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;
}
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(void)
{
flint_rand_t state;
int iter;
printf("one/is_one....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
nmod_poly_mat_t A;
long m, n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 10);
n = n_randint(state, 10);
nmod_poly_mat_init(A, m, n, mod);
nmod_poly_mat_randtest(A, state, n_randint(state, 5));
nmod_poly_mat_one(A);
if (!nmod_poly_mat_is_one(A))
{
printf("FAIL: expected matrix to be one\n");
abort();
}
if (m > 0 && n > 0)
{
m = n_randint(state, m);
n = n_randint(state, n);
if (m != n)
nmod_poly_randtest_not_zero(nmod_poly_mat_entry(A, m, n),
state, 5);
else
do { nmod_poly_randtest_not_zero(nmod_poly_mat_entry(A, m, n),
state, 5); }
while (nmod_poly_is_one(nmod_poly_mat_entry(A, m, n)));
if (nmod_poly_mat_is_one(A))
{
printf("FAIL: expected matrix not to be one\n");
abort();
}
}
nmod_poly_mat_clear(A);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
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 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;
}
int
main(void)
{
int i, result = 1;
flint_rand_t state;
flint_randinit(state);
printf("interpolate_nmod_vec_fast....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
nmod_poly_t P, Q;
mp_ptr x, y;
mp_limb_t mod;
long j, n, npoints;
mod = n_randtest_prime(state, 0);
npoints = n_randint(state, FLINT_MIN(100, mod));
n = n_randint(state, npoints + 1);
nmod_poly_init(P, mod);
nmod_poly_init(Q, mod);
x = _nmod_vec_init(npoints);
y = _nmod_vec_init(npoints);
nmod_poly_randtest(P, state, n);
for (j = 0; j < npoints; j++)
x[j] = j;
nmod_poly_evaluate_nmod_vec_fast(y, P, x, npoints);
nmod_poly_interpolate_nmod_vec_fast(Q, x, y, npoints);
result = nmod_poly_equal(P, Q);
if (!result)
{
printf("FAIL:\n");
printf("mod=%lu, n=%ld, npoints=%ld\n\n", mod, n, npoints);
nmod_poly_print(P), printf("\n\n");
nmod_poly_print(Q), printf("\n\n");
abort();
}
nmod_poly_clear(P);
nmod_poly_clear(Q);
_nmod_vec_clear(x);
_nmod_vec_clear(y);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int main(void)
{
flint_rand_t state;
long i, j;
printf("bell_number_nmod....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 10; i++)
{
mp_ptr b;
long n;
nmod_t mod;
mp_limb_t p;
n = n_randint(state, 1000);
p = n_randtest_prime(state, 0);
nmod_init(&mod, p);
b = _nmod_vec_init(n + 1);
bell_number_nmod_vec(b, n + 1, mod);
for (j = 0; j <= n; j++)
{
mp_limb_t u = bell_number_nmod(j, mod);
if (u != b[j])
{
printf("FAIL: p = %lu, i = %ld\n", p, j);
abort();
}
}
_nmod_vec_clear(b);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i;
flint_rand_t state;
printf("sqrt... ");
fflush(stdout);
flint_randinit(state);
/* Test aliasing */
for (i = 0; i < 2000; i++)
{
nmod_poly_t a, b;
int square1, square2;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
nmod_poly_init(a, mod);
nmod_poly_init(b, mod);
nmod_poly_randtest(a, state, 1 + n_randint(state, 50));
if (n_randint(state, 2))
nmod_poly_mul(a, a, a);
square1 = nmod_poly_sqrt(b, a);
square2 = nmod_poly_sqrt(a, a);
if ((square1 != square2) || (square1 && !nmod_poly_equal(a, b)))
{
printf("FAIL: aliasing:\n");
printf("square1 = %d, square2 = %d\n\n", square1, square2);
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
}
/* Test random squares */
for (i = 0; i < 2000; i++)
{
nmod_poly_t a, b, c;
int square;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
nmod_poly_init(a, mod);
nmod_poly_init(b, mod);
nmod_poly_init(c, mod);
nmod_poly_randtest(a, state, 1 + n_randint(state, 50));
nmod_poly_mul(b, a, a);
square = nmod_poly_sqrt(c, b);
if (!square)
{
printf("FAIL: square reported nonsquare:\n");
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
printf("c: "); nmod_poly_print(c); printf("\n\n");
abort();
}
nmod_poly_mul(c, c, c);
if (!nmod_poly_equal(c, b))
{
printf("FAIL: sqrt(b)^2 != b:\n");
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
printf("c: "); nmod_poly_print(c); printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(c);
}
/* Test "almost" squares */
for (i = 0; i < 2000; i++)
{
nmod_poly_t a, b, c;
long j;
int square;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
nmod_poly_init(a, mod);
nmod_poly_init(b, mod);
nmod_poly_init(c, mod);
nmod_poly_randtest_not_zero(a, state, 1 + n_randint(state, 50));
nmod_poly_mul(b, a, a);
j = n_randint(state, nmod_poly_length(b));
b->coeffs[j] = n_randint(state, mod);
_nmod_poly_normalise(b);
square = nmod_poly_sqrt(c, b);
if (square)
{
nmod_poly_mul(c, c, c);
if (!nmod_poly_equal(c, b))
{
printf("FAIL: sqrt(b)^2 != b:\n");
