int
main(void)
{
int i;
flint_rand_t state;
flint_randinit(state);
printf("init/clear....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
nmod_poly_mat_t a;
mp_limb_t mod;
long j, k;
long rows = n_randint(state, 100);
long cols = n_randint(state, 100);
mod = n_randtest_prime(state, 0);
nmod_poly_mat_init(a, rows, cols, mod);
for (j = 0; j < rows; j++)
for (k = 0; k < cols; k++)
nmod_poly_zero(nmod_poly_mat_entry(a, j, k));
nmod_poly_mat_clear(a);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
void nmod_poly_factor_set(nmod_poly_factor_t res, const nmod_poly_factor_t fac)
{
if (res != fac)
{
if (fac->num == 0)
{
nmod_poly_factor_clear(res);
nmod_poly_factor_init(res);
}
else
{
slong i;
nmod_poly_factor_fit_length(res, fac->num);
for (i = 0; i < fac->num; i++)
{
nmod_poly_set(res->p + i, fac->p + i);
(res->p + i)->mod = (fac->p + i)->mod;
res->exp[i] = fac->exp[i];
}
for ( ; i < res->num; i++)
{
nmod_poly_zero(res->p + i);
res->exp[i] = 0;
}
res->num = fac->num;
}
}
}
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);
}
void nmod_poly_divrem_newton(nmod_poly_t Q, nmod_poly_t R,
const nmod_poly_t A, const nmod_poly_t B)
{
const long lenA = A->length, lenB = B->length;
mp_ptr q, r;
if (lenB == 0)
{
printf("Exception: division by zero in nmod_poly_divrem_newton\n");
abort();
}
if (lenA < lenB)
{
nmod_poly_set(R, A);
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
q = _nmod_vec_init(lenA - lenB + 1);
}
else
{
nmod_poly_fit_length(Q, lenA - lenB + 1);
q = Q->coeffs;
}
if (R == A || R == B)
{
r = _nmod_vec_init(lenB - 1);
}
else
{
nmod_poly_fit_length(R, lenB - 1);
r = R->coeffs;
}
_nmod_poly_divrem_newton(q, r, A->coeffs, lenA,
B->coeffs, lenB, B->mod);
if (Q == A || Q == B)
{
_nmod_vec_clear(Q->coeffs);
Q->coeffs = q;
Q->alloc = lenA - lenB + 1;
}
if (R == A || R == B)
{
_nmod_vec_clear(R->coeffs);
R->coeffs = r;
R->alloc = lenB - 1;
}
Q->length = lenA - lenB + 1;
R->length = lenB - 1;
_nmod_poly_normalise(R);
}
int pq_nmod_inv(pq_nmod_elt_t res, const pq_nmod_elt_t x, const pq_nmod_t A) {
_pq_nmod_insure_mono(x, A);
if (nmod_poly_invmod(res->mono, x->mono, A->M)) {
nmod_poly_zero(res->dual);
return 1;
} else {
return 0;
}
}
void
nmod_poly_compose_series_horner(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, long n)
{
long len1 = poly1->length;
long len2 = poly2->length;
long lenr;
if (len2 != 0 && poly2->coeffs[0] != 0)
{
printf("exception: nmod_poly_compose_series_horner: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
nmod_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = poly1->coeffs[0];
res->length = 1;
_nmod_poly_normalise(res);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
nmod_poly_fit_length(res, lenr);
_nmod_poly_compose_series_horner(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, res->mod);
res->length = lenr;
_nmod_poly_normalise(res);
}
else
{
nmod_poly_t t;
nmod_poly_init2_preinv(t, res->mod.n, res->mod.ninv, lenr);
_nmod_poly_compose_series_horner(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, res->mod);
