void
nmod_poly_cosh_series(nmod_poly_t g, const nmod_poly_t h, long n)
{
mp_ptr g_coeffs, h_coeffs;
nmod_poly_t t1;
long h_len;
h_len = h->length;
if (h_len > 0 && h->coeffs[0] != 0UL)
{
printf("Exception: nmod_poly_cosh_series: constant term != 0\n");
abort();
}
if (h_len == 1 || n < 2)
{
nmod_poly_zero(g);
if (n > 0)
nmod_poly_set_coeff_ui(g, 0, 1UL);
return;
}
if (h_len < n)
{
h_coeffs = _nmod_vec_init(n);
mpn_copyi(h_coeffs, h->coeffs, h_len);
mpn_zero(h_coeffs + h_len, n - h_len);
}
else
h_coeffs = h->coeffs;
if (h == g && h_len >= n)
{
nmod_poly_init2(t1, h->mod.n, n);
g_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(g, n);
g_coeffs = g->coeffs;
}
_nmod_poly_cosh_series(g_coeffs, h_coeffs, n, h->mod);
if (h == g && h_len >= n)
{
nmod_poly_swap(g, t1);
nmod_poly_clear(t1);
}
g->length = n;
if (h_len < n)
_nmod_vec_free(h_coeffs);
_nmod_poly_normalise(g);
}
explicit
Flintzz_pX(const zz_pX& a)
{
long da = deg(a);
nmod_poly_init2(value, zz_p::modulus(), da+1);
for (long i = 0; i <= da; i++) {
nmod_poly_set_coeff_ui(value, i, rep(a[i]));
}
}
int main (void)
{
double t;
nmod_poly_t f, g, h;
for (int i= 15001;i < 16000; i++)
{
nmod_poly_init2 (f, 17, i/2+1);
nmod_poly_init2 (g, 17, i+1);
nmod_poly_set_coeff_ui (f, i/2, 1);
nmod_poly_set_coeff_ui (f, 1, 1);
nmod_poly_set_coeff_ui (f, 0, ((i%17)*(i%17)+3) % 17);
nmod_poly_set_coeff_ui (g, i, 1);
nmod_poly_set_coeff_ui (g, i/2+1, 1);
nmod_poly_set_coeff_ui (g, 1, ((i % 17)+1)%17);
nmod_poly_set_coeff_ui (g, 0, 15);
nmod_poly_init (h, 17);
nmod_poly_gcd (h, f, g);
if (!nmod_poly_is_one (h))
{
flint_printf ("i= %d\n", i);
nmod_poly_factor_t factors;
nmod_poly_factor_init (factors);
t= clock();
nmod_poly_factor (factors, h);
t = (clock() - t) / CLOCKS_PER_SEC;
flint_printf("factorization %.2lf\n", t);
nmod_poly_factor_clear (factors);
}
nmod_poly_clear (f);
nmod_poly_clear (g);
nmod_poly_clear (h);
}
return EXIT_SUCCESS;
}
void
nmod_poly_revert_series_lagrange(nmod_poly_t Qinv,
const nmod_poly_t Q, long n)
{
mp_ptr Qinv_coeffs, Q_coeffs;
nmod_poly_t t1;
long Qlen;
Qlen = Q->length;
if (Qlen < 2 || Q->coeffs[0] != 0 || Q->coeffs[1] == 0)
{
printf("exception: nmod_poly_revert_series_lagrange: input must have "
"zero constant and an invertible coefficient of x^1");
abort();
}
if (Qlen < n)
{
Q_coeffs = _nmod_vec_init(n);
mpn_copyi(Q_coeffs, Q->coeffs, Qlen);
mpn_zero(Q_coeffs + Qlen, n - Qlen);
}
else
Q_coeffs = Q->coeffs;
if (Q == Qinv && Qlen >= n)
{
nmod_poly_init2(t1, Q->mod.n, n);
Qinv_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Qinv, n);
Qinv_coeffs = Qinv->coeffs;
}
_nmod_poly_revert_series_lagrange(Qinv_coeffs, Q_coeffs, n, Q->mod);
if (Q == Qinv && Qlen >= n)
{
nmod_poly_swap(Qinv, t1);
nmod_poly_clear(t1);
}
Qinv->length = n;
if (Qlen < n)
_nmod_vec_clear(Q_coeffs);
_nmod_poly_normalise(Qinv);
}
void
nmod_poly_inv_series_basecase(nmod_poly_t Qinv,
const nmod_poly_t Q, long n)
{
mp_ptr Qinv_coeffs, Q_coeffs;
nmod_poly_t t1;
long Qlen;
Qlen = Q->length;
if (n == 0 || Q->length == 0 || Q->coeffs[0] == 0)
{
printf("Exception: division by zero in nmod_poly_inv_series_basecase\n");
abort();
}
if (Qlen < n)
{
Q_coeffs = _nmod_vec_init(n);
mpn_copyi(Q_coeffs, Q->coeffs, Qlen);
mpn_zero(Q_coeffs + Qlen, n - Qlen);
}
else
Q_coeffs = Q->coeffs;
if (Q == Qinv && Qlen >= n)
{
nmod_poly_init2(t1, Q->mod.n, n);
Qinv_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Qinv, n);
Qinv_coeffs = Qinv->coeffs;
}
_nmod_poly_inv_series_basecase(Qinv_coeffs, Q_coeffs, n, Q->mod);
if (Q == Qinv && Qlen >= n)
{
