int
main(void)
{
int i, result = 1;
flint_rand_t state;
flint_randinit(state);
printf("log_series_monomial_ui....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
nmod_poly_t A, logA, res;
long n;
mp_limb_t mod;
ulong power;
mp_limb_t coeff;
mod = n_randtest_prime(state, 0);
n = n_randtest(state) % 100;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(logA, mod);
nmod_poly_init(res, mod);
coeff = n_randlimb(state) % mod;
power = 1 + n_randint(state, 2*n + 1);
nmod_poly_set_coeff_ui(A, 0, 1UL);
nmod_poly_set_coeff_ui(A, power, coeff);
nmod_poly_log_series(logA, A, n);
nmod_poly_log_series_monomial_ui(res, coeff, power, n);
result = nmod_poly_equal(logA, res);
if (!result)
{
printf("FAIL:\n");
printf("n = %ld, mod = %lu\n", n, mod);
printf("power = %lu, coeff = %lu\n", power, coeff);
printf("A: "); nmod_poly_print(A), printf("\n\n");
printf("log(A): "); nmod_poly_print(logA), printf("\n\n");
printf("res: "); nmod_poly_print(res), printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(logA);
nmod_poly_clear(res);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
int iter;
FLINT_TEST_INIT(state);
flint_printf("inflate....");
fflush(stdout);
for (iter = 0; iter < 100 * flint_test_multiplier(); iter++)
{
nmod_poly_t poly1, poly2, poly3, xp;
mp_limb_t modulus;
ulong inflation;
modulus = n_randtest_prime(state, 0);
nmod_poly_init(poly1, modulus);
nmod_poly_init(poly2, modulus);
nmod_poly_init(poly3, modulus);
nmod_poly_init(xp, modulus);
nmod_poly_randtest(poly1, state, n_randint(state, 20));
inflation = n_randint(state, 10);
nmod_poly_inflate(poly2, poly1, inflation);
nmod_poly_set_coeff_ui(xp, inflation, 1);
nmod_poly_compose(poly3, poly1, xp);
if (!nmod_poly_equal(poly2, poly3))
{
flint_printf("FAIL: not equal to compose (inflation = %wu)\n", inflation);
flint_printf("poly1:\n"); nmod_poly_print(poly1); flint_printf("\n\n");
flint_printf("poly2:\n"); nmod_poly_print(poly2); flint_printf("\n\n");
flint_printf("poly3:\n"); nmod_poly_print(poly3); flint_printf("\n\n");
abort();
}
nmod_poly_inflate(poly1, poly1, inflation);
if (!nmod_poly_equal(poly1, poly2))
{
flint_printf("FAIL: aliasing (inflation = %wu)\n", inflation);
flint_printf("poly1:\n"); nmod_poly_print(poly1); flint_printf("\n\n");
flint_printf("poly2:\n"); nmod_poly_print(poly2); flint_printf("\n\n");
abort();
}
nmod_poly_clear(poly1);
nmod_poly_clear(poly2);
nmod_poly_clear(poly3);
nmod_poly_clear(xp);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main() {
slong i;
mp_limb_t p, w;
nmod_poly_t f;
mp_ptr res, res2, vect;
// p premier
// Le cardinal du groupe multiplicatif doit être une puissance de 2
// Ne marche que pour p = 0, 1, 2, 3, 5, 17, 257, 65537.
