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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::ModIsReduced;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::polynomial::{ModMakeMonic, ModMakeMonicAssign};
use crate::unsigned_polynomial::UnsignedPolynomial;
// Multiplies every coefficient by the inverse of the leading coefficient, which makes the leading
// coefficient 1, or returns the GCD of the leading coefficient and m when there is no inverse.
fn mod_make_monic_in_place<T: PrimitiveUnsigned>(coefficients: &mut [T], m: T) -> Result<(), T> {
let Some(&leading) = coefficients.last() else {
return Ok(());
};
let Some(inverse) = leading.mod_inverse(m) else {
return Err(leading.gcd(m));
};
if inverse != T::ONE {
let data = T::precompute_mod_mul_data(&m);
for c in coefficients {
c.mod_mul_precomputed_assign(inverse, m, &data);
}
}
Ok(())
}
fn assert_reduced<T: PrimitiveUnsigned>(p: &UnsignedPolynomial<T>, m: T) {
assert!(
p.mod_is_reduced(&m),
"self must be reduced mod m, but {p} has a coefficient >= {m}"
);
}
impl<T: PrimitiveUnsigned> ModMakeMonic<T> for UnsignedPolynomial<T> {
type Output = Self;
type Factor = T;
/// Makes an [`UnsignedPolynomial`] monic modulo `m`, by multiplying it by the inverse of its
/// leading coefficient, taking the polynomial by value. The coefficients must already be
/// reduced modulo `m`.
///
/// If the leading coefficient has no inverse modulo `m`, the error is its GCD with `m`, a
/// nontrivial factor of `m`. The zero polynomial is returned unchanged.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::ModMakeMonic;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// // 3 * 5 = 15, which is 1 mod 7.
/// let p = UnsignedPolynomial::<u8>::from_str("3*x^2+x+2").unwrap();
/// assert_eq!(
/// p.clone().mod_make_monic(7).unwrap().to_string(),
/// "x^2+5*x+3"
/// );
/// // 2 has no inverse mod 4, and shares the factor 2 with it.
/// let p = UnsignedPolynomial::<u8>::from_str("2*x+1").unwrap();
/// assert_eq!(p.clone().mod_make_monic(4), Err(2));
/// assert_eq!(
/// UnsignedPolynomial::<u8>::ZERO.mod_make_monic(7),
/// Ok(UnsignedPolynomial::ZERO)
/// );
/// ```
///
/// This is equivalent to `fmpz_mod_poly_make_monic_f` from `fmpz_mod_poly/make_monic.c`, FLINT
/// 3.6.0, with the factor returned as the error; `nmod_poly_make_monic` aborts instead.
fn mod_make_monic(mut self, m: T) -> Result<Self, T> {
assert_reduced(&self, m);
mod_make_monic_in_place(&mut self.coefficients, m)?;
Ok(self)
}
}
impl<T: PrimitiveUnsigned> ModMakeMonic<T> for &UnsignedPolynomial<T> {
type Output = UnsignedPolynomial<T>;
type Factor = T;
/// Makes an [`UnsignedPolynomial`] monic modulo `m`, by multiplying it by the inverse of its
/// leading coefficient, taking the polynomial by reference. The coefficients must already be
/// reduced modulo `m`.
///
/// If the leading coefficient has no inverse modulo `m`, the error is its GCD with `m`, a
/// nontrivial factor of `m`. The zero polynomial is returned unchanged.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_base::polynomial::ModMakeMonic;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// // 3 * 5 = 15, which is 1 mod 7.
/// let p = UnsignedPolynomial::<u8>::from_str("3*x^2+x+2").unwrap();
/// assert_eq!((&p).mod_make_monic(7).unwrap().to_string(), "x^2+5*x+3");
/// // 2 has no inverse mod 4, and shares the factor 2 with it.
/// let p = UnsignedPolynomial::<u8>::from_str("2*x+1").unwrap();
/// assert_eq!((&p).mod_make_monic(4), Err(2));
/// assert_eq!(
/// (&UnsignedPolynomial::<u8>::ZERO).mod_make_monic(7),
/// Ok(UnsignedPolynomial::ZERO)
/// );
/// ```
///
/// This is equivalent to `fmpz_mod_poly_make_monic_f` from `fmpz_mod_poly/make_monic.c`, FLINT
/// 3.6.0, with the factor returned as the error; `nmod_poly_make_monic` aborts instead.
fn mod_make_monic(self, m: T) -> Result<UnsignedPolynomial<T>, T> {
assert_reduced(self, m);
let mut coefficients = self.coefficients.clone();
mod_make_monic_in_place(&mut coefficients, m)?;
Ok(UnsignedPolynomial { coefficients })
}
}
impl<T: PrimitiveUnsigned> ModMakeMonicAssign<T> for UnsignedPolynomial<T> {
type Factor = T;
/// Makes an [`UnsignedPolynomial`] monic modulo `m` in place, by multiplying it by the inverse
/// of its leading coefficient. The coefficients must already be reduced modulo `m`.
///
/// If the leading coefficient has no inverse modulo `m`, the polynomial is left unchanged and
/// the error is the leading coefficient's GCD with `m`, a nontrivial factor of `m`. The zero
/// polynomial is left unchanged.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.len()`.
///
/// # Panics
/// Panics if `m` is 0, or if any coefficient of `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::ModMakeMonicAssign;
/// use malachite_base::unsigned_polynomial::UnsignedPolynomial;
///
/// let mut p = UnsignedPolynomial::<u8>::from_str("3*x^2+x+2").unwrap();
/// assert_eq!(p.mod_make_monic_assign(7), Ok(()));
/// assert_eq!(p.to_string(), "x^2+5*x+3");
///
/// let mut p = UnsignedPolynomial::<u8>::from_str("2*x+1").unwrap();
/// assert_eq!(p.mod_make_monic_assign(4), Err(2));
/// assert_eq!(p.to_string(), "2*x+1");
/// ```
fn mod_make_monic_assign(&mut self, m: T) -> Result<(), T> {
assert_reduced(self, m);
mod_make_monic_in_place(&mut self.coefficients, m)
}
}