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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::{Mod, ModAssign};
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::polynomial::Polynomial;
use crate::unsigned_polynomial::UnsignedPolynomial;
use alloc::vec::Vec;
use core::ops::{Rem, RemAssign};
impl<T: PrimitiveUnsigned> Rem<T> for UnsignedPolynomial<T> {
type Output = Self;
/// Divides every coefficient of a [`UnsignedPolynomial`] by a [`u64`], keeping the remainders,
/// taking the polynomial by value.
///
/// $p \\% m$ is the polynomial whose $i$th coefficient is $p_i \\% m$, and this is the
/// remainder of dividing $p$ by the constant polynomial $m$ — under the convention that
/// applies over the integers, where a remainder is bounded coefficient by coefficient rather
/// than by degree. Over a field the answer would be different: there a remainder must have
/// lower degree than the divisor, and a nonzero constant has degree 0, so dividing by one
/// leaves a remainder of 0. The `T`s are not a field, division by $m$ is not exact, and
/// bounding the remainder's coefficients is what is left.
///
/// There is a quotient to go with it: the polynomial whose $i$th coefficient is $p_i / m$, for
/// which $p = mq + r$ holds exactly.
///
/// The result is reduced modulo $m$, which is to say that
/// [`mod_is_reduced`](crate::num::arithmetic::traits::ModIsReduced::mod_is_reduced) returns
/// `true` for it.
///
/// 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 $4x^2 + 3$ modulo $4$ is the constant $3$, not a quadratic with a zero
/// leading coefficient.
///
/// $$
/// f(p, m) = q, \\quad \text{where} \\quad q_i = p_i - m \left \lfloor \frac{p_i}{m}
/// \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Panics
/// Panics if `m` is 0.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// // Every coefficient is taken modulo 3.
/// assert_eq!(
/// (UnsignedPolynomial::<u64>::from_str("x^2+4*x+5").unwrap() % 3).to_string(),
/// "x^2+x+2"
/// );
///
/// // Reducing the leading coefficient to zero lowers the degree.
/// assert_eq!(
/// (UnsignedPolynomial::<u64>::from_str("4*x^2+3").unwrap() % 4).to_string(),
/// "3"
/// );
///
/// // Modulo 1 every coefficient is zero, so the whole polynomial is.
/// assert_eq!(
/// (UnsignedPolynomial::<u64>::from_str("x^2+4*x+5").unwrap() % 1).to_string(),
/// "0"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_scalar_mod_fmpz` from `fmpz_poly/scalar_mod_fmpz.c`, FLINT
/// 3.6.0, for a polynomial whose coefficients are all nonnegative.
#[inline]
fn rem(mut self, m: T) -> Self {
self %= m;
self
}
}
impl<T: PrimitiveUnsigned> Rem<T> for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Divides every coefficient of a [`UnsignedPolynomial`] by a [`u64`], keeping the remainders,
/// taking the polynomial by reference.
///
/// See the documentation for the [`Rem`] implementation on [`UnsignedPolynomial`] for details,
/// including how reducing can lower the degree.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Panics
/// Panics if `m` is 0.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u64>::from_str("4*x^2+3").unwrap();
/// assert_eq!((&p % 4).to_string(), "3");
/// // The polynomial is left alone.
/// assert_eq!(p.to_string(), "4*x^2+3");
/// ```
#[inline]
fn rem(self, m: T) -> UnsignedPolynomial<T> {
assert_ne!(m, T::ZERO, "division by zero");
// `from_coefficients_asc` trims, which is what makes the degree fall when the leading
// coefficient reduces to zero.
UnsignedPolynomial::from_coefficients_asc(
self.coefficients_asc()
.iter()
.map(|&c| c % m)
.collect::<Vec<_>>(),
)
}
}
impl<T: PrimitiveUnsigned> RemAssign<T> for UnsignedPolynomial<T> {
/// Divides every coefficient of a [`UnsignedPolynomial`] by a [`u64`], replacing the polynomial
/// by the one whose coefficients are the remainders.
///
/// See the documentation for the [`Rem`] implementation on [`UnsignedPolynomial`] for details,
/// including how reducing can lower the degree.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Panics
/// Panics if `m` is 0.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u64>::from_str("x^2+4*x+5").unwrap();
/// p %= 3;
/// assert_eq!(p.to_string(), "x^2+x+2");
///
/// let mut p = UnsignedPolynomial::<u64>::from_str("4*x^2+3").unwrap();
/// p %= 4;
/// assert_eq!(p.to_string(), "3");
/// ```
fn rem_assign(&mut self, m: T) {
assert_ne!(m, T::ZERO, "division by zero");
for c in &mut self.coefficients {
*c %= m;
}
self.trim();
}
}
impl<T: PrimitiveUnsigned> Mod<T> for UnsignedPolynomial<T> {
type Output = Self;
/// Divides every coefficient of a [`UnsignedPolynomial`] by a [`u64`], keeping the remainders,
/// taking the polynomial by value.
///
/// A [`UnsignedPolynomial`]'s coefficients are never negative, so there is nothing for this to
/// do that `%` does not: the two agree everywhere, and this is the same operation under the
/// name the mod-family traits use. See the documentation for the [`Rem`] implementation for
/// details, including how reducing can lower the degree.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Panics
/// Panics if `m` is 0.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Mod;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// assert_eq!(
/// UnsignedPolynomial::<u64>::from_str("x^2+4*x+5")
/// .unwrap()
/// .mod_op(3)
/// .to_string(),
/// "x^2+x+2"
/// );
///
/// // Reducing the leading coefficient to zero lowers the degree.
/// assert_eq!(
/// UnsignedPolynomial::<u64>::from_str("4*x^2+3")
/// .unwrap()
/// .mod_op(4)
/// .to_string(),
/// "3"
/// );
/// ```
#[inline]
fn mod_op(self, m: T) -> Self {
self % m
}
}
impl<T: PrimitiveUnsigned> Mod<T> for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
/// Divides every coefficient of a [`UnsignedPolynomial`] by a [`u64`], keeping the remainders,
/// taking the polynomial by reference.
///
/// This agrees with `%` everywhere, a [`UnsignedPolynomial`]'s coefficients never being
/// negative. See the documentation for the [`Rem`] implementation on [`UnsignedPolynomial`] for
/// details.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Panics
/// Panics if `m` is 0.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Mod;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let p = UnsignedPolynomial::<u64>::from_str("4*x^2+3").unwrap();
/// assert_eq!((&p).mod_op(4).to_string(), "3");
/// // The polynomial is left alone.
/// assert_eq!(p.to_string(), "4*x^2+3");
/// ```
#[inline]
fn mod_op(self, m: T) -> UnsignedPolynomial<T> {
self % m
}
}
impl<T: PrimitiveUnsigned> ModAssign<T> for UnsignedPolynomial<T> {
/// Divides every coefficient of a [`UnsignedPolynomial`] by a [`u64`], replacing the polynomial
/// by the one whose coefficients are the remainders.
///
/// This agrees with `%=` everywhere, a [`UnsignedPolynomial`]'s coefficients never being
/// negative. See the documentation for the [`Rem`] implementation on [`UnsignedPolynomial`] for
/// details.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Panics
/// Panics if `m` is 0.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModAssign;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u64>::from_str("x^2+4*x+5").unwrap();
/// p.mod_assign(3);
/// assert_eq!(p.to_string(), "x^2+x+2");
/// ```
#[inline]
fn mod_assign(&mut self, m: T) {
*self %= m;
}
}