int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("mul... ");
fflush(stdout);
/* Check aliasing: a = a * b */
for (i = 0; i < 2000; i++)
{
fmpz_t p;
slong d, N;
qadic_ctx_t ctx;
qadic_t a, b, c;
fmpz_init_set_ui(p, n_randprime(state, 2 + n_randint(state, 3), 1));
d = n_randint(state, 10) + 1;
N = z_randint(state, 50) + 1;
qadic_ctx_init_conway(ctx, p, d, FLINT_MAX(0,N-10), FLINT_MAX(0,N+10), "a", PADIC_SERIES);
qadic_init2(a, N);
qadic_init2(b, N);
qadic_init2(c, N);
qadic_randtest(a, state, ctx);
qadic_randtest(b, state, ctx);
qadic_mul(c, a, b, ctx);
qadic_mul(a, a, b, ctx);
result = (qadic_equal(a, c));
if (!result)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "), qadic_print_pretty(a, ctx), flint_printf("\n");
flint_printf("b = "), qadic_print_pretty(b, ctx), flint_printf("\n");
flint_printf("c = "), qadic_print_pretty(c, ctx), flint_printf("\n");
abort();
}
qadic_clear(a);
qadic_clear(b);
qadic_clear(c);
fmpz_clear(p);
qadic_ctx_clear(ctx);
}
/* Check aliasing: b = a * b */
for (i = 0; i < 2000; i++)
{
fmpz_t p;
slong d, N;
qadic_ctx_t ctx;
qadic_t a, b, c;
fmpz_init_set_ui(p, n_randprime(state, 2 + n_randint(state, 3), 1));
d = n_randint(state, 10) + 1;
N = z_randint(state, 50) + 1;
qadic_ctx_init_conway(ctx, p, d, FLINT_MAX(0, N-10), FLINT_MAX(0, N+10), "a", PADIC_SERIES);
qadic_init2(a, N);
qadic_init2(b, N);
qadic_init2(c, N);
qadic_randtest(a, state, ctx);
qadic_randtest(b, state, ctx);
qadic_mul(c, a, b, ctx);
qadic_mul(b, a, b, ctx);
result = (qadic_equal(b, c));
if (!result)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "), qadic_print_pretty(a, ctx), flint_printf("\n");
flint_printf("b = "), qadic_print_pretty(b, ctx), flint_printf("\n");
flint_printf("c = "), qadic_print_pretty(c, ctx), flint_printf("\n");
abort();
}
qadic_clear(a);
qadic_clear(b);
qadic_clear(c);
fmpz_clear(p);
qadic_ctx_clear(ctx);
}
/* Check aliasing: a = a + a */
for (i = 0; i < 2000; i++)
{
fmpz_t p;
slong d, N;
qadic_ctx_t ctx;
qadic_t a, c;
fmpz_init_set_ui(p, n_randprime(state, 2 + n_randint(state, 3), 1));
d = n_randint(state, 10) + 1;
N = z_randint(state, 50) + 1;
qadic_ctx_init_conway(ctx, p, d, FLINT_MAX(0,N-10), FLINT_MAX(0,N+10), "a", PADIC_SERIES);
qadic_init2(a, N);
qadic_init2(c, N);
qadic_randtest(a, state, ctx);
qadic_add(c, a, a, ctx);
qadic_add(a, a, a, ctx);
result = (qadic_equal(a, c));
if (!result)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "), qadic_print_pretty(a, ctx), flint_printf("\n");
flint_printf("c = "), qadic_print_pretty(c, ctx), flint_printf("\n");
abort();
}
qadic_clear(a);
qadic_clear(c);
fmpz_clear(p);
qadic_ctx_clear(ctx);
}
/* Check that a * b == b * a */
for (i = 0; i < 2000; i++)
{
fmpz_t p;
slong d, N;
qadic_ctx_t ctx;
qadic_t a, b, c1, c2;
fmpz_init_set_ui(p, n_randprime(state, 2 + n_randint(state, 3), 1));
d = n_randint(state, 10) + 1;
N = z_randint(state, 50) + 1;
qadic_ctx_init_conway(ctx, p, d, FLINT_MAX(0,N-10), FLINT_MAX(0,N+10), "a", PADIC_SERIES);
qadic_init2(a, N);
qadic_init2(b, N);
qadic_init2(c1, N);
qadic_init2(c2, N);
qadic_randtest(a, state, ctx);
qadic_randtest(b, state, ctx);
qadic_mul(c1, a, b, ctx);
qadic_mul(c2, b, a, ctx);