p = 17;
nmod_poly_init(f, p);
nmod_poly_set_coeff_ui(f, 0, 0);
nmod_poly_set_coeff_ui(f, 1, 1);
nmod_poly_set_coeff_ui(f, 2, 2);
nmod_poly_set_coeff_ui(f, 3, 1);
nmod_poly_set_coeff_ui(f, 4, 1);
w = n_primitive_root_prime(p);
res = _nmod_vec_init(p);
nmod_poly_fft_pow2(res, f, w);
flint_printf("w : %d\n", w);
_fmpz_vec_print(res, p);
flint_printf("\n");
vect = _nmod_vec_init(p);
for(i = 0 ; i < p ; i++) {
vect[i] = i;
}
res2 = _nmod_vec_init(p);
nmod_poly_evaluate_nmod_vec(res2, f, vect, p);
_fmpz_vec_print(res2, p);
flint_printf("\nBooléen d'égalité : %d\n", _nmod_vec_equal(res,res2,p));
nmod_poly_clear(f);
_nmod_vec_clear(res);
_nmod_vec_clear(res2);
_nmod_vec_clear(vect);
return 0;
}
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_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);
}
int
main(void)
{
int i, result = 1;
FLINT_TEST_INIT(state);
flint_printf("exp_series_monomial_ui....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_poly_t A, expA, res;
slong n;
mp_limb_t mod;
ulong power;
mp_limb_t coeff;
mod = n_randtest_prime(state, 0);
n = n_randtest(state) % 100;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(expA, mod);
nmod_poly_init(res, mod);
coeff = n_randlimb(state) % mod;
power = 1 + n_randint(state, 2*n + 1);
nmod_poly_set_coeff_ui(A, power, coeff);
nmod_poly_exp_series(expA, A, n);
nmod_poly_exp_series_monomial_ui(res, coeff, power, n);
result = nmod_poly_equal(expA, res);
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("n = %wd, mod = %wu\n", n, mod);
flint_printf("power = %wu, coeff = %wu\n", power, coeff);
flint_printf("A: "); nmod_poly_print(A), flint_printf("\n\n");
flint_printf("exp(A): "); nmod_poly_print(expA), flint_printf("\n\n");
flint_printf("res: "); nmod_poly_print(res), flint_printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(expA);
nmod_poly_clear(res);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
fq_zech_get_fq_nmod(fq_nmod_t rop, const fq_zech_t op, const fq_zech_ctx_t ctx)
{
slong i;
mp_limb_t q, r;
nmod_poly_fit_length(rop, fq_zech_ctx_degree(ctx));
q = ctx->eval_table[op->value];
i = 0;
while (q >= ctx->p)
{
r = n_divrem2_precomp(&q, q, ctx->p, ctx->ppre);
nmod_poly_set_coeff_ui(rop, i, r);
i ++;
}
nmod_poly_set_coeff_ui(rop, i, q);
}
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]));
}
}
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);
}
int
main(void)
{
int i, result;
ulong j;
FLINT_TEST_INIT(state);
flint_printf("get/set_coeff_ui....");
fflush(stdout);
/* Check aliasing of a and b */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_poly_t a;
mp_limb_t n = n_randtest_not_zero(state);
mp_limb_t c1 = n_randtest(state), c2;
j = n_randint(state, 100);
nmod_poly_init(a, n);
nmod_poly_randtest(a, state, n_randint(state, 100));
nmod_poly_set_coeff_ui(a, j, c1);
c2 = nmod_poly_get_coeff_ui(a, j);
result = (c2 == c1 % n);
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("j = %wu, c1 = %wu, c2 = %wu, n = %wu\n", j, c1, c2, a->mod.n);
nmod_poly_print(a), flint_printf("\n\n");
abort();
}
nmod_poly_clear(a);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
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 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);
}
