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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 crate::natural_polynomial::arithmetic::add::{add_assign_ref, add_assign_val};
use malachite_base::polynomial::{AddTruncated, AddTruncatedAssign, Polynomial};
// The first `len` elements of `xs`, or all of them if there are fewer.
fn prefix(xs: &[Natural], len: u64) -> &[Natural] {
&xs[..usize::try_from(len).map_or(xs.len(), |len| len.min(xs.len()))]
}
impl AddTruncated<Self> for NaturalPolynomial {
type Output = Self;
/// Adds two [`NaturalPolynomial`]s, keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking both by value.
///
/// $$
/// f(p, q, n) = (p + q) \bmod x^n.
/// $$
///
/// The polynomials need not already be truncated: this is the sum of their images modulo $x^n$,
/// so only the first `len` coefficients of each are read. Natural coefficients cannot cancel,
/// but the kept part of either operand can end in zeros, so the sum is trimmed.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// first `len` coefficients of both polynomials.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::AddTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// NaturalPolynomial::from_str("x^3+2*x^2+x+5")
/// .unwrap()
/// .add_truncated(NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 3)
/// .to_string(),
/// "6*x^2+2*x+7"
/// );
/// // Only the constant and linear coefficients are kept.
/// assert_eq!(
/// NaturalPolynomial::from_str("x^3+2*x^2+x+5")
/// .unwrap()
/// .add_truncated(NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 2)
/// .to_string(),
/// "2*x+7"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_add_series` from `fmpz_poly/add_series.c`, FLINT 3.6.0.
fn add_truncated(mut self, mut other: Self, len: u64) -> Self {
self.truncate_assign(len);
other.truncate_assign(len);
add_assign_val(&mut self.coefficients, other.coefficients);
self.trim();
self
}
}
impl AddTruncated<&Self> for NaturalPolynomial {
type Output = Self;
/// Adds two [`NaturalPolynomial`]s, keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking the first by value and the second by reference.
///
/// $$
/// f(p, q, n) = (p + q) \bmod x^n.
/// $$
///
/// The polynomials need not already be truncated: this is the sum of their images modulo $x^n$,
/// so only the first `len` coefficients of each are read. Natural coefficients cannot cancel,
/// but the kept part of either operand can end in zeros, so the sum is trimmed.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// first `len` coefficients of both polynomials.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::AddTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// NaturalPolynomial::from_str("x^3+2*x^2+x+5")
/// .unwrap()
/// .add_truncated(&NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 3)
/// .to_string(),
/// "6*x^2+2*x+7"
/// );
/// // Only the constant and linear coefficients are kept.
/// assert_eq!(
/// NaturalPolynomial::from_str("x^3+2*x^2+x+5")
/// .unwrap()
/// .add_truncated(&NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 2)
/// .to_string(),
/// "2*x+7"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_add_series` from `fmpz_poly/add_series.c`, FLINT 3.6.0.
fn add_truncated(mut self, other: &Self, len: u64) -> Self {
self.truncate_assign(len);
add_assign_ref(&mut self.coefficients, prefix(&other.coefficients, len));
self.trim();
self
}
}
impl AddTruncated<NaturalPolynomial> for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Adds two [`NaturalPolynomial`]s, keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking the first by reference and the second by value.
///
/// $$
/// f(p, q, n) = (p + q) \bmod x^n.
/// $$
///
/// The polynomials need not already be truncated: this is the sum of their images modulo $x^n$,
/// so only the first `len` coefficients of each are read. Natural coefficients cannot cancel,
/// but the kept part of either operand can end in zeros, so the sum is trimmed.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// first `len` coefficients of both polynomials.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::AddTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap())
/// .add_truncated(NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 3)
/// .to_string(),
/// "6*x^2+2*x+7"
/// );
/// // Only the constant and linear coefficients are kept.
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap())
/// .add_truncated(NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 2)
/// .to_string(),
/// "2*x+7"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_add_series` from `fmpz_poly/add_series.c`, FLINT 3.6.0.
fn add_truncated(self, mut other: NaturalPolynomial, len: u64) -> NaturalPolynomial {
other.truncate_assign(len);
add_assign_ref(&mut other.coefficients, prefix(&self.coefficients, len));
other.trim();
other
}
}
impl AddTruncated<&NaturalPolynomial> for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Adds two [`NaturalPolynomial`]s, keeping only the coefficients of $x^i$ for $i$ less than
/// `len`, taking both by reference.