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
printf("c: "); nmod_poly_print(c); printf("\n\n");
abort();
}
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(c);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int main()
{
flint_rand_t state;
long iter;
printf("poly_divrem_basecase....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
ring_t ZZ, ZZp, ZZpx[3];
ring_struct * ring;
elem_ptr p;
long size[3];
elem_poly_t A, B, C, Q, Q2, R, R2;
ring_init_limb(ZZ);
ELEM_TMP_INIT(p, ZZ);
elem_set_ui(p, n_randtest_prime(state, 0), ZZ);
ring_init_mod(ZZp, ZZ, p);
ring_init_poly(ZZpx[0], ZZp);
ring_init_poly(ZZpx[1], ZZpx[0]);
ring_init_poly(ZZpx[2], ZZpx[1]);
ring = ZZpx[n_randint(state, 2)];
size[0] = 1 + n_randint(state, 30);
size[1] = 1 + n_randint(state, 30);
size[2] = 1 + n_randint(state, 30);
elem_init(A, ring);
elem_init(B, ring);
elem_init(C, ring);
elem_init(Q, ring);
elem_init(Q2, ring);
elem_init(R, ring);
elem_init(R2, ring);
elem_randtest(A, state, size, ring);
elem_randtest_not_zero(B, state, size, ring);
elem_mul(C, A, B, ring);
elem_poly_divrem_basecase(Q, R, C, B, ring);
if (!elem_equal(Q, A, ring) || !elem_is_zero(R, ring))
{
printf("FAIL: (A * B) / B = A\n");
elem_print(A, ring); printf("\n\n");
elem_print(B, ring); printf("\n\n");
elem_print(C, ring); printf("\n\n");
elem_print(Q, ring); printf("\n\n");
elem_print(R, ring); printf("\n\n");
abort();
}
elem_divrem(Q, R, A, B, ring);
elem_mul(C, Q, B, ring);
elem_add(C, C, R, ring);
if (!elem_equal(C, A, ring))
{
printf("FAIL: Q * B + R = A\n");
elem_print(A, ring); printf("\n\n");
elem_print(B, ring); printf("\n\n");
elem_print(C, ring); printf("\n\n");
elem_print(Q, ring); printf("\n\n");
elem_print(R, ring); printf("\n\n");
abort();
}
elem_randtest(A, state, size, ring);
elem_randtest_not_zero(B, state, size, ring);
elem_poly_divrem_basecase(Q, R, A, B, ring);
elem_poly_divrem_basecase(A, R2, A, B, ring);
if (!elem_equal(A, Q, ring) || !elem_equal(R, R2, ring))
{
printf("FAIL: aliasing Q, A\n");
elem_print(A, ring); printf("\n\n");
elem_print(B, ring); printf("\n\n");
elem_print(Q, ring); printf("\n\n");
elem_print(R, ring); printf("\n\n");
elem_print(R2, ring); printf("\n\n");
abort();
}
elem_randtest(A, state, size, ring);
elem_randtest_not_zero(B, state, size, ring);
elem_poly_divrem_basecase(Q, R, A, B, ring);
elem_poly_divrem_basecase(Q2, A, A, B, ring);
if (!elem_equal(A, R, ring) || !elem_equal(Q, Q2, ring))
{
printf("FAIL: aliasing R, A\n");
elem_print(A, ring); printf("\n\n");
elem_print(B, ring); printf("\n\n");
elem_print(Q, ring); printf("\n\n");
elem_print(Q2, ring); printf("\n\n");
elem_print(R, ring); printf("\n\n");
abort();
}
elem_randtest(A, state, size, ring);
elem_randtest_not_zero(B, state, size, ring);
elem_poly_divrem_basecase(Q, R, A, B, ring);
elem_poly_divrem_basecase(Q2, B, A, B, ring);
if (!elem_equal(B, R, ring) || !elem_equal(Q, Q2, ring))
{
printf("FAIL: aliasing R, B\n");
elem_print(A, ring); printf("\n\n");
elem_print(B, ring); printf("\n\n");
elem_print(Q, ring); printf("\n\n");
elem_print(Q2, ring); printf("\n\n");
elem_print(R, ring); printf("\n\n");
abort();
}
elem_randtest(A, state, size, ring);
elem_randtest_not_zero(B, state, size, ring);
elem_poly_divrem_basecase(Q, R, A, B, ring);
elem_poly_divrem_basecase(B, R2, A, B, ring);
if (!elem_equal(B, Q, ring) || !elem_equal(R, R2, ring))
{
printf("FAIL: aliasing Q, B\n");
elem_print(A, ring); printf("\n\n");
elem_print(B, ring); printf("\n\n");
elem_print(Q, ring); printf("\n\n");
elem_print(R, ring); printf("\n\n");
elem_print(R2, ring); printf("\n\n");
abort();
}
elem_clear(A, ring);
elem_clear(B, ring);
elem_clear(C, ring);
elem_clear(Q, ring);
elem_clear(Q2, ring);
elem_clear(R, ring);
elem_clear(R2, ring);
ring_clear(ZZpx[2]);
ring_clear(ZZpx[1]);
ring_clear(ZZpx[0]);
ring_clear(ZZp);
ELEM_TMP_CLEAR(p, ZZ);
ring_clear(ZZ);
}
printf("PASS\n");
flint_randclear(state);
return EXIT_SUCCESS;
}
/*------------------------------------------------------------*/
void check(int opt){
long i;
flint_rand_t state;
flint_randinit(state);
for (i = 1; i < 1000; i+=10){
mp_limb_t n = 0;
while (n < i)
n = n_randtest_prime(state, 0);
nmod_poly_t P;
mp_ptr roots;
nmod_poly_t A;
nmod_poly_init(P, n);
roots = _nmod_vec_init(i);
_nmod_vec_randtest(roots, state, i, P->mod);
nmod_poly_product_roots_nmod_vec(P, roots, i);
nmod_poly_init(A, n);
nmod_poly_rand_dense(A, state, i);
if (opt == 1){
mp_limb_t tr1 = nmod_poly_trace(A, P);
mp_limb_t tr2 = 0;
long j;
for (j = 0; j < i; j++)
tr2 = nmod_add(tr2, nmod_poly_evaluate_nmod(A, roots[j]), P->mod);
sage_output_init(P->mod);