t->length = lenr;
_nmod_poly_normalise(t);
nmod_poly_swap(res, t);
nmod_poly_clear(t);
}
}
void
nmod_poly_div_basecase(nmod_poly_t Q, const nmod_poly_t A,
const nmod_poly_t B)
{
mp_ptr Q_coeffs, W;
nmod_poly_t t1;
long Alen, Blen;
Blen = B->length;
if (Blen == 0)
{
printf("Exception: division by zero in nmod_poly_div_basecase\n");
abort();
}
Alen = A->length;
if (Alen < Blen)
{
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
nmod_poly_init2_preinv(t1, B->mod.n, B->mod.ninv,
Alen - Blen + 1);
Q_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Q, Alen - Blen + 1);
Q_coeffs = Q->coeffs;
}
W = _nmod_vec_init(NMOD_DIV_BC_ITCH(Alen, Blen, A->mod));
_nmod_poly_div_basecase(Q_coeffs, W, A->coeffs, Alen,
B->coeffs, Blen, B->mod);
if (Q == A || Q == B)
{
nmod_poly_swap(Q, t1);
nmod_poly_clear(t1);
}
Q->length = Alen - Blen + 1;
_nmod_vec_clear(W);
_nmod_poly_normalise(Q);
}
void embeddings_isomorphism(nmod_poly_t G, mp_srcptr F,
const embeddings_t FP, const embeddings_t FQ, const embeddings_t FR){
long m = nmod_poly_degree(FP->P);
long n = nmod_poly_degree(FQ->P);
long i;
nmod_poly_t tmpF, tmpG, S, X;
nmod_t mod = FP->P->mod;
nmod_poly_init(tmpF, mod.n);
nmod_poly_init(tmpG, mod.n);
nmod_poly_init(S, mod.n);
nmod_poly_init(X, mod.n);
nmod_poly_zero(G);
nmod_poly_zero(X);
nmod_poly_set_coeff_ui(X, 1, 1);
embeddings_embed(S, X, FP, FQ, FR);
for (i = m-1; i >= 0; i--){
nmod_poly_fit_length(tmpF, n);
long j;
long offset = i*n;
for (j = 0; j < n; j++)
tmpF->coeffs[j] = F[offset+j];
tmpF->length = n;
_nmod_poly_normalise(tmpF);
embeddings_embed(tmpG, tmpF, FQ, FP, FR);
nmod_poly_mulmod(G, G, S, FR->P);
nmod_poly_add(G, G, tmpG);
}
nmod_poly_clear(tmpF);
nmod_poly_clear(tmpG);
nmod_poly_clear(X);
nmod_poly_clear(S);
}
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 pq_nmod_mul(pq_nmod_elt_t res, const pq_nmod_elt_t x,
const pq_nmod_elt_t y, const pq_nmod_t A) {
switch (nmod_poly_is_zero(y->mono) |
(nmod_poly_is_zero(y->dual) << 1) |
(nmod_poly_is_zero(x->mono) << 4) |
(nmod_poly_is_zero(x->dual) << 5)) {
const pq_nmod_elt_struct* tmp;
case 0x22:
// Both have only dual -> add mono to x
_pq_nmod_insure_mono(x, A);
case 0x12:
case 0x32:
// x has mono, y has dual -> swap them
tmp = x;
x = y;
y = tmp;
case 0x21:
case 0x23:
// y has mono, x has dual
nmod_poly_fit_length(res->dual, A->degree);
nmod_poly_tmulmod(res->dual->coeffs, x->dual->coeffs, y->mono, A->M, A->S);
nmod_poly_zero(res->mono);
break;
case 0x11:
case 0x13:
case 0x31:
case 0x33:
// both have mono
nmod_poly_mulmod(res->mono, x->mono, y->mono, A->M);
nmod_poly_zero(res->dual);
break;
default:
// in any other case, result is 0
nmod_poly_zero(res->mono);
nmod_poly_zero(res->dual);
break;
}
}
void
nmod_poly_mulmod(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, const nmod_poly_t f)
{
long len1, len2, lenf;
mp_ptr fcoeffs;
lenf = f->length;
len1 = poly1->length;
len2 = poly2->length;
if (lenf == 0)
{
printf("Exception: nmod_poly_mulmod: divide by zero\n");
abort();
}
if (lenf == 1 || len1 == 0 || len2 == 0)