nmod_poly_swap(Qinv, t1);
nmod_poly_clear(t1);
}
Qinv->length = n;
if (Qlen < n)
_nmod_vec_free(Q_coeffs);
_nmod_poly_normalise(Qinv);
}
void
nmod_poly_pow(nmod_poly_t res, const nmod_poly_t poly, ulong e)
{
const slong len = poly->length;
slong rlen;
if ((len < 2) | (e < UWORD(3)))
{
if (len == 0)
nmod_poly_zero(res);
else if (len == 1)
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = n_powmod2_ui_preinv(poly->coeffs[0], e,
poly->mod.n, poly->mod.ninv);
res->length = 1;
_nmod_poly_normalise(res);
}
else if (e == UWORD(0))
{
nmod_poly_set_coeff_ui(res, 0, UWORD(1));
res->length = 1;
_nmod_poly_normalise(res);
}
else if (e == UWORD(1))
nmod_poly_set(res, poly);
else /* e == UWORD(2) */
nmod_poly_mul(res, poly, poly);
return;
}
rlen = (slong) e * (len - 1) + 1;
if (res != poly)
{
nmod_poly_fit_length(res, rlen);
_nmod_poly_pow(res->coeffs, poly->coeffs, len, e, poly->mod);
}
else
{
nmod_poly_t t;
nmod_poly_init2(t, poly->mod.n, rlen);
_nmod_poly_pow(t->coeffs, poly->coeffs, len, e, poly->mod);
nmod_poly_swap(res, t);
nmod_poly_clear(t);
}
res->length = rlen;
_nmod_poly_normalise(res);
}
void nmod_poly_mulhigh(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, long n)
{
long len1, len2, len_out;
len1 = poly1->length;
len2 = poly2->length;
len_out = poly1->length + poly2->length - 1;
if (n > len_out)
n = len_out;
if (len1 == 0 || len2 == 0 || n == 0)
{
nmod_poly_zero(res);
return;
}
if (res == poly1 || res == poly2)
{
nmod_poly_t temp;
nmod_poly_init2(temp, poly1->mod.n, len_out);
if (len1 >= len2)
_nmod_poly_mulhigh(temp->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, n, poly1->mod);
else
_nmod_poly_mulhigh(temp->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1, n, poly1->mod);
nmod_poly_swap(temp, res);
nmod_poly_clear(temp);
} else
{
nmod_poly_fit_length(res, len_out);
if (len1 >= len2)
_nmod_poly_mulhigh(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, n, poly1->mod);
else
_nmod_poly_mulhigh(res->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1, n, poly1->mod);
}
res->length = len_out;
_nmod_poly_normalise(res);
}
void
nmod_poly_div_divconquer(nmod_poly_t Q,
const nmod_poly_t A, const nmod_poly_t B)
{
nmod_poly_t tQ;
mp_ptr q;
long Alen, Blen;
Blen = B->length;
if (Blen == 0)
{
printf("Exception: division by zero in nmod_poly_div_divconquer\n");
abort();
}
Alen = A->length;
if (Alen < Blen)
{
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
nmod_poly_init2(tQ, A->mod.n, Alen - Blen + 1);
q = tQ->coeffs;
}
else
{
nmod_poly_fit_length(Q, Alen - Blen + 1);
q = Q->coeffs;
}
_nmod_poly_div_divconquer(q, A->coeffs, Alen,
B->coeffs, Blen, A->mod);
if (Q == A || Q == B)
{
nmod_poly_swap(tQ, Q);
nmod_poly_clear(tQ);
}
Q->length = Alen - Blen + 1;
}
void
nmod_poly_compose_divconquer(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
long lenr;
if (len1 == 0)
{
nmod_poly_zero(res);
return;
}
if (len1 == 1 || len2 == 0)
{
nmod_poly_set_coeff_ui(res, 0, poly1->coeffs[0]);
nmod_poly_truncate(res, 1);
return;
}
lenr = (len1 - 1) * (len2 - 1) + 1;
if (res != poly1 && res != poly2)
{
nmod_poly_fit_length(res, lenr);
_nmod_poly_compose_divconquer(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, poly1->mod);
}
else
{
nmod_poly_t t;
nmod_poly_init2(t, poly1->mod.n, lenr);
_nmod_poly_compose_divconquer(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, poly1->mod);
nmod_poly_swap(res, t);
nmod_poly_clear(t);
}
res->length = lenr;
_nmod_poly_normalise(res);
}
/*------------------------------------------------------------*/
void check(int opt){
