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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of Calcium.
Calcium 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "ca_poly.h"
void
_ca_poly_set_roots(ca_ptr poly, ca_srcptr xs, const ulong * exp, slong n, ca_ctx_t ctx)
{
if (n == 0 || (n == 1 && exp[0] == 0))
{
ca_one(poly, ctx);
}
else if (n == 1)
{
if (exp[0] == 1)
{
ca_neg(poly, xs, ctx);
ca_one(poly + 1, ctx);
}
else if (exp[0] == 2)
{
ca_sqr(poly, xs, ctx);
ca_mul_si(poly + 1, xs, -2, ctx);
ca_one(poly + 2, ctx);
}
else
{
slong i, e;
e = exp[0];
ca_one(poly + e, ctx);
for (i = e - 1; i >= 0; i--)
{
ca_mul(poly + i, poly + i + 1, xs, ctx);
ca_mul_si(poly + i, poly + i, -(i + 1), ctx);
ca_div_ui(poly + i, poly + i, e - i, ctx);
}
}
}
else if (n == 2 && exp[0] == 1 && exp[1] == 1)
{
ca_mul(poly, xs + 0, xs + 1, ctx);
ca_add(poly + 1, xs + 0, xs + 1, ctx);
ca_neg(poly + 1, poly + 1, ctx);
ca_one(poly + 2, ctx);
}
else
{
slong i, m, deg_left, deg_right;
ca_ptr tmp;
/* todo: balance degrees */
m = (n + 1) / 2;
deg_left = deg_right = 0;
for (i = 0; i < m; i++)
deg_left += exp[i];
for (i = m; i < n; i++)
deg_right += exp[i];
tmp = _ca_vec_init(deg_left + deg_right + 2, ctx);
_ca_poly_set_roots(tmp, xs, exp, m, ctx);
_ca_poly_set_roots(tmp + deg_left + 1, xs + m, exp + m, n - m, ctx);
_ca_poly_mul(poly, tmp, deg_left + 1, tmp + deg_left + 1, deg_right + 1, ctx);
_ca_vec_clear(tmp, deg_left + deg_right + 2, ctx);
}
}
void
ca_poly_set_roots(ca_poly_t poly, ca_vec_t roots, const ulong * exp, ca_ctx_t ctx)
{
slong i, deg, len;
len = ca_vec_length(roots, ctx);
/* todo: check for overflow? */
deg = 0;
for (i = 0; i < len; i++)
deg += exp[i];
ca_poly_fit_length(poly, deg + 1, ctx);
_ca_poly_set_roots(poly->coeffs, roots->entries, exp, len, ctx);
_ca_poly_set_length(poly, deg + 1, ctx);
}
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