sage_output_assign_poly(P, "P");
printf("tr1 = %lu\n", tr1);
printf("tr2 = %lu\n", tr2);
printf("tr1 == tr2\n");
}
else{
double t, u;
long j;
t = util_gettime();
for (j = 0; j < 10000; j++)
nmod_poly_trace(A, P);
t = util_gettime() - t;
nmod_poly_t tmp1, tmp2, tmp3;
nmod_poly_init(tmp1, n);
nmod_poly_init(tmp2, n);
nmod_poly_init(tmp3, n);
nmod_poly_rand_dense(tmp1, state, i);
nmod_poly_rand_dense(tmp2, state, i);
u = util_gettime();
for (j = 0; j < 10000; j++)
nmod_poly_mul(tmp3, tmp1, tmp2);
u = util_gettime() - u;
nmod_poly_clear(tmp1);
nmod_poly_clear(tmp2);
nmod_poly_clear(tmp3);
printf("%lu %f %f\n", i, t, u);
}
nmod_poly_clear(P);
nmod_poly_clear(A);
_nmod_vec_clear(roots);
}
}
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;
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)
{
flint_rand_t state;
long i;
printf("mul_interpolate....");
fflush(stdout);
flint_randinit(state);
/* Check evaluation homomorphism */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B, C;
nmod_mat_t a, b, c, d;
mp_limb_t mod, x;
long m, n, k, deg;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
k = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, n, mod);
nmod_poly_mat_init(B, n, k, mod);
nmod_poly_mat_init(C, m, k, mod);
nmod_mat_init(a, m, n, mod);
nmod_mat_init(b, n, k, mod);
nmod_mat_init(c, m, k, mod);
nmod_mat_init(d, m, k, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
if (nmod_poly_mat_max_length(A)
+ nmod_poly_mat_max_length(B) - 1 <= mod)
{
nmod_poly_mat_mul_interpolate(C, A, B);
x = n_randint(state, mod);
nmod_poly_mat_evaluate_nmod(a, A, x);
nmod_poly_mat_evaluate_nmod(b, B, x);
nmod_poly_mat_evaluate_nmod(d, C, x);
nmod_mat_mul(c, a, b);
if (!nmod_mat_equal(c, d))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
nmod_poly_mat_clear(C);
nmod_mat_clear(a);
nmod_mat_clear(b);
nmod_mat_clear(c);
nmod_mat_clear(d);
}
/* Check aliasing C and A */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B, C;
long m, n, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, n, mod);
nmod_poly_mat_init(B, n, n, mod);
nmod_poly_mat_init(C, m, n, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
if (nmod_poly_mat_max_length(A)
+ nmod_poly_mat_max_length(B) - 1 <= mod)
{
nmod_poly_mat_mul_interpolate(C, A, B);
nmod_poly_mat_mul_interpolate(A, A, B);
if (!nmod_poly_mat_equal(C, A))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
nmod_poly_mat_clear(C);
}
/* Check aliasing C and B */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B, C;
long m, n, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
n = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(B, m, n, mod);
nmod_poly_mat_init(C, m, n, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
if (nmod_poly_mat_max_length(A)
+ nmod_poly_mat_max_length(B) - 1 <= mod)
{
nmod_poly_mat_mul_interpolate(C, A, B);
nmod_poly_mat_mul_interpolate(B, A, B);
if (!nmod_poly_mat_equal(C, B))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
nmod_poly_mat_clear(C);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
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)
{
flint_rand_t state;
long i;
printf("sqr....");
fflush(stdout);
flint_randinit(state);
/* Check evaluation homomorphism */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, C;
nmod_mat_t a, c, d;
mp_limb_t x, mod;
long m, deg;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(C, m, m, mod);
nmod_mat_init(a, m, m, mod);
nmod_mat_init(c, m, m, mod);
nmod_mat_init(d, m, m, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(C, state, deg); /* noise in output */
nmod_poly_mat_sqr(C, A);
x = n_randint(state, 0);
nmod_poly_mat_evaluate_nmod(a, A, x);
nmod_poly_mat_evaluate_nmod(d, C, x);
nmod_mat_mul(c, a, a);
if (!nmod_mat_equal(c, d))
{
printf("FAIL:\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(C);
nmod_mat_clear(a);
nmod_mat_clear(c);
nmod_mat_clear(d);
}
/* Check aliasing B and A */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B;
long m, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 20);
deg = 1 + n_randint(state, 10);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(B, m, m, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_randtest(B, state, deg); /* noise in output */
nmod_poly_mat_sqr(B, A);
nmod_poly_mat_sqr(A, A);
if (!nmod_poly_mat_equal(B, A))
{
printf("FAIL (aliasing):\n");
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("\n");
abort();
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int iter;
FLINT_TEST_INIT(state);
flint_printf("factor_squarefree....");
fflush(stdout);
for (iter = 0; iter < 300; iter++)