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 ARingGFFlint::fromSmallIntegerCoefficients(ElementType& result, const std::vector<long>& poly) const
{
fq_nmod_t f;
fq_nmod_init(f, mBigContext);
#if 0
printf("input = ");
for (long i=0; i<poly.size(); i++)
printf("%ld ", poly[i]);
printf("\n");
#endif
for (long i=poly.size()-1; i>=0; i--)
{
long a = poly[i];
if (a == 0) continue;
if (a < 0) a += characteristic();
nmod_poly_set_coeff_ui(f, i, a);
}
#if 0
printf(" result before reduction = ");
fq_nmod_print_pretty(f, mBigContext);
printf("\n");
#endif
fq_nmod_reduce(f, mBigContext);
#if 0
printf(" result = ");
fq_nmod_print_pretty(f, mBigContext);
printf("\n");
#endif
fq_zech_set_fq_nmod(&result, f, mContext);
#if 0
printf(" zech result = %lu", result.value);
printf("\n");
#endif
fq_nmod_clear(f, mBigContext);
}
int main()
{
flint_rand_t state;
slong nmax, n, bound, count;
mp_limb_t p, pinv, m1, m2;
nmod_poly_t A;
flint_printf("rev....");
fflush(stdout);
flint_randinit(state);
bound = 100000;
p = n_nextprime(UWORD(1) << (FLINT_BITS - 1), 0);
pinv = n_preinvert_limb(p);
nmod_poly_init(A, p);
nmod_poly_set_coeff_ui(A, 1, 1);
nmod_poly_exp_series(A, A, bound);
nmod_poly_shift_right(A, A, 1);
nmod_poly_inv_series(A, A, bound);
m1 = 1;
for (n = 0; n < A->length; n++)
{
A->coeffs[n] = n_mulmod2_preinv(A->coeffs[n], m1, p, pinv);
m1 = n_mulmod2_preinv(m1, n + 1, p, pinv);
}
for (nmax = 0; nmax < bound; nmax = 1.5 * nmax + 2)
{
fmpz_t numer, denom;
bernoulli_rev_t iter;
fmpz_init(numer);
fmpz_init(denom);
nmax += (nmax % 2);
bernoulli_rev_init(iter, nmax);
if (nmax < 8000)
count = 4000;
else
count = 100;
/* flint_printf("nmax = %wd, count = %wd\n", nmax, count); */
for (n = nmax; n >= 0 && count > 0; n -= 2, count--)
{
bernoulli_rev_next(numer, denom, iter);
m1 = fmpz_fdiv_ui(numer, p);
m2 = fmpz_fdiv_ui(denom, p);
m2 = n_invmod(m2, p);
m1 = n_mulmod2_preinv(m1, m2, p, pinv);
m2 = nmod_poly_get_coeff_ui(A, n);
if (m1 != m2)
{
flint_printf("FAIL:\n");
flint_printf("nmax = %wd, n = %wd\n", nmax, n);
flint_printf("m1 = %wu mod %wu\n", m1, p);
flint_printf("m2 = %wu mod %wu\n", m2, p);
abort();
}
}
bernoulli_rev_clear(iter);
fmpz_clear(numer);
fmpz_clear(denom);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result = 1;
FLINT_TEST_INIT(state);
flint_printf("atanh_series....");
fflush(stdout);
/* Check 2*atanh(A) = atanh(2*A/(1+A^2)) */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
nmod_poly_t A, B, atanhA, atanhB;
slong n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
n = 1 + n_randtest(state) % 100;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(B, mod);
nmod_poly_init(atanhA, mod);
nmod_poly_init(atanhB, mod);
nmod_poly_randtest(A, state, n_randint(state, 100));
nmod_poly_set_coeff_ui(A, 0, UWORD(0));
nmod_poly_mullow(B, A, A, n);
nmod_poly_set_coeff_ui(B, 0, UWORD(1));
nmod_poly_div_series(B, A, B, n);
nmod_poly_add(B, B, B);
nmod_poly_atanh_series(atanhA, A, n);
nmod_poly_atanh_series(atanhB, B, n);
nmod_poly_add(atanhA, atanhA, atanhA);
result = nmod_poly_equal(atanhA, atanhB);
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("n = %wd, mod = %wu\n", n, mod);
flint_printf("A: "); nmod_poly_print(A), flint_printf("\n\n");
flint_printf("B: "); nmod_poly_print(B), flint_printf("\n\n");