result = (qadic_equal(c1, c2));
if (!result)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "), qadic_print_pretty(a, ctx), flint_printf("\n");
flint_printf("b = "), qadic_print_pretty(b, ctx), flint_printf("\n");
flint_printf("c1 = "), qadic_print_pretty(c1, ctx), flint_printf("\n");
flint_printf("c2 = "), qadic_print_pretty(c2, ctx), flint_printf("\n");
abort();
}
qadic_clear(a);
qadic_clear(b);
qadic_clear(c1);
qadic_clear(c2);
fmpz_clear(p);
qadic_ctx_clear(ctx);
}
/* Check that (a * b) * c == a * (b * c) for integral values */
for (i = 0; i < 2000; i++)
{
fmpz_t p;
slong d, N;
qadic_ctx_t ctx;
qadic_t a, b, c, lhs, rhs;
fmpz_init_set_ui(p, n_randprime(state, 2 + n_randint(state, 3), 1));
d = n_randint(state, 10) + 1;
N = n_randint(state, 50) + 1;
qadic_ctx_init_conway(ctx, p, d, FLINT_MAX(0,N-10), FLINT_MAX(0,N+10), "a", PADIC_SERIES);
qadic_init2(a, N);
qadic_init2(b, N);
qadic_init2(c, N);
qadic_init2(lhs, N);
qadic_init2(rhs, N);
qadic_randtest_int(a, state, ctx);
qadic_randtest_int(b, state, ctx);
qadic_randtest_int(c, state, ctx);
qadic_mul(lhs, a, b, ctx);
qadic_mul(lhs, lhs, c, ctx);
qadic_mul(rhs, b, c, ctx);
qadic_mul(rhs, a, rhs, ctx);
result = (qadic_equal(lhs, rhs));
if (!result)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "), qadic_print_pretty(a, ctx), flint_printf("\n");
flint_printf("b = "), qadic_print_pretty(b, ctx), flint_printf("\n");
flint_printf("c = "), qadic_print_pretty(c, ctx), flint_printf("\n");
flint_printf("lhs = "), qadic_print_pretty(lhs, ctx), flint_printf("\n");
flint_printf("rhs = "), qadic_print_pretty(rhs, ctx), flint_printf("\n");
abort();
}
qadic_clear(a);
qadic_clear(b);
qadic_clear(c);
qadic_clear(lhs);
qadic_clear(rhs);
fmpz_clear(p);
qadic_ctx_clear(ctx);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("submul_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c, d;
fmpz_t x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
fmpz_init(x);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
fmpz_randtest(x, state, 1 + n_randint(state, 2000));
prec = 2 + n_randint(state, 2000);
arb_set_fmpz(b, x);
arb_set(d, c);
arb_submul_fmpz(c, a, x, prec);
arb_submul(d, a, b, prec);
if (!arb_equal(c, d))
{
printf("FAIL\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
printf("d = "); arb_print(d); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
fmpz_clear(x);
}
/* aliasing */
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
fmpz_t x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
fmpz_init(x);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
fmpz_randtest(x, state, 1 + n_randint(state, 2000));
prec = 2 + n_randint(state, 2000);
arb_set_fmpz(b, x);
arb_set(c, a);
arb_submul_fmpz(c, a, x, prec);
arb_submul_fmpz(a, a, x, prec);
if (!arb_equal(a, c))
{
printf("FAIL (aliasing)\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpz_clear(x);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main(void)
{
char *str; /* String for the input polynomial P */
mpoly_t P; /* Input polynomial P */
long n; /* Number of variables minus one */
long K; /* Required t-adic precision */
long N, Nw;
long i, b;
mat_t M;