{
int result = 1;
fmpz_mod_poly_t pol1, poly, quot, rem;
fmpz_mod_poly_factor_t res;
fmpz_t modulus;
slong exp[5], prod1;
slong length, i, j, num;
fmpz_init_set_ui(modulus, n_randtest_prime(state, 0));
fmpz_mod_poly_init(pol1, modulus);
fmpz_mod_poly_init(poly, modulus);
fmpz_mod_poly_init(quot, modulus);
fmpz_mod_poly_init(rem, modulus);
fmpz_mod_poly_zero(pol1);
fmpz_mod_poly_set_coeff_ui(pol1, 0, 1);
length = n_randint(state, 7) + 2;
do
{
fmpz_mod_poly_randtest(poly, state, length);
fmpz_mod_poly_make_monic(poly, poly);
}
while ((!fmpz_mod_poly_is_irreducible(poly)) || (poly->length < 2));
exp[0] = n_randprime(state, 5, 0);
prod1 = exp[0];
for (i = 0; i < exp[0]; i++)
fmpz_mod_poly_mul(pol1, pol1, poly);
num = n_randint(state, 5) + 1;
for (i = 1; i < num; i++)
{
do
{
length = n_randint(state, 7) + 2;
fmpz_mod_poly_randtest(poly, state, length);
if (poly->length)
{
fmpz_mod_poly_make_monic(poly, poly);
fmpz_mod_poly_divrem(quot, rem, pol1, poly);
}
}
while ((!fmpz_mod_poly_is_irreducible(poly)) ||
(poly->length < 2) || (rem->length == 0));
do
exp[i] = n_randprime(state, 5, 0);
while (prod1 % exp[i] == 0);
prod1 *= exp[i];
for (j = 0; j < exp[i]; j++)
fmpz_mod_poly_mul(pol1, pol1, poly);
}
fmpz_mod_poly_factor_init(res);
fmpz_mod_poly_factor_squarefree(res, pol1);
result &= (res->num == num);
if (result)
{
ulong prod2 = 1;
for (i = 0; i < num; i++)
prod2 *= res->exp[i];
result &= (prod1 == prod2);
}
if (!result)
{
flint_printf("Error: exp don't match. Modulus = ");
fmpz_print(modulus);
flint_printf("\n");
for (i = 0; i < res->num; i++)
flint_printf("%wd ", res->exp[i]);
flint_printf("\n");
for (i = 0; i < num; i++)
flint_printf("%wd ", exp[i]);
flint_printf("\n");
abort();
}
fmpz_clear(modulus);
fmpz_mod_poly_clear(quot);
fmpz_mod_poly_clear(rem);
fmpz_mod_poly_clear(pol1);
fmpz_mod_poly_clear(poly);
fmpz_mod_poly_factor_clear(res);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
padic_ctx_t ctx;
fmpz_t p;
slong N;
FLINT_TEST_INIT(state);
flint_printf("inv_series... ");
fflush(stdout);
/* Check aliasing */
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
slong n;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_randtest(a, state, n_randint(state, 100) + 1, ctx);
if (fmpz_is_zero(a->coeffs))
{
fmpz_randtest_not_zero(a->coeffs, state, 20);
fmpz_remove(a->coeffs, a->coeffs, p);
padic_poly_reduce(a, ctx);
} else
fmpz_remove(a->coeffs, a->coeffs, p);
padic_poly_set(b, a, ctx);
n = n_randint(state, 100) + 1;
padic_poly_inv_series(c, b, n, ctx);
padic_poly_inv_series(b, b, n, ctx);
result = (padic_poly_equal(b, c) && padic_poly_is_reduced(b, ctx));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), padic_poly_print(a, ctx), flint_printf("\n\n");
flint_printf("b = "), padic_poly_print(b, ctx), flint_printf("\n\n");
flint_printf("c = "), padic_poly_print(c, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/*
Check correctness:
If ord_p(a) = v then we can compute b = a^{-1} mod p^N
and we will have a b = 1 mod p^{N-|v|}. Thus, require
that N - |v| > 0.
*/
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
slong n, N2;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - 1) + 1;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
{
slong i, len = n_randint(state, 10) + 1;
int alloc;
fmpz_t pow;
padic_poly_fit_length(a, len);
_padic_poly_set_length(a, len);
a->val = n_randint(state, N);
if (n_randint(state, 2))
a->val = - a->val;
alloc = _padic_ctx_pow_ui(pow, N - a->val, ctx);
for (i = 0; i < len; i++)
fmpz_randm(a->coeffs + i, state, pow);
while (fmpz_is_zero(a->coeffs))
fmpz_randm(a->coeffs, state, pow);
fmpz_remove(a->coeffs, a->coeffs, p);
_padic_poly_normalise(a);
if (alloc)
fmpz_clear(pow);
}
n = n_randint(state, 100) + 1;
N2 = N - FLINT_ABS(a->val);
padic_poly_init2(c, 0, N2);
padic_poly_inv_series(b, a, n, ctx);
padic_poly_mul(c, a, b, ctx);
padic_poly_truncate(c, n, p);
result = (padic_poly_is_one(c) && padic_poly_is_reduced(b, ctx));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), padic_poly_print(a, ctx), flint_printf("\n\n");
flint_printf("b = "), padic_poly_print(b, ctx), flint_printf("\n\n");
flint_printf("c = "), padic_poly_print(c, ctx), flint_printf("\n\n");
flint_printf("N = %wd\n", N);
flint_printf("N2 = %wd\n", N2);
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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;
}
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;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("log... ");
fflush(stdout);
/** p == 2 *******************************************************************/
/* Check aliasing: a = log(a) */