flint_printf("2*atanh(A): "); nmod_poly_print(atanhA), flint_printf("\n\n");
flint_printf("atanh(B): "); nmod_poly_print(atanhB), flint_printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(B);
nmod_poly_clear(atanhA);
nmod_poly_clear(atanhB);
}
/* Check aliasing */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
nmod_poly_t A, B;
slong n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
n = n_randtest(state) % 50;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(B, mod);
nmod_poly_randtest(A, state, n_randint(state, 50));
nmod_poly_set_coeff_ui(A, 0, UWORD(0));
nmod_poly_atanh_series(B, A, n);
nmod_poly_atanh_series(A, A, n);
result = nmod_poly_equal(A, B);
if (!result)
{
flint_printf("FAIL:\n");
nmod_poly_print(A), flint_printf("\n\n");
nmod_poly_print(B), flint_printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(B);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
nmod_poly_factor_squarefree(nmod_poly_factor_t res, const nmod_poly_t f)
{
nmod_poly_t f_d, g, g_1;
mp_limb_t p;
slong deg, i;
if (f->length <= 1)
{
res->num = 0;
return;
}
if (f->length == 2)
{
nmod_poly_factor_insert(res, f, 1);
return;
}
p = nmod_poly_modulus(f);
deg = nmod_poly_degree(f);
/* Step 1, look at f', if it is zero then we are done since f = h(x)^p
for some particular h(x), clearly f(x) = sum a_k x^kp, k <= deg(f) */
nmod_poly_init(g_1, p);
nmod_poly_init(f_d, p);
nmod_poly_init(g, p);
nmod_poly_derivative(f_d, f);
/* Case 1 */
if (nmod_poly_is_zero(f_d))
{
nmod_poly_factor_t new_res;
nmod_poly_t h;
nmod_poly_init(h, p);
for (i = 0; i <= deg / p; i++) /* this will be an integer since f'=0 */
{
nmod_poly_set_coeff_ui(h, i, nmod_poly_get_coeff_ui(f, i * p));
}
/* Now run square-free on h, and return it to the pth power */
nmod_poly_factor_init(new_res);
nmod_poly_factor_squarefree(new_res, h);
nmod_poly_factor_pow(new_res, p);
nmod_poly_factor_concat(res, new_res);
nmod_poly_clear(h);
nmod_poly_factor_clear(new_res);
}
else
{
nmod_poly_t h, z;
nmod_poly_gcd(g, f, f_d);
nmod_poly_div(g_1, f, g);
i = 1;
nmod_poly_init(h, p);
nmod_poly_init(z, p);
/* Case 2 */
while (!nmod_poly_is_one(g_1))
{
nmod_poly_gcd(h, g_1, g);
nmod_poly_div(z, g_1, h);
/* out <- out.z */
if (z->length > 1)
{
nmod_poly_factor_insert(res, z, 1);
nmod_poly_make_monic(res->p + (res->num - 1),
res->p + (res->num - 1));
if (res->num)
res->exp[res->num - 1] *= i;
}
i++;
nmod_poly_set(g_1, h);
nmod_poly_div(g, g, h);
}
nmod_poly_clear(h);
nmod_poly_clear(z);
nmod_poly_make_monic(g, g);
if (!nmod_poly_is_one(g))
{
/* so now we multiply res with square-free(g^1/p) ^ p */
nmod_poly_t g_p; /* g^(1/p) */
nmod_poly_factor_t new_res_2;
nmod_poly_init(g_p, p);
for (i = 0; i <= nmod_poly_degree(g) / p; i++)
nmod_poly_set_coeff_ui(g_p, i, nmod_poly_get_coeff_ui(g, i*p));
nmod_poly_factor_init(new_res_2);
/* square-free(g^(1/p)) */
nmod_poly_factor_squarefree(new_res_2, g_p);
nmod_poly_factor_pow(new_res_2, p);
nmod_poly_factor_concat(res, new_res_2);
nmod_poly_clear(g_p);
nmod_poly_factor_clear(new_res_2);
}
}
nmod_poly_clear(g_1);
nmod_poly_clear(f_d);
nmod_poly_clear(g);
}
int
main(void)
{
int i, result = 1;
flint_rand_t state;
flint_randinit(state);
printf("asin_series....");
fflush(stdout);
/* Check asin(A) = atan(A/sqrt(1-A^2)) */