{
nmod_poly_zero(res);
return;
}
if (len1 + len2 - lenf > 0)
{
if (f == res)
{
fcoeffs = flint_malloc(sizeof(mp_limb_t) * lenf);
_nmod_vec_set(fcoeffs, f->coeffs, lenf);
}
else
fcoeffs = f->coeffs;
nmod_poly_fit_length(res, lenf - 1);
_nmod_poly_mulmod(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2,
fcoeffs, lenf,
res->mod);
if (f == res)
flint_free(fcoeffs);
res->length = lenf - 1;
_nmod_poly_normalise(res);
}
else
{
nmod_poly_mul(res, poly1, poly2);
}
}
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_mullow_classical(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
slong trunc)
{
slong len_out;
if (poly1->length == 0 || poly2->length == 0 || trunc == 0)
{
nmod_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
if (trunc > len_out)
trunc = len_out;
if (res == poly1 || res == poly2)
{
nmod_poly_t temp;
nmod_poly_init2_preinv(temp, poly1->mod.n, poly1->mod.ninv, trunc);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_classical(temp->coeffs, poly1->coeffs,
poly1->length, poly2->coeffs,
poly2->length, trunc, poly1->mod);
else
_nmod_poly_mullow_classical(temp->coeffs, poly2->coeffs,
poly2->length, poly1->coeffs,
poly1->length, trunc, poly1->mod);
nmod_poly_swap(res, temp);
nmod_poly_clear(temp);
}
else
{
nmod_poly_fit_length(res, trunc);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_classical(res->coeffs, poly1->coeffs,
poly1->length, poly2->coeffs,
poly2->length, trunc, poly1->mod);
else
_nmod_poly_mullow_classical(res->coeffs, poly2->coeffs,
poly2->length, poly1->coeffs,
poly1->length, trunc, poly1->mod);
}
res->length = trunc;
_nmod_poly_normalise(res);
}
void
nmod_poly_mullow_KS(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
mp_bitcnt_t bits, long n)
{
long len_out;
if ((poly1->length == 0) || (poly2->length == 0))
{
nmod_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
if (n > len_out)
n = len_out;
if (res == poly1 || res == poly2)
{
nmod_poly_t temp;
nmod_poly_init2_preinv(temp, poly1->mod.n, poly1->mod.ninv, len_out);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_KS(temp->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, bits,
n, poly1->mod);
else
_nmod_poly_mullow_KS(temp->coeffs, poly2->coeffs, poly2->length,
poly1->coeffs, poly1->length, bits,
n, poly1->mod);
nmod_poly_swap(res, temp);
nmod_poly_clear(temp);
}
else
{
nmod_poly_fit_length(res, len_out);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_KS(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, bits,
n, poly1->mod);
else
_nmod_poly_mullow_KS(res->coeffs, poly2->coeffs, poly2->length,
poly1->coeffs, poly1->length, bits,
n, poly1->mod);
}
res->length = n;
_nmod_poly_normalise(res);
}
void
_fmpz_vec_get_nmod_poly(nmod_poly_t res, const fmpz * coeffs, slong len)
{
if (len == 0)
{
nmod_poly_zero(res);
}
else
{
slong i;
nmod_poly_fit_length(res, len);
for (i = 0; i < len; i++)
res->coeffs[i] = fmpz_fdiv_ui(coeffs + i, res->mod.n);
_nmod_poly_set_length(res, len);
_nmod_poly_normalise(res);
}
}
void