for (i = 0; i < 1000; i++)
{
fmpz_t p = {WORD(2)};
slong N;
padic_ctx_t ctx;
padic_t a, b;
int ans1, ans2;
N = __rand_prec(state, i);
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_init2(a, N);
padic_init2(b, N);
padic_randtest(a, state, ctx);
padic_one(b);
padic_add(a, a, b, ctx);
ans1 = padic_log(b, a, ctx);
ans2 = padic_log(a, a, ctx);
result = (ans1 == ans2) && (!ans1 || padic_equal(a, b));
if (!result)
{
flint_printf("FAIL (aliasing):\n\n");
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
abort();
}
padic_clear(a);
padic_clear(b);
padic_ctx_clear(ctx);
}
/* Check: log(a) + log(b) == log(a * b) */
for (i = 0; i < 10000; i++)
{
fmpz_t p = {WORD(2)};
slong N;
padic_ctx_t ctx;
padic_t a, b, c, d, e, f, g;
int ans1, ans2, ans3;
N = __rand_prec(state, i);
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_init2(a, N);
padic_init2(b, N);
padic_init2(c, N);
padic_init2(d, N);
padic_init2(e, N);
padic_init2(f, N);
padic_init2(g, N);
padic_randtest(a, state, ctx);
padic_randtest(b, state, ctx);
padic_one(c);
padic_add(a, a, c, ctx);
padic_add(b, b, c, ctx);
padic_mul(c, a, b, ctx);
ans1 = padic_log(d, a, ctx);
ans2 = padic_log(e, b, ctx);
padic_add(f, d, e, ctx);
ans3 = padic_log(g, c, ctx);
result = (!ans1 || !ans2 || (ans3 && padic_equal(f, g)));
if (!result)
{
flint_printf("FAIL (functional equation):\n\n");
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
flint_printf("c = a * b = "), padic_print(c, ctx), flint_printf("\n");
flint_printf("d = log(a) = "), padic_print(d, ctx), flint_printf("\n");
flint_printf("e = log(b) = "), padic_print(e, ctx), flint_printf("\n");
flint_printf("f = log(a) + log(b) = "), padic_print(f, ctx), flint_printf("\n");
flint_printf("g = log(a * b) = "), padic_print(g, ctx), flint_printf("\n");
abort();
}
padic_clear(a);
padic_clear(b);
padic_clear(c);
padic_clear(d);
padic_clear(e);
padic_clear(f);
padic_clear(g);
padic_ctx_clear(ctx);
}
/* Check: log(exp(x)) == x */
for (i = 0; i < 10000; i++)
{
fmpz_t p = {WORD(2)};
slong N;
padic_ctx_t ctx;
padic_t a, b, c;
int ans1, ans2;
N = __rand_prec(state, i);
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_init2(a, N);
padic_init2(b, N);
padic_init2(c, N);
padic_randtest(a, state, ctx);
ans1 = padic_exp(b, a, ctx);
if (ans1)
ans2 = padic_log(c, b, ctx);
result = !ans1 || (ans1 == ans2 && padic_equal(a, c));
if (!result)
{
flint_printf("FAIL (log(exp(x)) == x):\n\n");
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
flint_printf("c = "), padic_print(c, ctx), flint_printf("\n");
flint_printf("ans1 = %d\n", ans1);
flint_printf("ans2 = %d\n", ans2);
abort();
}
padic_clear(a);
padic_clear(b);
padic_clear(c);
padic_ctx_clear(ctx);
}
/** p > 2 ********************************************************************/
/* Check aliasing: a = log(a) */
for (i = 0; i < 1000; i++)
{
fmpz_t p;
slong N;
padic_ctx_t ctx;
padic_t a, b;
int ans1, ans2;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = __rand_prec(state, i);
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_init2(a, N);
padic_init2(b, N);
padic_randtest(a, state, ctx);
padic_one(b);
padic_add(a, a, b, ctx);
ans1 = padic_log(b, a, ctx);
ans2 = padic_log(a, a, ctx);
result = (ans1 == ans2) && (!ans1 || padic_equal(a, b));
if (!result)
{
flint_printf("FAIL (aliasing):\n\n");
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
abort();
}
padic_clear(a);
padic_clear(b);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
/* Check: log(a) + log(b) == log(a * b) */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
slong N;
padic_ctx_t ctx;
padic_t a, b, c, d, e, f, g;
int ans1, ans2, ans3;
/* fmpz_init_set_ui(p, n_randtest_prime(state, 0)); */
fmpz_init_set_ui(p, n_randprime(state, 5, 1));
N = __rand_prec(state, i);
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_init2(a, N);
padic_init2(b, N);
padic_init2(c, N);
padic_init2(d, N);
padic_init2(e, N);
padic_init2(f, N);
padic_init2(g, N);
padic_randtest(a, state, ctx);
padic_randtest(b, state, ctx);
padic_one(c);
padic_add(a, a, c, ctx);
padic_one(c);
padic_add(b, b, c, ctx);
padic_mul(c, a, b, ctx);
ans1 = padic_log(d, a, ctx);
ans2 = padic_log(e, b, ctx);
padic_add(f, d, e, ctx);
ans3 = padic_log(g, c, ctx);
result = (!ans1 || !ans2 || (ans3 && padic_equal(f, g)));
if (!result)
{
flint_printf("FAIL (functional equation):\n\n");
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
flint_printf("c = a * b = "), padic_print(c, ctx), flint_printf("\n");
flint_printf("d = log(a) = "), padic_print(d, ctx), flint_printf("\n");
flint_printf("e = log(b) = "), padic_print(e, ctx), flint_printf("\n");