mp_limb_t n = 12345;
nmod_t Zn;
nmod_init(&Zn, n);
sage_output_init(Zn);
nmod_poly_t a;
nmod_poly_init2(a, n, 10);
long i;
for (i = 0; i < 10; i++)
a->coeffs[i] = i;
a->length = 10;
_nmod_poly_normalise(a);
sage_output_print_poly(a);
printf("\n");
nmod_poly_zero(a);
sage_output_print_poly(a);
printf("\n");
nmod_poly_clear(a);
}
void
nmod_poly_exp_series(nmod_poly_t f, const nmod_poly_t h, long n)
{
mp_ptr f_coeffs, h_coeffs;
nmod_poly_t t1;
long hlen, k;
nmod_poly_fit_length(f, n);
hlen = h->length;
if (hlen > 0 && h->coeffs[0] != 0UL)
{
printf("Exception: nmod_poly_exp_series: constant term != 0\n");
abort();
}
if (n <= 1 || hlen == 0)
{
if (n == 0)
{
nmod_poly_zero(f);
}
else
{
f->coeffs[0] = 1UL;
f->length = 1;
}
return;
}
/* Handle monomials */
for (k = 0; h->coeffs[k] == 0UL && k < n - 1; k++);
if (k == hlen - 1 || k == n - 1)
{
hlen = FLINT_MIN(hlen, n);
_nmod_poly_exp_series_monomial_ui(f->coeffs,
h->coeffs[hlen-1], hlen - 1, n, f->mod);
f->length = n;
_nmod_poly_normalise(f);
return;
}
if (n < NMOD_NEWTON_EXP_CUTOFF2)
{
_nmod_poly_exp_series_basecase(f->coeffs, h->coeffs, hlen, n, f->mod);
f->length = n;
_nmod_poly_normalise(f);
return;
}
if (hlen < n)
{
h_coeffs = _nmod_vec_init(n);
mpn_copyi(h_coeffs, h->coeffs, hlen);
mpn_zero(h_coeffs + hlen, n - hlen);
}
else
h_coeffs = h->coeffs;
if (h == f && hlen >= n)
{
nmod_poly_init2(t1, h->mod.n, n);
f_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(f, n);
f_coeffs = f->coeffs;
}
_nmod_poly_exp_series(f_coeffs, h_coeffs, n, f->mod);
if (h == f && hlen >= n)
{
nmod_poly_swap(f, t1);
nmod_poly_clear(t1);
}
f->length = n;
if (hlen < n)
_nmod_vec_free(h_coeffs);
_nmod_poly_normalise(f);
}
void
nmod_poly_xgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
const nmod_poly_t A, const nmod_poly_t B)
{
const long lenA = A->length, lenB = B->length;
mp_limb_t inv;
if (lenA == 0)
{
if (lenB == 0)
{
nmod_poly_zero(G);
nmod_poly_zero(S);
nmod_poly_zero(T);
}
else
{
inv = n_invmod(B->coeffs[lenB - 1], B->mod.n);
nmod_poly_scalar_mul_nmod(G, B, inv);
nmod_poly_zero(S);
nmod_poly_set_coeff_ui(T, 0, inv);
T->length = 1;
}
}
else if (lenB == 0)
{
inv = n_invmod(A->coeffs[lenA - 1], A->mod.n);
nmod_poly_scalar_mul_nmod(G, A, inv);
nmod_poly_zero(T);
nmod_poly_set_coeff_ui(S, 0, inv);
S->length = 1;
}
else
{
nmod_poly_t tG, tS, tT;
mp_ptr g, s, t;
long lenG;
if (G == A || G == B)
{
nmod_poly_init2(tG, A->mod.n, FLINT_MIN(lenA, lenB));
g = tG->coeffs;
}
else
{
nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
g = G->coeffs;
}
if (S == A || S == B)
{
nmod_poly_init2(tS, A->mod.n, lenB - 1);
s = tS->coeffs;
}
else
{
nmod_poly_fit_length(S, lenB - 1);
s = S->coeffs;
}
if (T == A || T == B)
{
nmod_poly_init2(tT, A->mod.n, lenA - 1);
t = tT->coeffs;
}
else
{
nmod_poly_fit_length(T, lenA - 1);
t = T->coeffs;
}
if (lenA >= lenB)
lenG = _nmod_poly_xgcd(g, s, t, A->coeffs, lenA,
B->coeffs, lenB, A->mod);
else
lenG = _nmod_poly_xgcd(g, t, s, B->coeffs, lenB,
A->coeffs, lenA, A->mod);
if (G == A || G == B)
{
nmod_poly_swap(tG, G);
nmod_poly_clear(tG);
}
if (S == A || S == B)
{
nmod_poly_swap(tS, S);
nmod_poly_clear(tS);
}
if (T == A || T == B)
{
nmod_poly_swap(tT, T);
nmod_poly_clear(tT);
}
G->length = lenG;
S->length = lenB - lenG;
T->length = lenA - lenG;
MPN_NORM(S->coeffs, S->length);
MPN_NORM(T->coeffs, T->length);
if (G->coeffs[lenG - 1] != 1)
{
inv = n_invmod(G->coeffs[lenG - 1], A->mod.n);
nmod_poly_scalar_mul_nmod(G, G, inv);
nmod_poly_scalar_mul_nmod(S, S, inv);
nmod_poly_scalar_mul_nmod(T, T, inv);
}
}
}