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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::Natural;
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::{ModIsReduced, ModMulAssign, ModProduct};
use malachite_base::num::basic::traits::Zero;
use malachite_base::polynomial::Polynomial;
fn assert_reduced(p: &NaturalPolynomial, m: &Natural) {
assert!(
p.mod_is_reduced(m),
"every polynomial must be reduced mod m, but {p} has a coefficient >= {m}"
);
}
// Multiplies the polynomials together one at a time. Once the partial product is zero it stays
// zero, so the factors after the one that made it zero are not examined; this happens more often
// than for numbers, since modulo a power of 2 or a composite number two nonzero polynomials can
// multiply to zero.
fn mod_product_owned<I: Iterator<Item = NaturalPolynomial>>(
xs: I,
m: &Natural,
) -> NaturalPolynomial {
assert_ne!(*m, 0u32, "m cannot be zero");
// The constant 1, reduced: the zero polynomial when the modulus is 1.
let mut product = if *m == 1u32 {
NaturalPolynomial::ZERO
} else {
NaturalPolynomial::one()
};
for p in xs {
assert_reduced(&p, m);
product.mod_mul_assign(p, m);
if product == NaturalPolynomial::ZERO {
break;
}
}
product
}
fn mod_product_ref<'a, I: Iterator<Item = &'a NaturalPolynomial>>(
xs: I,
m: &Natural,
) -> NaturalPolynomial {
assert_ne!(*m, 0u32, "m cannot be zero");
// The constant 1, reduced: the zero polynomial when the modulus is 1.
let mut product = if *m == 1u32 {
NaturalPolynomial::ZERO
} else {
NaturalPolynomial::one()
};
for p in xs {
assert_reduced(p, m);
product.mod_mul_assign(p, m);
if product == NaturalPolynomial::ZERO {
break;
}
}
product
}
impl ModProduct<Self, Natural> for NaturalPolynomial {
/// Multiplies together all the [`NaturalPolynomial`]s in an iterator modulo another number $m$,
/// taking the polynomials by value and the modulus by value. The coefficients must already be
/// reduced.
///
/// The product of no polynomials is the constant 1, reduced: the zero polynomial when $m = 1$.
///
/// $f((p_i)_ {i=0}^{n-1}) = q$, where every coefficient of $q$ is less than $m$ and $\prod_
/// {i=0}^{n-1} p_i \equiv q \mod m$, coefficient by coefficient.
///
/// # Worst-case complexity
/// $T(n) = O(n^2)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of coefficients of
/// all the polynomials.
///
/// # Panics
/// Panics if `m` is zero or if any coefficient is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining polynomials are not examined, so an unreduced
/// coefficient after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let ps = ["x+3", "2*x+1", "x^2+5"].map(|s| NaturalPolynomial::from_str(s).unwrap());
/// assert_eq!(
/// NaturalPolynomial::mod_product(ps.into_iter(), Natural::from(9u32)).to_string(),
/// "2*x^4+7*x^3+4*x^2+8*x+6"
/// );
/// ```
#[inline]
fn mod_product<I: Iterator<Item = Self>>(xs: I, m: Natural) -> Self {
mod_product_owned(xs, &m)
}
}
impl<'b> ModProduct<Self, &'b Natural> for NaturalPolynomial {
/// Multiplies together all the [`NaturalPolynomial`]s in an iterator modulo another number $m$,
/// taking the polynomials by value and the modulus by reference. The coefficients must already
/// be reduced.
///
/// The product of no polynomials is the constant 1, reduced: the zero polynomial when $m = 1$.
///
/// $f((p_i)_ {i=0}^{n-1}) = q$, where every coefficient of $q$ is less than $m$ and $\prod_
/// {i=0}^{n-1} p_i \equiv q \mod m$, coefficient by coefficient.
///
/// # Worst-case complexity
/// $T(n) = O(n^2)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of coefficients of
/// all the polynomials.
///
/// # Panics
/// Panics if `m` is zero or if any coefficient is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining polynomials are not examined, so an unreduced
/// coefficient after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let ps = ["x+3", "2*x+1", "x^2+5"].map(|s| NaturalPolynomial::from_str(s).unwrap());
/// assert_eq!(
/// NaturalPolynomial::mod_product(ps.into_iter(), &Natural::from(9u32)).to_string(),
/// "2*x^4+7*x^3+4*x^2+8*x+6"
/// );
/// ```
#[inline]
fn mod_product<I: Iterator<Item = Self>>(xs: I, m: &'b Natural) -> Self {
mod_product_owned(xs, m)
}
}
impl<'a> ModProduct<&'a Self, Natural> for NaturalPolynomial {
/// Multiplies together all the [`NaturalPolynomial`]s in an iterator modulo another number $m$,
/// taking the polynomials by reference and the modulus by value. The coefficients must already
/// be reduced.
///
/// The product of no polynomials is the constant 1, reduced: the zero polynomial when $m = 1$.
///
/// $f((p_i)_ {i=0}^{n-1}) = q$, where every coefficient of $q$ is less than $m$ and $\prod_
/// {i=0}^{n-1} p_i \equiv q \mod m$, coefficient by coefficient.
///
/// # Worst-case complexity
/// $T(n) = O(n^2)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of coefficients of
/// all the polynomials.
///
/// # Panics
/// Panics if `m` is zero or if any coefficient is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining polynomials are not examined, so an unreduced
/// coefficient after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let ps = ["x+3", "2*x+1", "x^2+5"].map(|s| NaturalPolynomial::from_str(s).unwrap());
/// assert_eq!(
/// NaturalPolynomial::mod_product(ps.iter(), Natural::from(9u32)).to_string(),
/// "2*x^4+7*x^3+4*x^2+8*x+6"
/// );
/// ```
#[inline]
fn mod_product<I: Iterator<Item = &'a Self>>(xs: I, m: Natural) -> Self {
mod_product_ref(xs, &m)
}
}
impl<'a, 'b> ModProduct<&'a Self, &'b Natural> for NaturalPolynomial {
/// Multiplies together all the [`NaturalPolynomial`]s in an iterator modulo another number $m$,
/// taking the polynomials by reference and the modulus by reference. The coefficients must
/// already be reduced.
///
/// The product of no polynomials is the constant 1, reduced: the zero polynomial when $m = 1$.
///
/// $f((p_i)_ {i=0}^{n-1}) = q$, where every coefficient of $q$ is less than $m$ and $\prod_
/// {i=0}^{n-1} p_i \equiv q \mod m$, coefficient by coefficient.
///
/// # Worst-case complexity
/// $T(n) = O(n^2)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of coefficients of
/// all the polynomials.
///
/// # Panics
/// Panics if `m` is zero or if any coefficient is greater than or equal to `m`. As soon as the
/// partial product is zero, the remaining polynomials are not examined, so an unreduced
/// coefficient after that point is not detected.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModProduct;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let ps = ["x+3", "2*x+1", "x^2+5"].map(|s| NaturalPolynomial::from_str(s).unwrap());
/// assert_eq!(
/// NaturalPolynomial::mod_product(ps.iter(), &Natural::from(9u32)).to_string(),
/// "2*x^4+7*x^3+4*x^2+8*x+6"
/// );
/// ```
#[inline]
fn mod_product<I: Iterator<Item = &'a Self>>(xs: I, m: &'b Natural) -> Self {
mod_product_ref(xs, m)
}
}