for (i = 0; i < 1000; i++)
{
nmod_poly_t A, B, asinA, atanB;
long n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
n = 1 + n_randtest(state) % 100;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(B, mod);
nmod_poly_init(asinA, mod);
nmod_poly_init(atanB, mod);
nmod_poly_randtest(A, state, n_randint(state, 100));
nmod_poly_set_coeff_ui(A, 0, 0UL);
nmod_poly_mullow(B, A, A, n);
nmod_poly_neg(B, B);
nmod_poly_set_coeff_ui(B, 0, 1UL);
nmod_poly_invsqrt_series(B, B, n);
nmod_poly_mullow(B, A, B, n);
nmod_poly_asin_series(asinA, A, n);
nmod_poly_atan_series(atanB, B, n);
result = nmod_poly_equal(asinA, atanB);
if (!result)
{
printf("FAIL:\n");
printf("n = %ld, mod = %lu\n", n, mod);
printf("A: "); nmod_poly_print(A), printf("\n\n");
printf("B: "); nmod_poly_print(B), printf("\n\n");
printf("asin(A): "); nmod_poly_print(asinA), printf("\n\n");
printf("atan(B): "); nmod_poly_print(atanB), printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(B);
nmod_poly_clear(asinA);
nmod_poly_clear(atanB);
}
/* Check aliasing */
for (i = 0; i < 1000; i++)
{
nmod_poly_t A, B;
long n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
n = n_randtest(state) % 50;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(B, mod);
nmod_poly_randtest(A, state, n_randint(state, 50));
nmod_poly_set_coeff_ui(A, 0, 0UL);
nmod_poly_asin_series(B, A, n);
nmod_poly_asin_series(A, A, n);
result = nmod_poly_equal(A, B);
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(A), printf("\n\n");
nmod_poly_print(B), printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(B);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
flint_randinit(state);
printf("invsqrt_series....");
fflush(stdout);
/* Check 1/g^2 = h mod x^m */
for (i = 0; i < 1000; i++)
{
nmod_poly_t h, g, r;
long m;
mp_limb_t n;
do n = n_randtest_prime(state, 0);
while (n == 2UL);
nmod_poly_init(h, n);
nmod_poly_init(g, n);
nmod_poly_init(r, n);
do nmod_poly_randtest(h, state, n_randint(state, 1000));
while (h->length == 0);
nmod_poly_set_coeff_ui(h, 0, 1UL);
m = n_randint(state, h->length) + 1;
nmod_poly_invsqrt_series(g, h, m);
nmod_poly_mullow(r, g, g, m);
nmod_poly_inv_series(r, r, m);
nmod_poly_truncate(h, m);
result = (nmod_poly_equal(r, h));
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(h), printf("\n\n");
nmod_poly_print(g), printf("\n\n");
nmod_poly_print(r), printf("\n\n");
printf("n = %ld\n", n);
abort();
}
nmod_poly_clear(h);
nmod_poly_clear(g);
nmod_poly_clear(r);
}
/* Check aliasing of h and g */
for (i = 0; i < 1000; i++)
{
nmod_poly_t g, h;
long m;
mp_limb_t n;
do n = n_randtest_prime(state, 0);
while (n == 2UL);
nmod_poly_init(h, n);
nmod_poly_init(g, n);
do nmod_poly_randtest(h, state, n_randint(state, 500));
while (h->length == 0);
nmod_poly_set_coeff_ui(h, 0, 1UL);
m = n_randint(state, h->length) + 1;
nmod_poly_invsqrt_series(g, h, m);
nmod_poly_invsqrt_series(h, h, m);
result = (nmod_poly_equal(g, h));
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(h), printf("\n\n");
nmod_poly_print(g), printf("\n\n");
printf("n = %ld, m = %ld\n", n, m);
abort();
}
nmod_poly_clear(g);
nmod_poly_clear(h);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("taylor_shift_horner....");
fflush(stdout);
