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
|
/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include "arith.h"
void
_arith_chebyshev_u_polynomial(fmpz * coeffs, ulong n)
{
slong k, i, d, m;
d = n % 2;
fmpz_zero(coeffs);
fmpz_set_ui(coeffs + d, d ? n + 1 : 1);
if (n % 4 >= 2)
fmpz_neg(coeffs + d, coeffs + d);
m = n / 2;
for (k = 1; k <= m; k++)
{
i = 2 * k + d;
fmpz_mul2_uiui(coeffs + i, coeffs + i - 2, 4*(m-k+1), n+k-m);
fmpz_divexact2_uiui(coeffs + i, coeffs + i, n+2*k-2*m-1, n+2*k-2*m);
fmpz_neg(coeffs + i, coeffs + i);
fmpz_zero(coeffs + i - 1);
}
}
void
arith_chebyshev_u_polynomial(fmpz_poly_t poly, ulong n)
{
if (n == 0)
{
fmpz_poly_set_ui(poly, UWORD(1));
return;
}
fmpz_poly_fit_length(poly, n + 1);
if (n == 1)
{
fmpz_zero(poly->coeffs);
fmpz_set_ui(poly->coeffs + 1, UWORD(2));
}
else
_arith_chebyshev_u_polynomial(poly->coeffs, n);
_fmpz_poly_set_length(poly, n + 1);
}
|