ctx_t ctxM;
mon_t *rows, *cols;
padic_mat_struct *C;
fmpz_t p;
printf("valuations... \n");
fflush(stdout);
/* Example 3-1-1 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[1 1 1]"; */
/* Example 4-4-2 */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[3 1 0 0] (2 0 1)[1 0 1 2] (2 0 1)[0 1 0 3]"; */
/* Example 3-3-6 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 314)[2 1 0] (2 0 42)[0 2 1] (2 0 271)[1 0 2] (2 0 -23)[1 1 1]"; */
/* Example 3-3-2 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[2 1 0] (2 0 1)[0 2 1] (2 0 1)[1 0 2]"; */
/* Example ... */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[1 1 1 1]"; */
/* Cubic surface from AKR */
str = "4 (1 3)[0 3 0 0] (2 0 3)[0 1 2 0] "
"(2 0 -1)[1 1 1 0] (2 0 3)[1 1 0 1] "
"(2 0 -1)[2 1 0 0] [0 0 3 0] (2 0 -1)[1 0 2 0] "
"(1 2)[0 0 0 3] [3 0 0 0]";
n = atoi(str) - 1;
N = 10;
Nw = 22;
K = 616;
ctx_init_fmpz_poly_q(ctxM);
mpoly_init(P, n + 1, ctxM);
mpoly_set_str(P, str, ctxM);
printf("P = "), mpoly_print(P, ctxM), printf("\n");
b = gmc_basis_size(n, mpoly_degree(P, -1, ctxM));
mat_init(M, b, b, ctxM);
gmc_compute(M, &rows, &cols, P, ctxM);
mat_print(M, ctxM);
printf("\n");
fmpz_init(p);
fmpz_set_ui(p, 5);
gmde_solve(&C, K, p, N, Nw, M, ctxM);
printf("Valuations\n");
for (i = 0; i < K; i++)
{
long v = padic_mat_val(C + i);
if (v < LONG_MAX)
printf(" i = %ld val = %ld val/log(i) = %f\n", i, v,
(i > 1) ? (double) v / log(i) : 0);
else
printf(" i = %ld val = +infty\n", i);
}
fmpz_clear(p);
mpoly_clear(P, ctxM);
mat_clear(M, ctxM);
for (i = 0; i < K; i++)
padic_mat_clear(C + i);
free(C);
ctx_clear(ctxM);
return EXIT_SUCCESS;
}
void frob(const mpoly_t P, const ctx_t ctxFracQt,
const qadic_t t1, const qadic_ctx_t Qq,
prec_t *prec, const prec_t *prec_in,
int verbose)
{
const padic_ctx_struct *Qp = &Qq->pctx;
const fmpz *p = Qp->p;
const long a = qadic_ctx_degree(Qq);
const long n = P->n - 1;
const long d = mpoly_degree(P, -1, ctxFracQt);
const long b = gmc_basis_size(n, d);
long i, j, k;
/* Diagonal fibre */
padic_mat_t F0;
/* Gauss--Manin Connection */
mat_t M;
mon_t *bR, *bC;
fmpz_poly_t r;
/* Local solution */
fmpz_poly_mat_t C, Cinv;
long vC, vCinv;
/* Frobenius */
fmpz_poly_mat_t F;
long vF;
fmpz_poly_mat_t F1;
long vF1;
fmpz_poly_t cp;
clock_t c0, c1;
double c;
if (verbose)
{
printf("Input:\n");
printf(" P = "), mpoly_print(P, ctxFracQt), printf("\n");
printf(" p = "), fmpz_print(p), printf("\n");
printf(" t1 = "), qadic_print_pretty(t1, Qq), printf("\n");
printf("\n");
fflush(stdout);
}
/* Step 1 {M, r} *********************************************************/
c0 = clock();
mat_init(M, b, b, ctxFracQt);
fmpz_poly_init(r);
gmc_compute(M, &bR, &bC, P, ctxFracQt);
{
fmpz_poly_t t;
fmpz_poly_init(t);
fmpz_poly_set_ui(r, 1);
for (i = 0; i < M->m; i++)
for (j = 0; j < M->n; j++)
{
fmpz_poly_lcm(t, r, fmpz_poly_q_denref(
(fmpz_poly_q_struct *) mat_entry(M, i, j, ctxFracQt)));
fmpz_poly_swap(r, t);
}
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Gauss-Manin connection:\n");
printf(" r(t) = "), fmpz_poly_print_pretty(r, "t"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
{
qadic_t t;
qadic_init2(t, 1);