/* Check aliasing */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_poly_t f, g;
mp_limb_t c, mod;
mod = n_randtest_prime(state, 0);
nmod_poly_init(f, mod);
nmod_poly_init(g, mod);
nmod_poly_randtest(f, state, 1 + n_randint(state, 50));
c = n_randtest(state) % mod;
nmod_poly_taylor_shift_horner(g, f, c);
nmod_poly_taylor_shift_horner(f, f, c);
if (!nmod_poly_equal(g, f))
{
flint_printf("FAIL\n");
nmod_poly_print(f); flint_printf("\n");
nmod_poly_print(g); flint_printf("\n");
abort();
}
nmod_poly_clear(f);
nmod_poly_clear(g);
}
/* Compare with composition */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_poly_t f, g, h1, h2;
mp_limb_t mod, c;
mod = n_randtest_prime(state, 0);
nmod_poly_init(f, mod);
nmod_poly_init(g, mod);
nmod_poly_init(h1, mod);
nmod_poly_init(h2, mod);
nmod_poly_randtest(f, state, 1 + n_randint(state, 50));
c = n_randtest(state) % mod;
nmod_poly_set_coeff_ui(g, 1, 1);
nmod_poly_set_coeff_ui(g, 0, c);
nmod_poly_taylor_shift_horner(h1, f, c);
nmod_poly_compose(h2, f, g);
if (!nmod_poly_equal(h1, h2))
{
flint_printf("FAIL\n");
nmod_poly_print(f); flint_printf("\n");
nmod_poly_print(g); flint_printf("\n");
nmod_poly_print(h1); flint_printf("\n");
nmod_poly_print(h2); flint_printf("\n");
abort();
}
nmod_poly_clear(f);
nmod_poly_clear(g);
nmod_poly_clear(h1);
nmod_poly_clear(h2);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
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
main(void)
{
int i, result = 1;
FLINT_TEST_INIT(state);
flint_printf("tan_series....");
fflush(stdout);
/* Check atan(tan(A)) = A */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
nmod_poly_t A, tanA, B;
slong n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
n = 1 + n_randtest(state) % 100;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(tanA, mod);
nmod_poly_init(B, mod);
nmod_poly_randtest(A, state, n_randint(state, 100));
nmod_poly_set_coeff_ui(A, 0, UWORD(0));
nmod_poly_tan_series(tanA, A, n);
nmod_poly_atan_series(B, tanA, n);
nmod_poly_truncate(A, n);
result = nmod_poly_equal(A, B);
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("n = %wd, mod = %wu\n", n, mod);
flint_printf("A: "); nmod_poly_print(A), flint_printf("\n\n");
flint_printf("tan(A): "); nmod_poly_print(tanA), flint_printf("\n\n");
flint_printf("B: "); nmod_poly_print(B), flint_printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(tanA);
nmod_poly_clear(B);
}
/* Check aliasing */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
nmod_poly_t A, B;
slong n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
n = n_randtest(state) % 50;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(B, mod);
nmod_poly_randtest(A, state, n_randint(state, 50));
nmod_poly_set_coeff_ui(A, 0, UWORD(0));
nmod_poly_tan_series(B, A, n);
nmod_poly_tan_series(A, A, n);
result = nmod_poly_equal(A, B);
if (!result)
{
flint_printf("FAIL:\n");
nmod_poly_print(A), flint_printf("\n\n");
nmod_poly_print(B), flint_printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(B);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("revert_series....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing */
for (i = 0; i < 100; i++)
{
nmod_poly_t f, g;
mp_limb_t m;
long n;
m = n_randtest_prime(state, 0);
nmod_poly_init(f, m);
nmod_poly_init(g, m);
do {