nmod_poly_interpolate_nmod_vec_barycentric(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, slong n)
{
if (n == 0)
{
nmod_poly_zero(poly);
}
else
{
nmod_poly_fit_length(poly, n);
poly->length = n;
_nmod_poly_interpolate_nmod_vec_barycentric(poly->coeffs,
xs, ys, n, poly->mod);
_nmod_poly_normalise(poly);
}
}
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
nmod_poly_exp_series_monomial_ui(nmod_poly_t res, mp_limb_t coeff,
ulong power, slong n)
{
if (n == 0)
{
nmod_poly_zero(res);
return;
}
if (coeff == UWORD(0))
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = UWORD(1);
res->length = 1;
return;
}
if (power == 0)
{
flint_printf("Exception (nmod_poly_exp_series_monomial_ui). \n"
"Constant term != 0.\n");
abort();
}
if (coeff != UWORD(1))
coeff = n_mod2_preinv(coeff, res->mod.n, res->mod.ninv);
if (n == 1 || power >= n)
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = UWORD(1);
res->length = 1;
}
nmod_poly_fit_length(res, n);
_nmod_poly_exp_series_monomial_ui(res->coeffs, coeff, power, n, res->mod);
res->length = n;
_nmod_poly_normalise(res);
}
void nmod_poly_div_newton(nmod_poly_t Q, const nmod_poly_t A,
const nmod_poly_t B)
{
const slong lenA = A->length, lenB = B->length, lenQ = lenA - lenB + 1;
mp_ptr q;
if (lenB == 0)
{
flint_printf("Exception (nmod_poly_div_newton). Division by zero.\n");
abort();
}
if (lenA < lenB)
{
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
q = flint_malloc(lenQ * sizeof(mp_limb_t));
}
else
{
nmod_poly_fit_length(Q, lenQ);
q = Q->coeffs;
}
_nmod_poly_div_newton(q, A->coeffs, lenA, B->coeffs, lenB, B->mod);
if (Q == A || Q == B)
{
flint_free(Q->coeffs);
Q->coeffs = q;
Q->alloc = lenQ;
}
Q->length = lenQ;
}
void
nmod_poly_mat_randtest_sparse(nmod_poly_mat_t A, flint_rand_t state, long len,
float density)
{
long i, j;
for (i = 0; i < A->r; i++)
{
for (j = 0; j < A->c; j++)
{
if (n_randint(state, 1000) < density * 1000)
{
long l = n_randint(state, len + 1);
l = FLINT_MAX(l, 1);
nmod_poly_randtest(nmod_poly_mat_entry(A, i, j), state, l);
}
else
{
nmod_poly_zero(nmod_poly_mat_entry(A, i, j));
}
}
}
}
void
nmod_poly_asin_series(nmod_poly_t g, const nmod_poly_t h, slong n)
{
mp_ptr h_coeffs;
slong h_len = h->length;
if (h_len > 0 && h->coeffs[0] != UWORD(0))
{
flint_printf("Exception (nmod_poly_asin_series). Constant term != 0.\n");
abort();
}
if (h_len == 1 || n < 2)
{
nmod_poly_zero(g);
return;
}
nmod_poly_fit_length(g, n);
if (h_len < n)
{
h_coeffs = _nmod_vec_init(n);
flint_mpn_copyi(h_coeffs, h->coeffs, h_len);
flint_mpn_zero(h_coeffs + h_len, n - h_len);
}
else
h_coeffs = h->coeffs;
_nmod_poly_asin_series(g->coeffs, h_coeffs, n, h->mod);
if (h_len < n)
_nmod_vec_clear(h_coeffs);
g->length = n;
_nmod_poly_normalise(g);
}
void
nmod_poly_tanh_series(nmod_poly_t g, const nmod_poly_t h, long n)
{
mp_ptr h_coeffs;
long h_len = h->length;
if (h_len > 0 && h->coeffs[0] != 0UL)
{
printf("Exception: nmod_poly_tanh_series: constant term != 0\n");
abort();
}
if (h_len == 1 || n < 2)
{
nmod_poly_zero(g);
return;
}
nmod_poly_fit_length(g, n);
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;