///
/// $$
/// f(p, q, n) = (p + q) \bmod x^n.
/// $$
///
/// The polynomials need not already be truncated: this is the sum of their images modulo $x^n$,
/// so only the first `len` coefficients of each are read. Natural coefficients cannot cancel,
/// but the kept part of either operand can end in zeros, so the sum is trimmed.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// first `len` coefficients of both polynomials.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::AddTruncated;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap())
/// .add_truncated(&NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 3)
/// .to_string(),
/// "6*x^2+2*x+7"
/// );
/// // Only the constant and linear coefficients are kept.
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap())
/// .add_truncated(&NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 2)
/// .to_string(),
/// "2*x+7"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_add_series` from `fmpz_poly/add_series.c`, FLINT 3.6.0.
fn add_truncated(self, other: &NaturalPolynomial, len: u64) -> NaturalPolynomial {
let mut coefficients = prefix(&self.coefficients, len).to_vec();
add_assign_ref(&mut coefficients, prefix(&other.coefficients, len));
NaturalPolynomial::from_coefficients_asc(coefficients)
}
}
impl AddTruncatedAssign<Self> for NaturalPolynomial {
/// Adds a [`NaturalPolynomial`] to a [`NaturalPolynomial`] in place, keeping only the
/// coefficients of $x^i$ for $i$ less than `len`, taking the second polynomial by value.
///
/// $$
/// p \gets (p + q) \bmod x^n.
/// $$
///
/// The polynomials need not already be truncated: this is the sum of their images modulo $x^n$,
/// so only the first `len` coefficients of each are read. Natural coefficients cannot cancel,
/// but the kept part of either operand can end in zeros, so the sum is trimmed.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// first `len` coefficients of both polynomials.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::AddTruncatedAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap();
/// p.add_truncated_assign(NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 3);
/// assert_eq!(p.to_string(), "6*x^2+2*x+7");
///
/// // Only the constant and linear coefficients are kept.
/// let mut p = NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap();
/// p.add_truncated_assign(NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 2);
/// assert_eq!(p.to_string(), "2*x+7");
/// ```
///
/// This is equivalent to `fmpz_poly_add_series` from `fmpz_poly/add_series.c`, FLINT 3.6.0.
fn add_truncated_assign(&mut self, mut other: Self, len: u64) {
self.truncate_assign(len);
other.truncate_assign(len);
add_assign_val(&mut self.coefficients, other.coefficients);
self.trim();
}
}
impl AddTruncatedAssign<&Self> for NaturalPolynomial {
/// Adds a [`NaturalPolynomial`] to a [`NaturalPolynomial`] in place, keeping only the
/// coefficients of $x^i$ for $i$ less than `len`, taking the second polynomial by reference.
///
/// $$
/// p \gets (p + q) \bmod x^n.
/// $$
///
/// The polynomials need not already be truncated: this is the sum of their images modulo $x^n$,
/// so only the first `len` coefficients of each are read. Natural coefficients cannot cancel,
/// but the kept part of either operand can end in zeros, so the sum is trimmed.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// first `len` coefficients of both polynomials.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::polynomial::AddTruncatedAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap();
/// p.add_truncated_assign(&NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 3);
/// assert_eq!(p.to_string(), "6*x^2+2*x+7");
///
/// // Only the constant and linear coefficients are kept.
/// let mut p = NaturalPolynomial::from_str("x^3+2*x^2+x+5").unwrap();
/// p.add_truncated_assign(&NaturalPolynomial::from_str("4*x^2+x+2").unwrap(), 2);
/// assert_eq!(p.to_string(), "2*x+7");
/// ```
///
/// This is equivalent to `fmpz_poly_add_series` from `fmpz_poly/add_series.c`, FLINT 3.6.0.
fn add_truncated_assign(&mut self, other: &Self, len: u64) {
self.truncate_assign(len);
add_assign_ref(&mut self.coefficients, prefix(&other.coefficients, len));
self.trim();
}
}