fmpz_poly_evaluate_qadic(t, r, t1, Qq);
if (qadic_is_zero(t))
{
printf("Exception (deformation_frob).\n");
printf("The resultant r evaluates to zero (mod p) at t1.\n");
abort();
}
qadic_clear(t);
}
/* Precisions ************************************************************/
if (prec_in != NULL)
{
*prec = *prec_in;
}
else
{
deformation_precisions(prec, p, a, n, d, fmpz_poly_degree(r));
}
if (verbose)
{
printf("Precisions:\n");
printf(" N0 = %ld\n", prec->N0);
printf(" N1 = %ld\n", prec->N1);
printf(" N2 = %ld\n", prec->N2);
printf(" N3 = %ld\n", prec->N3);
printf(" N3i = %ld\n", prec->N3i);
printf(" N3w = %ld\n", prec->N3w);
printf(" N3iw = %ld\n", prec->N3iw);
printf(" N4 = %ld\n", prec->N4);
printf(" m = %ld\n", prec->m);
printf(" K = %ld\n", prec->K);
printf(" r = %ld\n", prec->r);
printf(" s = %ld\n", prec->s);
printf("\n");
fflush(stdout);
}
/* Initialisation ********************************************************/
padic_mat_init2(F0, b, b, prec->N4);
fmpz_poly_mat_init(C, b, b);
fmpz_poly_mat_init(Cinv, b, b);
fmpz_poly_mat_init(F, b, b);
vF = 0;
fmpz_poly_mat_init(F1, b, b);
vF1 = 0;
fmpz_poly_init(cp);
/* Step 2 {F0} ***********************************************************/
{
padic_ctx_t pctx_F0;
fmpz *t;
padic_ctx_init(pctx_F0, p, FLINT_MIN(prec->N4 - 10, 0), prec->N4, PADIC_VAL_UNIT);
t = _fmpz_vec_init(n + 1);
c0 = clock();
mpoly_diagonal_fibre(t, P, ctxFracQt);
diagfrob(F0, t, n, d, prec->N4, pctx_F0, 0);
padic_mat_transpose(F0, F0);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Diagonal fibre:\n");
printf(" P(0) = {"), _fmpz_vec_print(t, n + 1), printf("}\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
_fmpz_vec_clear(t, n + 1);
padic_ctx_clear(pctx_F0);
}
/* Step 3 {C, Cinv} ******************************************************/
/*
Compute C as a matrix over Z_p[[t]]. A is the same but as a series
of matrices over Z_p. Mt is the matrix -M^t, and Cinv is C^{-1}^t,
the local solution of the differential equation replacing M by Mt.
*/
c0 = clock();
{
const long K = prec->K;
padic_mat_struct *A;
gmde_solve(&A, K, p, prec->N3, prec->N3w, M, ctxFracQt);
gmde_convert_soln(C, &vC, A, K, p);
for(i = 0; i < K; i++)
padic_mat_clear(A + i);
free(A);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Local solution:\n");
printf(" Time for C = %f\n", c);
fflush(stdout);
}
c0 = clock();
{
const long K = (prec->K + (*p) - 1) / (*p);
mat_t Mt;
padic_mat_struct *Ainv;
mat_init(Mt, b, b, ctxFracQt);
mat_transpose(Mt, M, ctxFracQt);
mat_neg(Mt, Mt, ctxFracQt);
gmde_solve(&Ainv, K, p, prec->N3i, prec->N3iw, Mt, ctxFracQt);
gmde_convert_soln(Cinv, &vCinv, Ainv, K, p);
fmpz_poly_mat_transpose(Cinv, Cinv);
fmpz_poly_mat_compose_pow(Cinv, Cinv, *p);
for(i = 0; i < K; i++)
padic_mat_clear(Ainv + i);
free(Ainv);
mat_clear(Mt, ctxFracQt);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf(" Time for C^{-1} = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 4 {F(t) := C(t) F(0) C(t^p)^{-1}} ********************************/
/*
Computes the product C(t) F(0) C(t^p)^{-1} modulo (p^{N_2}, t^K).
This is done by first computing the unit part of the product
exactly over the integers modulo t^K.