flint_printf("f = log(a) + log(b) = "), padic_print(f, ctx), flint_printf("\n");
flint_printf("g = log(a * b) = "), padic_print(g, ctx), flint_printf("\n");
flint_printf("ans1 = %d\n", ans1);
flint_printf("ans2 = %d\n", ans2);
flint_printf("ans3 = %d\n", ans3);
abort();
}
padic_clear(a);
padic_clear(b);
padic_clear(c);
padic_clear(d);
padic_clear(e);
padic_clear(f);
padic_clear(g);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
/* Check: log(exp(x)) == x */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
slong N;
padic_ctx_t ctx;
padic_t a, b, c;
int ans1, ans2;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = __rand_prec(state, i);
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_init2(a, N);
padic_init2(b, N);
padic_init2(c, N);
padic_randtest(a, state, ctx);
ans1 = padic_exp(b, a, ctx);
if (ans1)
ans2 = padic_log(c, b, ctx);
result = !ans1 || (ans1 == ans2 && padic_equal(a, c));
if (!result)
{
flint_printf("FAIL (log(exp(x)) == x):\n\n");
flint_printf("a = "), padic_print(a, ctx), flint_printf("\n");
flint_printf("b = "), padic_print(b, ctx), flint_printf("\n");
flint_printf("c = "), padic_print(c, ctx), flint_printf("\n");
flint_printf("ans1 = %d\n", ans1);
flint_printf("ans2 = %d\n", ans2);
abort();
}
padic_clear(a);
padic_clear(b);
padic_clear(c);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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 i, result;
FLINT_TEST_INIT(state);
flint_printf("xgcd....");
fflush(stdout);
/* Generic case, most likely co-prime arguments ******************************/
/* Compare with result from GCD and check correctness */
for (i = 0; i < 1000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, d, g, s, t, v, w;
fmpz_init(p);
fmpz_set_ui(p, n_randtest_prime(state, 0));
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(d, p);
fmpz_mod_poly_init(g, p);
fmpz_mod_poly_init(s, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_init(v, p);
fmpz_mod_poly_init(w, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest(b, state, n_randint(state, 100));
fmpz_mod_poly_gcd(d, a, b);
fmpz_mod_poly_xgcd(g, s, t, a, b);
fmpz_mod_poly_mul(v, s, a);
fmpz_mod_poly_mul(w, t, b);
fmpz_mod_poly_add(w, v, w);
result = (fmpz_mod_poly_equal(d, g) && fmpz_mod_poly_equal(g, w));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_mod_poly_print(a), flint_printf("\n\n");
fmpz_mod_poly_print(b), flint_printf("\n\n");
fmpz_mod_poly_print(d), flint_printf("\n\n");
fmpz_mod_poly_print(g), flint_printf("\n\n");
fmpz_mod_poly_print(s), flint_printf("\n\n");
fmpz_mod_poly_print(t), flint_printf("\n\n");
fmpz_mod_poly_print(v), flint_printf("\n\n");
fmpz_mod_poly_print(w), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(d);
fmpz_mod_poly_clear(g);
fmpz_mod_poly_clear(s);
fmpz_mod_poly_clear(t);
fmpz_mod_poly_clear(v);
fmpz_mod_poly_clear(w);
fmpz_clear(p);
}
/* Special case, arguments share a factor ********************************/
/* Compare with result from GCD and check correctness */
for (i = 0; i < 1000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, d, f, g, s, t, v, w;
fmpz_init(p);
fmpz_set_ui(p, n_randtest_prime(state, 0));
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(d, p);
fmpz_mod_poly_init(f, p);
fmpz_mod_poly_init(g, p);
fmpz_mod_poly_init(s, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_init(v, p);
fmpz_mod_poly_init(w, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest(b, state, n_randint(state, 100));
fmpz_mod_poly_randtest(f, state, n_randint(state, 20));
fmpz_mod_poly_mul(a, a, f);
fmpz_mod_poly_mul(b, b, f);
fmpz_mod_poly_gcd(d, a, b);
fmpz_mod_poly_xgcd(g, s, t, a, b);
fmpz_mod_poly_mul(v, s, a);
fmpz_mod_poly_mul(w, t, b);
fmpz_mod_poly_add(w, v, w);
result = (fmpz_mod_poly_equal(d, g) && fmpz_mod_poly_equal(g, w));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_mod_poly_print(a), flint_printf("\n\n");
fmpz_mod_poly_print(b), flint_printf("\n\n");
fmpz_mod_poly_print(d), flint_printf("\n\n");
fmpz_mod_poly_print(f), flint_printf("\n\n");
fmpz_mod_poly_print(g), flint_printf("\n\n");
fmpz_mod_poly_print(s), flint_printf("\n\n");
fmpz_mod_poly_print(t), flint_printf("\n\n");
fmpz_mod_poly_print(v), flint_printf("\n\n");
fmpz_mod_poly_print(w), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(d);
fmpz_mod_poly_clear(f);
fmpz_mod_poly_clear(g);
fmpz_mod_poly_clear(s);
fmpz_mod_poly_clear(t);
fmpz_mod_poly_clear(v);
fmpz_mod_poly_clear(w);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
flint_rand_t state;
long i;
printf("pow....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B, C;
