1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
// 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::arithmetic::square::square_ref;
use crate::natural_polynomial::NaturalPolynomial;
use malachite_base::num::arithmetic::traits::{Square, SquareAssign};
impl Square for NaturalPolynomial {
type Output = Self;
/// Squares an [`NaturalPolynomial`], taking it by value.
///
/// $$
/// f(p) = p^2.
/// $$
///
/// Squaring takes roughly half the coefficient multiplications of multiplying two different
/// polynomials of the same length.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the length of the polynomial, and $m$ is
/// the largest number of significant bits of any of its coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Square;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (NaturalPolynomial::from_str("x^2+3*x+2").unwrap())
/// .square()
/// .to_string(),
/// "x^4+6*x^3+13*x^2+12*x+4"
/// );
/// assert_eq!(
/// (NaturalPolynomial::from_str("x+1").unwrap())
/// .square()
/// .to_string(),
/// "x^2+2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_sqr` from `fmpz_poly/sqr.c`, FLINT 3.6.0.
#[inline]
fn square(mut self) -> Self {
self.square_assign();
self
}
}
impl Square for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Squares an [`NaturalPolynomial`], taking it by reference.
///
/// $$
/// f(p) = p^2.
/// $$
///
/// Squaring takes roughly half the coefficient multiplications of multiplying two different
/// polynomials of the same length.
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the length of the polynomial, and $m$ is
/// the largest number of significant bits of any of its coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Square;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x^2+3*x+2").unwrap())
/// .square()
/// .to_string(),
/// "x^4+6*x^3+13*x^2+12*x+4"
/// );
/// assert_eq!(
/// (&NaturalPolynomial::from_str("x+1").unwrap())
/// .square()
/// .to_string(),
/// "x^2+2*x+1"
/// );
/// ```
///
/// This is equivalent to `fmpz_poly_sqr` from `fmpz_poly/sqr.c`, FLINT 3.6.0.
#[inline]
fn square(self) -> NaturalPolynomial {
NaturalPolynomial {
coefficients: square_ref(&self.coefficients),
}
}
}
impl SquareAssign for NaturalPolynomial {
/// Squares an [`NaturalPolynomial`] in place.
///
/// $$
/// p \gets p^2.
/// $$
///
/// # Worst-case complexity
/// $T(n, m) = O(n(m + \log n) \log (nm) \log\log (nm))$
///
/// $M(n, m) = O(n(m + \log n) \log (nm))$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the length of the polynomial, and $m$ is
/// the largest number of significant bits of any of its coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::SquareAssign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// p.square_assign();
/// assert_eq!(p.to_string(), "x^4+6*x^3+13*x^2+12*x+4");
/// ```
///
/// This is equivalent to `fmpz_poly_sqr` from `fmpz_poly/sqr.c`, FLINT 3.6.0.
#[inline]
fn square_assign(&mut self) {
// The square of a constant is computed in place.
if let [c] = self.coefficients.as_mut_slice() {
c.square_assign();
} else {
self.coefficients = square_ref(&self.coefficients);
}
}
}