_nmod_poly_tanh_series(g->coeffs, h_coeffs, n, h->mod);
if (h_len < n)
_nmod_vec_free(h_coeffs);
g->length = n;
_nmod_poly_normalise(g);
}
/*------------------------------------------------------------*/
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_hgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
const nmod_poly_t A, const nmod_poly_t B)
{
if (A->length < B->length)
{
nmod_poly_xgcd_hgcd(G, T, S, B, A);
}
else /* lenA >= lenB >= 0 */
{
const slong lenA = A->length, lenB = B->length;
mp_limb_t inv;
if (lenA == 0) /* lenA = lenB = 0 */
{
nmod_poly_zero(G);
nmod_poly_zero(S);
nmod_poly_zero(T);
}
else if (lenB == 0) /* lenA > 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 if (lenB == 1) /* lenA >= lenB = 1 */
{
nmod_poly_fit_length(T, 1);
T->length = 1;
T->coeffs[0] = n_invmod(B->coeffs[0], A->mod.n);
nmod_poly_one(G);
nmod_poly_zero(S);
}
else /* lenA >= lenB >= 2 */
{
mp_ptr g, s, t;
slong lenG;
if (G == A || G == B)
{
g = _nmod_vec_init(FLINT_MIN(lenA, lenB));
}
else
{
nmod_poly_fit_length(G, FLINT_MIN(lenA, lenB));
g = G->coeffs;
}
if (S == A || S == B)
{
s = _nmod_vec_init(FLINT_MAX(lenB - 1, 2));
}
else
{
nmod_poly_fit_length(S, FLINT_MAX(lenB - 1, 2));
s = S->coeffs;
}
if (T == A || T == B)
{
t = _nmod_vec_init(FLINT_MAX(lenA - 1, 2));
}
else
{
nmod_poly_fit_length(T, FLINT_MAX(lenA - 1, 2));
t = T->coeffs;
}
if (lenA >= lenB)
lenG = _nmod_poly_xgcd_hgcd(g, s, t, A->coeffs, lenA,
B->coeffs, lenB, A->mod);
else
lenG = _nmod_poly_xgcd_hgcd(g, t, s, B->coeffs, lenB,
A->coeffs, lenA, A->mod);
if (G == A || G == B)
{
flint_free(G->coeffs);
G->coeffs = g;
G->alloc = FLINT_MIN(lenA, lenB);
}
if (S == A || S == B)
{
flint_free(S->coeffs);
S->coeffs = s;
S->alloc = FLINT_MAX(lenB - 1, 2);
}
if (T == A || T == B)
{
flint_free(T->coeffs);
T->coeffs = t;
T->alloc = FLINT_MAX(lenA - 1, 2);
}
G->length = lenG;
S->length = FLINT_MAX(lenB - lenG, 1);
T->length = FLINT_MAX(lenA - lenG, 1);
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);
}
}
}
}
int
nmod_poly_mat_inv(nmod_poly_mat_t Ainv, nmod_poly_t den,
const nmod_poly_mat_t A)
{
slong n = nmod_poly_mat_nrows(A);
if (n == 0)
{
nmod_poly_one(den);
return 1;
}
else if (n == 1)
{
nmod_poly_set(den, E(A, 0, 0));
nmod_poly_one(E(Ainv, 0, 0));
return !nmod_poly_is_zero(den);
}
else if (n == 2)
{
nmod_poly_mat_det(den, A);
if (nmod_poly_is_zero(den))
{
return 0;
}
else if (Ainv == A)
{
nmod_poly_swap(E(A, 0, 0), E(A, 1, 1));
nmod_poly_neg(E(A, 0, 1), E(A, 0, 1));
nmod_poly_neg(E(A, 1, 0), E(A, 1, 0));
return 1;
}
else
{
nmod_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
nmod_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
nmod_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
nmod_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
return 1;
}
}
else
{
nmod_poly_mat_t LU, I;
slong * perm;
int result;
perm = _perm_init(n);
nmod_poly_mat_init_set(LU, A);
result = (nmod_poly_mat_fflu(LU, den, perm, LU, 1) == n);
if (result)
{
nmod_poly_mat_init(I, n, n, nmod_poly_mat_modulus(A));