nmod_poly_randtest(g, state, n_randint(state, 100));
} while (nmod_poly_get_coeff_ui(g, 1) == 0);
nmod_poly_set_coeff_ui(g, 0, 0);
do {
n = n_randint(state, 100);
} while (n >= m);
nmod_poly_revert_series(f, g, n);
nmod_poly_revert_series(g, g, n);
result = (nmod_poly_equal(f, g));
if (!result)
{
printf("FAIL (aliasing):\n");
nmod_poly_print(f), printf("\n\n");
nmod_poly_print(g), printf("\n\n");
abort();
}
nmod_poly_clear(f);
nmod_poly_clear(g);
}
/* Check f(f^(-1)) = id */
for (i = 0; i < 1000; i++)
{
nmod_poly_t f, g, h;
mp_limb_t m;
long n;
m = n_randtest_prime(state, 0);
nmod_poly_init(f, m);
nmod_poly_init(g, m);
nmod_poly_init(h, m);
do {
nmod_poly_randtest(g, state, n_randint(state, 100));
} while (nmod_poly_get_coeff_ui(g, 1) == 0);
nmod_poly_set_coeff_ui(g, 0, 0);
do {
n = n_randint(state, 100);
} while (n >= m);
nmod_poly_revert_series(f, g, n);
nmod_poly_compose_series(h, g, f, n);
result = ((n <= 1 && nmod_poly_is_zero(h)) ||
(h->length == 2 && h->coeffs[0] == 0 && h->coeffs[1] == 1));
if (!result)
{
printf("FAIL (comparison):\n");
nmod_poly_print(g), printf("\n\n");
nmod_poly_print(f), printf("\n\n");
nmod_poly_print(h), printf("\n\n");
abort();
}
nmod_poly_clear(f);
nmod_poly_clear(g);
nmod_poly_clear(h);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
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);
}
}
}
int
main(void)
{
int i, result = 1;
flint_rand_t state;
flint_randinit(state);
printf("tanh_series....");
fflush(stdout);
/* Check atanh(tanh(A)) = A */
for (i = 0; i < 1000; i++)
{
nmod_poly_t A, tanhA, B;
long n;
mp_limb_t mod;
do { mod = n_randtest_prime(state, 0); } while (mod == 2);
n = 1 + n_randtest(state) % 100;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(tanhA, mod);
nmod_poly_init(B, mod);
nmod_poly_randtest(A, state, n_randint(state, 100));
nmod_poly_set_coeff_ui(A, 0, 0UL);
nmod_poly_tanh_series(tanhA, A, n);
nmod_poly_atanh_series(B, tanhA, n);
nmod_poly_truncate(A, n);
result = nmod_poly_equal(A, B);
if (!result)
{
printf("FAIL:\n");
printf("n = %ld, mod = %lu\n", n, mod);
printf("A: "); nmod_poly_print(A), printf("\n\n");
printf("tanh(A): "); nmod_poly_print(tanhA), printf("\n\n");
printf("B: "); nmod_poly_print(B), printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(tanhA);
nmod_poly_clear(B);
}
/* Check aliasing */
for (i = 0; i < 1000; i++)
{
nmod_poly_t A, B;
long n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
n = n_randtest(state) % 50;
n = FLINT_MIN(n, mod);
nmod_poly_init(A, mod);
nmod_poly_init(B, mod);
nmod_poly_randtest(A, state, n_randint(state, 50));
nmod_poly_set_coeff_ui(A, 0, 0UL);
nmod_poly_tanh_series(B, A, n);
nmod_poly_tanh_series(A, A, n);
result = nmod_poly_equal(A, B);
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(A), printf("\n\n");
nmod_poly_print(B), printf("\n\n");
abort();
}
nmod_poly_clear(A);
nmod_poly_clear(B);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
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;
}
int
main(void)
{
int iter;
FLINT_TEST_INIT(state);
flint_printf("is_squarefree....");
fflush(stdout);
for (iter = 0; iter < 200 * flint_test_multiplier(); iter++)
{
nmod_poly_t poly, Q, R, t;
mp_limb_t modulus;
slong i, num_factors, exp, max_exp;
int v, result;
