void
nmod_poly_factor_cantor_zassenhaus(nmod_poly_factor_t res, const nmod_poly_t f)
{
nmod_poly_t h, v, g, x;
slong i, j, num;
nmod_poly_init_preinv(h, f->mod.n, f->mod.ninv);
nmod_poly_init_preinv(g, f->mod.n, f->mod.ninv);
nmod_poly_init_preinv(v, f->mod.n, f->mod.ninv);
nmod_poly_init_preinv(x, f->mod.n, f->mod.ninv);
nmod_poly_set_coeff_ui(h, 1, 1);
nmod_poly_set_coeff_ui(x, 1, 1);
nmod_poly_make_monic(v, f);
i = 0;
do
{
i++;
nmod_poly_powmod_ui_binexp(h, h, f->mod.n, v);
nmod_poly_sub(h, h, x);
nmod_poly_gcd(g, h, v);
nmod_poly_add(h, h, x);
if (g->length != 1)
{
nmod_poly_make_monic(g, g);
num = res->num;
nmod_poly_factor_equal_deg(res, g, i);
for (j = num; j < res->num; j++)
res->exp[j] = nmod_poly_remove(v, res->p + j);
}
}
while (v->length >= 2*i + 3);
if (v->length > 1)
nmod_poly_factor_insert(res, v, 1);
nmod_poly_clear(g);
nmod_poly_clear(h);
nmod_poly_clear(v);
nmod_poly_clear(x);
}
void
nmod_poly_compose_mod_horner(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
const nmod_poly_t poly3)
{
long len1 = poly1->length;
long len2 = poly2->length;
long len3 = poly3->length;
long len = len3 - 1;
mp_ptr ptr2;
if (len3 == 0)
{
printf("exception: division by zero in nmod_poly_compose_mod_horner\n");
abort();
}
if (len1 == 0 || len3 == 1)
{
nmod_poly_zero(res);
return;
}
if (len1 == 1)
{
nmod_poly_set(res, poly1);
return;
}
if (res == poly3 || res == poly1)
{
nmod_poly_t tmp;
nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv);
nmod_poly_compose_mod_horner(tmp, poly1, poly2, poly3);
nmod_poly_swap(tmp, res);
nmod_poly_clear(tmp);
return;
}
ptr2 = _nmod_vec_init(len);
if (len2 <= len)
{
mpn_copyi(ptr2, poly2->coeffs, len2);
mpn_zero(ptr2 + len2, len - len2);
}
else
{
_nmod_poly_rem(ptr2, poly2->coeffs, len2,
poly3->coeffs, len3, res->mod);
}
nmod_poly_fit_length(res, len);
_nmod_poly_compose_mod_horner(res->coeffs,
poly1->coeffs, len1, ptr2, poly3->coeffs, len3, res->mod);
res->length = len;
_nmod_poly_normalise(res);
_nmod_vec_clear(ptr2);
}
void
nmod_poly_compose_mod_brent_kung(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
const nmod_poly_t poly3)
{
long len1 = poly1->length;
long len2 = poly2->length;
long len3 = poly3->length;
long len = len3 - 1;
mp_ptr ptr2;
if (len3 == 0)
{
printf("exception: division by zero in "
"nmod_poly_compose_mod_brent_kung\n");
abort();
}
if (len1 >= len3)
{
printf("exception: nmod_poly_compose_brent_kung: the degree of the"
" first polynomial must be smaller than that of the modulus\n");
abort();
}
if (len1 == 0 || len3 == 1)
{
nmod_poly_zero(res);
return;
}
if (len1 == 1)
{
nmod_poly_set(res, poly1);
return;
}
if (res == poly3 || res == poly1)
{
nmod_poly_t tmp;
nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv);
nmod_poly_compose_mod_brent_kung(tmp, poly1, poly2, poly3);
nmod_poly_swap(tmp, res);
nmod_poly_clear(tmp);
return;
}
ptr2 = _nmod_vec_init(len);
if (len2 <= len)
{
mpn_copyi(ptr2, poly2->coeffs, len2);
mpn_zero(ptr2 + len2, len - len2);
}
else
{
_nmod_poly_rem(ptr2, poly2->coeffs, len2,
poly3->coeffs, len3, res->mod);
}
nmod_poly_fit_length(res, len);
_nmod_poly_compose_mod_brent_kung(res->coeffs,
poly1->coeffs, len1, ptr2, poly3->coeffs, len3, res->mod);
res->length = len;
_nmod_poly_normalise(res);
_nmod_vec_clear(ptr2);
}
