod(&Natural::from(10u32)).to_string(),
/// "-3*x+5"
/// );
/// ```
#[inline]
fn balanced_mod(self, m: &'a Natural) -> IntegerPolynomial {
(&self).balanced_mod(m)
}
}
impl BalancedMod<Natural> for &NaturalPolynomial {
type Output = IntegerPolynomial;
/// Reduces every coefficient of a [`NaturalPolynomial`] modulo a [`Natural`] to the
/// representative closest to zero, returning an [`IntegerPolynomial`], taking the polynomial by
/// reference and the modulus by value.
///
/// See the documentation for the [`BalancedMod`] implementation on [`NaturalPolynomial`] that
/// takes both arguments by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// polynomial's coefficients.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// // Each coefficient goes to the representative closest to zero.
/// let p = NaturalPolynomial::from_str("x^2+27*x+23").unwrap();
/// assert_eq!(
/// (&p).balanced_mod(Natural::from(10u32)).to_string(),
/// "x^2-3*x+3"
/// );
///
/// // Half the modulus stays positive, and reducing the leading coefficient to zero lowers the
/// // degree.
/// let p = NaturalPolynomial::from_str("10*x^2+7*x+5").unwrap();
/// assert_eq!(
/// (&p).balanced_mod(Natural::from(10u32)).to_string(),
/// "-3*x+5"
/// );
/// ```
#[inline]
fn balanced_mod(self, m: Natural) -> IntegerPolynomial {
self.balanced_mod(&m)
}
}
impl<'a> BalancedMod<&'a Natural> for &NaturalPolynomial {
type Output = IntegerPolynomial;
/// Reduces every coefficient of a [`NaturalPolynomial`] modulo a [`Natural`] to the
/// representative closest to zero, returning an [`IntegerPolynomial`], taking the polynomial by
/// reference and the modulus by reference.
///
/// See the documentation for the [`BalancedMod`] implementation on [`NaturalPolynomial`] that
/// takes both arguments by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits in the
/// polynomial's coefficients.
///
/// # Panics
/// Panics if `m` is zero.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedMod;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// // Each coefficient goes to the representative closest to zero.
/// let p = NaturalPolynomial::from_str("x^2+27*x+23").unwrap();
/// assert_eq!(
/// (&p).balanced_mod(&Natural::from(10u32)).to_string(),
/// "x^2-3*x+3"
/// );
///
/// // Half the modulus stays positive, and reducing the leading coefficient to zero lowers the
/// // degree.
/// let p = NaturalPolynomial::from_str("10*x^2+7*x+5").unwrap();
/// assert_eq!(
/// (&p).balanced_mod(&Natural::from(10u32)).to_string(),
/// "-3*x+5"
/// );
/// ```
fn balanced_mod(self, m: &'a Natural) -> IntegerPolynomial {
assert_ne!(*m, 0u32, "division by zero");
// `from_coefficients_asc` trims, which is what makes the degree fall when the leading
// coefficient reduces to zero.
IntegerPolynomial::from_coefficients_asc(
self.coefficients
.iter()
.map(|c| c.balanced_mod(m))
.collect::<Vec<_>>(),
)
}
}