long m, j, exp, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 6);
deg = 1 + n_randint(state, 6);
exp = n_randint(state, 20);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(B, m, m, mod);
nmod_poly_mat_init(C, m, m, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_pow(B, A, exp);
nmod_poly_mat_one(C);
for (j = 0; j < exp; j++)
nmod_poly_mat_mul(C, C, A);
if (!nmod_poly_mat_equal(C, B))
{
printf("FAIL:\n");
printf("exp = %ld\n", exp);
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("C:\n");
nmod_poly_mat_print(C, "x");
printf("\n");
abort();
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
nmod_poly_mat_clear(C);
}
/* Check aliasing B and A */
for (i = 0; i < 1000; i++)
{
nmod_poly_mat_t A, B;
long m, exp, deg;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 6);
deg = 1 + n_randint(state, 6);
exp = n_randint(state, 20);
nmod_poly_mat_init(A, m, m, mod);
nmod_poly_mat_init(B, m, m, mod);
nmod_poly_mat_randtest(A, state, deg);
nmod_poly_mat_pow(B, A, exp);
nmod_poly_mat_pow(A, A, exp);
if (!nmod_poly_mat_equal(A, B))
{
printf("FAIL (aliasing)\n");
printf("exp = %ld\n", exp);
printf("A:\n");
nmod_poly_mat_print(A, "x");
printf("B:\n");
nmod_poly_mat_print(B, "x");
printf("\n");
abort();
}
nmod_poly_mat_clear(A);
nmod_poly_mat_clear(B);
}
flint_randclear(state);
_fmpz_cleanup();
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()
{
long i, j;
int sign;
fmpz_t input;
fmpz_t result;
fmpz_t r1;
fmpz_t m1;
fmpz_t mprod;
ulong r2, m2;
flint_rand_t state;
printf("CRT_ui....");
fflush(stdout);
fmpz_init(input);
fmpz_init(result);
fmpz_init(r1);
fmpz_init(m1);
fmpz_init(mprod);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
long nprimes;
m2 = n_randtest_prime(state, 0);
nprimes = 1 + n_randint(state, 4);
fmpz_set_ui(m1, 1UL);
for (j = 0; j < nprimes; )
{
ulong t = n_randtest_prime(state, 0);
if (t != m2)
{
fmpz_mul_ui(m1, m1, t);
j++;
}
}
fmpz_mul_ui(mprod, m1, m2);
sign = n_randint(state, 2);
if (sign)
fmpz_randtest_mod_signed(input, state, mprod);
else
fmpz_randtest_mod(input, state, mprod);
fmpz_mod(r1, input, m1);
r2 = fmpz_fdiv_ui(input, m2);
if (sign)
fmpz_CRT_ui(result, r1, m1, r2, m2);
else
fmpz_CRT_ui_unsigned(result, r1, m1, r2, m2);
if (!fmpz_equal(result, input))
{
printf("FAIL:\n");
printf("m1: "); fmpz_print(m1); printf("\n");
printf("m2: %lu\n", m2);
printf("m1*m2: "); fmpz_print(mprod); printf("\n");
printf("input: "); fmpz_print(input); printf("\n");
printf("r1: "); fmpz_print(r1); printf("\n");
printf("r2: %lu\n", r2);
printf("result: "); fmpz_print(result); printf("\n");
printf("%ld Equalness: %d\n", i, fmpz_equal(result, input));
printf("\n");
abort();
}
}
fmpz_clear(input);
fmpz_clear(result);
fmpz_clear(r1);
fmpz_clear(m1);
fmpz_clear(mprod);
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
fmpz_t p;
slong N;
padic_ctx_t ctx;
slong m, n;
FLINT_TEST_INIT(state);
flint_printf("get/ set_entry_padic... ");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
padic_mat_t a;
padic_t x, y;
slong r, c;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
m = n_randint(state, 20) + 1;
n = n_randint(state, 20) + 1;
padic_mat_init2(a, m, n, N);
padic_init2(x, N);
padic_init2(y, N);
padic_mat_randtest(a, state, ctx);
padic_randtest_not_zero(x, state, ctx);
r = n_randint(state, m);
c = n_randint(state, n);
padic_mat_set_entry_padic(a, r, c, x, ctx);
padic_mat_get_entry_padic(y, a, r, c, ctx);
result = (padic_equal(x, y) && padic_mat_is_reduced(a, ctx));
if (!result)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "), padic_mat_print(a, ctx), flint_printf("\n");
flint_printf("x = "), padic_print(x, ctx), flint_printf("\n");
flint_printf("y = "), padic_print(y, ctx), flint_printf("\n");
abort();
}
padic_mat_clear(a);
padic_clear(x);
padic_clear(y);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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;
}
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;
}
int
main(void)
{
long i;
flint_rand_t state;
flint_randinit(state);
printf("solve_triu_recursive....");
fflush(stdout);
for (i = 0; i < 1000; i++)
{
nmod_mat_t A, X, B, Y;
mp_limb_t m;
long rows, cols;
int unit;
m = n_randtest_prime(state, 0);
rows = n_randint(state, 100);
cols = n_randint(state, 100);
unit = n_randint(state, 2);
nmod_mat_init(A, rows, rows, m);
nmod_mat_init(B, rows, cols, m);
nmod_mat_init(X, rows, cols, m);
nmod_mat_init(Y, rows, cols, m);
nmod_mat_randtriu(A, state, unit);
nmod_mat_randtest(X, state);
nmod_mat_mul(B, A, X);
/* Check Y = A^(-1) * (A * X) = X */
nmod_mat_solve_triu_recursive(Y, A, B, unit);
if (!nmod_mat_equal(Y, X))