modulus = n_randtest_prime(state, 0);
nmod_poly_init(poly, modulus);
nmod_poly_init(t, modulus);
nmod_poly_init(Q, modulus);
nmod_poly_init(R, modulus);
nmod_poly_set_coeff_ui(poly, 0, n_randint(state, modulus));
num_factors = n_randint(state, 5);
max_exp = 0;
for (i = 0; i < num_factors; i++)
{
do {
nmod_poly_randtest(t, state, n_randint(state, 10));
} while (!nmod_poly_is_irreducible(t) ||
(nmod_poly_length(t) < 2));
exp = n_randint(state, 4) + 1;
if (n_randint(state, 2) == 0)
exp = 1;
nmod_poly_divrem(Q, R, poly, t);
if (!nmod_poly_is_zero(R))
{
nmod_poly_pow(t, t, exp);
nmod_poly_mul(poly, poly, t);
max_exp = FLINT_MAX(exp, max_exp);
}
}
v = nmod_poly_is_squarefree(poly);
if (v == 1)
result = (max_exp <= 1 && !nmod_poly_is_zero(poly));
else
result = (max_exp > 1 || nmod_poly_is_zero(poly));
if (!result)
{
flint_printf("FAIL: %wu, %wd, %d\n", modulus, max_exp, v);
nmod_poly_print(poly); flint_printf("\n");
abort();
}
nmod_poly_clear(poly);
nmod_poly_clear(t);
nmod_poly_clear(Q);
nmod_poly_clear(R);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void embeddings_isomorphism_2(nmod_poly_t G, mp_srcptr F,
const embeddings_t FP, const embeddings_t FQ, const embeddings_t FR){
nmod_t mod = G->mod;
long m = nmod_poly_degree(FP->P);
long n = nmod_poly_degree(FQ->P);
long np = n + m - 1;
long p = ceil(sqrt(np));
long q = ceil((1.0*np)/p);
long i, j, k;
nmod_poly_t iT, iTm, T, X, tmp;
nmod_poly_struct *TT;
nmod_poly_init(iTm, mod.n);
nmod_poly_init(iT, mod.n);
nmod_poly_init(T, mod.n);
nmod_poly_init(X, mod.n);
nmod_poly_init(tmp, mod.n);
nmod_poly_mat_t MT, MH, MV;
nmod_poly_mat_init(MT, q, n, mod.n);
nmod_poly_mat_init(MH, p, q, mod.n);
nmod_poly_mat_init(MV, p, n, mod.n);
TT = flint_malloc(sizeof(nmod_poly_struct) * (q+1));
for (i = 0; i < q+1; i++)
nmod_poly_init(TT+i, mod.n);
nmod_poly_set_coeff_ui(X, 1, 1);
embeddings_embed(T, X, FQ, FP, FR);
nmod_poly_invmod(iT, T, FR->P);
nmod_poly_powmod_ui_binexp(iTm, iT, m-1, FR->P);
nmod_poly_zero(TT);
nmod_poly_set_coeff_ui(TT, 0, 1);
for (i = 1; i < q+1; i++)
nmod_poly_mulmod(TT+i, TT+(i-1), T, FR->P);
for (i = 0; i < q; i++)
for (j = 0; j < n; j++){
long jm = j*m;
for (k = 0; k < m; k++)
nmod_poly_set_coeff_ui(nmod_poly_mat_entry(MT, i, j), k, nmod_poly_get_coeff_ui(TT+i, k+jm));
}
for (i = 0; i < p; i++)
for (j = 0; j < q; j++){
long idx = i*q+j;
long lo = FLINT_MAX(0,m-1-idx);
long hi = FLINT_MIN(m,n+m-1-idx);
for (k = lo; k < hi; k++)
nmod_poly_set_coeff_ui(nmod_poly_mat_entry(MH, i, j), k, F[k*n+k+idx-m+1]);
}
nmod_poly_mat_mul(MV, MH, MT);
nmod_poly_zero(G);
for (i = p-1; i >= 0; i--){
nmod_poly_zero(tmp);
for (j = 0; j < n; j++){
long len = nmod_poly_mat_entry(MV, i, j)->length;
mp_ptr coefs = nmod_poly_mat_entry(MV, i, j)->coeffs;
long jm = j*m;
for (k = 0; k < len; k++)
nmod_poly_set_coeff_ui(tmp, k+jm, n_addmod(nmod_poly_get_coeff_ui(tmp, k+jm), coefs[k], mod.n));
}
nmod_poly_rem(tmp, tmp, FR->P);
nmod_poly_mulmod(G, G, TT+q, FR->P);
nmod_poly_add(G, G, tmp);
}
nmod_poly_mulmod(G, G, iTm, FR->P);
nmod_poly_clear(tmp);
nmod_poly_mat_clear(MT);
nmod_poly_mat_clear(MH);
nmod_poly_mat_clear(MV);
for (i = 0; i < q+1; i++)
nmod_poly_clear(TT+i);
flint_free(TT);
nmod_poly_clear(iTm);
nmod_poly_clear(iT);
nmod_poly_clear(T);
nmod_poly_clear(X);
}