nmod_poly_mat_one(I);
nmod_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
nmod_poly_mat_clear(I);
}
else
nmod_poly_zero(den);
if (_perm_parity(perm, n))
{
nmod_poly_mat_neg(Ainv, Ainv);
nmod_poly_neg(den, den);
}
_perm_clear(perm);
nmod_poly_mat_clear(LU);
return result;
}
}
void
nmod_poly_divrem_basecase(nmod_poly_t Q, nmod_poly_t R, const nmod_poly_t A,
const nmod_poly_t B)
{
const slong lenA = A->length, lenB = B->length;
mp_ptr Q_coeffs, R_coeffs, W;
nmod_poly_t t1, t2;
TMP_INIT;
if (lenB == 0)
{
flint_printf("Exception (nmod_poly_divrem). Division by zero.\n");
abort();
}
if (lenA < lenB)
{
nmod_poly_set(R, A);
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
nmod_poly_init2_preinv(t1, B->mod.n, B->mod.ninv, lenA - lenB + 1);
Q_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Q, lenA - lenB + 1);
Q_coeffs = Q->coeffs;
}
if (R == A || R == B)
{
nmod_poly_init2_preinv(t2, B->mod.n, B->mod.ninv, lenB - 1);
R_coeffs = t2->coeffs;
}
else
{
nmod_poly_fit_length(R, lenB - 1);
R_coeffs = R->coeffs;
}
TMP_START;
W = TMP_ALLOC(NMOD_DIVREM_BC_ITCH(lenA, lenB, A->mod)*sizeof(mp_limb_t));
_nmod_poly_divrem_basecase(Q_coeffs, R_coeffs, W, A->coeffs, lenA,
B->coeffs, lenB, B->mod);
if (Q == A || Q == B)
{
nmod_poly_swap(Q, t1);
nmod_poly_clear(t1);
}
if (R == A || R == B)
{
nmod_poly_swap(R, t2);
nmod_poly_clear(t2);
}
Q->length = lenA - lenB + 1;
R->length = lenB - 1;
TMP_END;
_nmod_poly_normalise(R);
}
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);
}
int
main(void)
{
int iter;
flint_rand_t state;
flint_randinit(state);
printf("factor....");
fflush(stdout);
/* Default algorithm */
for (iter = 0; iter < 100; iter++)
{
int result = 1;
nmod_poly_t pol1, poly, quot, rem, product;
nmod_poly_factor_t res;
mp_limb_t modulus, lead = 1;
long length, num, i, j;
ulong exp[5], prod1;
modulus = n_randtest_prime(state, 0);
nmod_poly_init(pol1, modulus);
nmod_poly_init(poly, modulus);
nmod_poly_init(quot, modulus);
nmod_poly_init(rem, modulus);
nmod_poly_zero(pol1);
nmod_poly_set_coeff_ui(pol1, 0, 1);
length = n_randint(state, 7) + 2;
do
{
nmod_poly_randtest(poly, state, length);
if (poly->length)
nmod_poly_make_monic(poly, poly);
}
while ((!nmod_poly_is_irreducible(poly)) || (poly->length < 2));
exp[0] = n_randint(state, 30) + 1;
prod1 = exp[0];
for (i = 0; i < exp[0]; i++)
nmod_poly_mul(pol1, pol1, poly);
num = n_randint(state, 5) + 1;
for (i = 1; i < num; i++)
{
do
{
length = n_randint(state, 7) + 2;
nmod_poly_randtest(poly, state, length);
if (poly->length)
{
nmod_poly_make_monic(poly, poly);
nmod_poly_divrem(quot, rem, pol1, poly);
}
}
while ((!nmod_poly_is_irreducible(poly)) ||
(poly->length < 2) || (rem->length == 0));
exp[i] = n_randint(state, 30) + 1;
prod1 *= exp[i];
for (j = 0; j < exp[i]; j++)
nmod_poly_mul(pol1, pol1, poly);
}
nmod_poly_factor_init(res);
switch (n_randint(state, 3))
{
case 0:
lead = nmod_poly_factor(res, pol1);
break;
case 1:
lead = nmod_poly_factor_with_berlekamp(res, pol1);
break;
case 2:
if (modulus == 2)
lead = nmod_poly_factor(res, pol1);