{
printf("FAIL!\n");
printf("A:\n");
nmod_mat_print_pretty(A);
printf("X:\n");
nmod_mat_print_pretty(X);
printf("B:\n");
nmod_mat_print_pretty(B);
printf("Y:\n");
nmod_mat_print_pretty(Y);
abort();
}
/* Check aliasing */
nmod_mat_solve_triu_recursive(B, A, B, unit);
if (!nmod_mat_equal(B, X))
{
printf("FAIL!\n");
printf("aliasing test failed");
printf("A:\n");
nmod_mat_print_pretty(A);
printf("B:\n");
nmod_mat_print_pretty(B);
abort();
}
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(X);
nmod_mat_clear(Y);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
padic_ctx_t ctx;
fmpz_t p;
slong N;
FLINT_TEST_INIT(state);
flint_printf("mul... ");
fflush(stdout);
/* Check aliasing of a and b */
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_randtest(b, state, n_randint(state, 50), ctx);
padic_poly_randtest(c, state, n_randint(state, 50), ctx);
padic_poly_mul(a, b, c, ctx);
padic_poly_mul(b, b, c, ctx);
result = (padic_poly_equal(a, b) && padic_poly_is_reduced(a, ctx));
if (!result)
{
flint_printf("FAIL (aliasing a and b):\n");
padic_poly_print(a, ctx), flint_printf("\n\n");
padic_poly_print(b, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/* Check aliasing of a and c */
for (i = 0; i < 1000; i++)
{
padic_poly_t a, b, c;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_randtest(b, state, n_randint(state, 50), ctx);
padic_poly_randtest(c, state, n_randint(state, 50), ctx);
padic_poly_mul(a, b, c, ctx);
padic_poly_mul(c, b, c, ctx);
result = (padic_poly_equal(a, c) && padic_poly_is_reduced(a, ctx));
if (!result)
{
flint_printf("FAIL (aliasing a and c):\n");
padic_poly_print(a, ctx), flint_printf("\n\n");
padic_poly_print(c, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/* Check (b * c) + (b * d) = b * (c + d) */
for (i = 0; i < 1000; i++)
{
padic_poly_t a1, a2, b, c, d, t;
slong v;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_init2(d, 0, N);
padic_poly_init2(t, 0, N);
padic_poly_randtest(b, state, n_randint(state, 100), ctx);
padic_poly_randtest(c, state, n_randint(state, 100), ctx);
padic_poly_randtest(d, state, n_randint(state, 100), ctx);
v = FLINT_MIN(b->val, c->val);
v = FLINT_MIN(v, d->val);
v = FLINT_MIN(v, 0);
if (v >= 0 || -v < N) /* Otherwise, no precision left */
{
slong N2 = (v >= 0) ? N : N + v;
padic_poly_init2(a1, 0, N2);
padic_poly_init2(a2, 0, N2);
padic_poly_mul(a1, b, c, ctx);
padic_poly_mul(t, b, d, ctx);
padic_poly_add(a1, a1, t, ctx); /* Lower precision */
padic_poly_add(t, c, d, ctx);
padic_poly_mul(a2, b, t, ctx); /* Lower precision */
result = (padic_poly_equal(a1, a2) && padic_poly_is_reduced(a1, ctx));
if (!result)
{
flint_printf("FAIL (distributivity):\n");
flint_printf("p = "), fmpz_print(ctx->p), flint_printf("\n\n");
flint_printf("N = %wd\n\n", N);
flint_printf("b = "), padic_poly_print(b, ctx), flint_printf("\n\n");
flint_printf("c = "), padic_poly_print(c, ctx), flint_printf("\n\n");
flint_printf("d = "), padic_poly_print(d, ctx), flint_printf("\n\n");
flint_printf("a1 = "), padic_poly_print(a1, ctx), flint_printf("\n\n");
flint_printf("a2 = "), padic_poly_print(a2, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a1);
padic_poly_clear(a2);
}
padic_poly_clear(b);
padic_poly_clear(c);
padic_poly_clear(d);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
/* Compare with Q */
for (i = 0; i < 10000; i++)
{
padic_poly_t a, b, c, d;
fmpq_poly_t x, y, z;
fmpz_init_set_ui(p, n_randtest_prime(state, 0));
N = n_randint(state, PADIC_TEST_PREC_MAX - PADIC_TEST_PREC_MIN)
+ PADIC_TEST_PREC_MIN;
padic_ctx_init(ctx, p, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), PADIC_SERIES);
padic_poly_init2(a, 0, N);
padic_poly_init2(b, 0, N);
padic_poly_init2(c, 0, N);
padic_poly_init2(d, 0, N);
fmpq_poly_init(x);
fmpq_poly_init(y);
fmpq_poly_init(z);
padic_poly_randtest(b, state, n_randint(state, 50), ctx);
padic_poly_randtest(c, state, n_randint(state, 50), ctx);
padic_poly_mul(a, b, c, ctx);
padic_poly_get_fmpq_poly(y, b, ctx);
padic_poly_get_fmpq_poly(z, c, ctx);
fmpq_poly_mul(x, y, z);
padic_poly_set_fmpq_poly(d, x, ctx);
result = (padic_poly_equal(a, d) && padic_poly_is_reduced(a, ctx));
if (!result)
{
flint_printf("FAIL (cmp with Q):\n");
flint_printf("N = %wd, val(b) = %wd, val(c) = %wd\n", N, b->val, c->val);
padic_poly_print(c, ctx), flint_printf("\n\n");
padic_poly_print(d, ctx), flint_printf("\n\n");
abort();
}
padic_poly_clear(a);
padic_poly_clear(b);
padic_poly_clear(c);
padic_poly_clear(d);
fmpq_poly_clear(x);
fmpq_poly_clear(y);
fmpq_poly_clear(z);
padic_ctx_clear(ctx);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}