else
lead = nmod_poly_factor_with_cantor_zassenhaus(res, pol1);
break;
}
result &= (res->num == num);
if (!result)
{
printf("Error: number of factors incorrect, %ld, %ld\n",
res->num, num);
abort();
}
nmod_poly_init(product, pol1->mod.n);
nmod_poly_set_coeff_ui(product, 0, 1);
for (i = 0; i < res->num; i++)
for (j = 0; j < res->exp[i]; j++)
nmod_poly_mul(product, product, res->p + i);
nmod_poly_scalar_mul_nmod(product, product, lead);
result &= nmod_poly_equal(pol1, product);
if (!result)
{
printf("Error: product of factors does not equal original polynomial\n");
nmod_poly_print(pol1); printf("\n");
nmod_poly_print(product); printf("\n");
abort();
}
nmod_poly_clear(product);
nmod_poly_clear(quot);
nmod_poly_clear(rem);
nmod_poly_clear(pol1);
nmod_poly_clear(poly);
nmod_poly_factor_clear(res);
}
/* Test deflation trick */
for (iter = 0; iter < 100; iter++)
{
nmod_poly_t pol1, poly, quot, rem;
nmod_poly_factor_t res, res2;
mp_limb_t modulus;
long length, num, i, j;
long exp[5], prod1;
ulong inflation;
int found;
do {
modulus = n_randtest_prime(state, 0);
} while (modulus == 2); /* To compare with CZ */
nmod_poly_init(pol1, modulus);
nmod_poly_init(poly, modulus);
nmod_poly_init(quot, modulus);
nmod_poly_init(rem, modulus);
nmod_poly_zero(pol1);
nmod_poly_set_coeff_ui(pol1, 0, 1);
inflation = n_randint(state, 7) + 1;
length = n_randint(state, 7) + 2;
do
{
nmod_poly_randtest(poly, state, length);
if (poly->length)
nmod_poly_make_monic(poly, poly);
}
while ((!nmod_poly_is_irreducible(poly)) || (poly->length < 2));
nmod_poly_inflate(poly, poly, inflation);
exp[0] = n_randint(state, 6) + 1;
prod1 = exp[0];
for (i = 0; i < exp[0]; i++)
nmod_poly_mul(pol1, pol1, poly);
num = n_randint(state, 5) + 1;
for (i = 1; i < num; i++)
{
do
{
length = n_randint(state, 6) + 2;
nmod_poly_randtest(poly, state, length);
if (poly->length)
{
nmod_poly_make_monic(poly, poly);
nmod_poly_divrem(quot, rem, pol1, poly);
}
}
while ((!nmod_poly_is_irreducible(poly)) ||
(poly->length < 2) || (rem->length == 0));
exp[i] = n_randint(state, 6) + 1;
prod1 *= exp[i];
nmod_poly_inflate(poly, poly, inflation);
for (j = 0; j < exp[i]; j++)
nmod_poly_mul(pol1, pol1, poly);
}
nmod_poly_factor_init(res);
nmod_poly_factor_init(res2);
switch (n_randint(state, 3))
{
case 0:
nmod_poly_factor(res, pol1);
break;
case 1:
nmod_poly_factor_with_berlekamp(res, pol1);
break;
case 2:
nmod_poly_factor_with_cantor_zassenhaus(res, pol1);
break;
}
nmod_poly_factor_cantor_zassenhaus(res2, pol1);
if (res->num != res2->num)
{
printf("FAIL: different number of factors found\n");
abort();
}
for (i = 0; i < res->num; i++)
{
found = 0;
for (j = 0; j < res2->num; j++)
{
if (nmod_poly_equal(res->p + i, res2->p + j) &&
res->exp[i] == res2->exp[j])
{
found = 1;
break;
}
}
if (!found)
{
printf("FAIL: factor not found\n");
abort();
}
}
nmod_poly_clear(quot);
nmod_poly_clear(rem);
nmod_poly_clear(pol1);
nmod_poly_clear(poly);
nmod_poly_factor_clear(res);
nmod_poly_factor_clear(res2);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