*/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
for (i = 0; i < b; i++)
{
/* Find the unique k s.t. F0(i,k) is non-zero */
for (k = 0; k < b; k++)
if (!fmpz_is_zero(padic_mat_entry(F0, i, k)))
break;
if (k == b)
{
printf("Exception (frob). F0 is singular.\n\n");
abort();
}
for (j = 0; j < b; j++)
{
fmpz_poly_scalar_mul_fmpz(fmpz_poly_mat_entry(T, i, j),
fmpz_poly_mat_entry(Cinv, k, j),
padic_mat_entry(F0, i, k));
}
}
fmpz_poly_mat_mul(F, C, T);
fmpz_poly_mat_truncate(F, prec->K);
vF = vC + padic_mat_val(F0) + vCinv;
/* Canonicalise (F, vF) */
{
long v = fmpz_poly_mat_ord_p(F, p);
if (v == LONG_MAX)
{
printf("ERROR (deformation_frob). F(t) == 0.\n");
abort();
}
else if (v > 0)
{
fmpz_pow_ui(pN, p, v);
fmpz_poly_mat_scalar_divexact_fmpz(F, F, pN);
vF = vF + v;
}
}
/* Reduce (F, vF) modulo p^{N2} */
fmpz_pow_ui(pN, p, prec->N2 - vF);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Matrix for F(t):\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 5 {G = r(t)^m F(t)} **********************************************/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_t t;
fmpz_init(pN);
fmpz_poly_init(t);
fmpz_pow_ui(pN, p, prec->N2 - vF);
/* Compute r(t)^m mod p^{N2-vF} */
if (prec->denR == NULL)
{
fmpz_mod_poly_t _t;
fmpz_mod_poly_init(_t, pN);
fmpz_mod_poly_set_fmpz_poly(_t, r);
fmpz_mod_poly_pow(_t, _t, prec->m);
fmpz_mod_poly_get_fmpz_poly(t, _t);
fmpz_mod_poly_clear(_t);
}
else
{
/* TODO: We don't really need a copy */
fmpz_poly_set(t, prec->denR);
}
fmpz_poly_mat_scalar_mul_fmpz_poly(F, F, t);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
/* TODO: This should not be necessary? */
fmpz_poly_mat_truncate(F, prec->K);
fmpz_clear(pN);
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Analytic continuation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Steps 6 and 7 *********************************************************/
if (a == 1)
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t f, g, t, pN;
fmpz_init(f);
fmpz_init(g);
fmpz_init(t);
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_padic_teichmuller(f, t1->coeffs + 0, p, N);
if (prec->denR == NULL)
{
_fmpz_mod_poly_evaluate_fmpz(g, r->coeffs, r->length, f, pN);
fmpz_powm_ui(t, g, prec->m, pN);
}
else
{
_fmpz_mod_poly_evaluate_fmpz(t, prec->denR->coeffs, prec->denR->length, f, pN);
}
_padic_inv(g, t, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
if (len == 0)
{
fmpz_poly_zero(fmpz_poly_mat_entry(F1, i, j));
}
else
{
fmpz_poly_fit_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_mod_poly_evaluate_fmpz(t, poly->coeffs, len, f, pN);
fmpz_mul(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, g, t);
fmpz_mod(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0,
fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, pN);
_fmpz_poly_set_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_poly_normalise(fmpz_poly_mat_entry(F1, i, j));
}
}
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(t);
fmpz_clear(pN);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
else
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t pN;
fmpz *f, *g, *t;
fmpz_init(pN);
f = _fmpz_vec_init(a);
g = _fmpz_vec_init(2 * a - 1);
t = _fmpz_vec_init(2 * a - 1);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_qadic_teichmuller(f, t1->coeffs, t1->length, Qq->a, Qq->j, Qq->len, p, N);
if (prec->denR == NULL)
{
fmpz_t e;
fmpz_init_set_ui(e, prec->m);
_fmpz_mod_poly_compose_smod(g, r->coeffs, r->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
_qadic_pow(t, g, a, e, Qq->a, Qq->j, Qq->len, pN);
fmpz_clear(e);
}
else
{
_fmpz_mod_poly_reduce(prec->denR->coeffs, prec->denR->length, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_normalise(prec->denR);
_fmpz_mod_poly_compose_smod(t, prec->denR->coeffs, prec->denR->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
}
_qadic_inv(g, t, a, Qq->a, Qq->j, Qq->len, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
fmpz_poly_struct *poly2 = fmpz_poly_mat_entry(F1, i, j);
if (len == 0)
{
fmpz_poly_zero(poly2);
}
else
{
_fmpz_mod_poly_compose_smod(t, poly->coeffs, len, f, a,
Qq->a, Qq->j, Qq->len, pN);
fmpz_poly_fit_length(poly2, 2 * a - 1);
_fmpz_poly_mul(poly2->coeffs, g, a, t, a);
_fmpz_mod_poly_reduce(poly2->coeffs, 2 * a - 1, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_set_length(poly2, a);
_fmpz_poly_normalise(poly2);
}
}
/* Now the matrix for p^{-1} F_p at t=t_1 is (F1, vF1). */
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
_fmpz_vec_clear(f, a);
_fmpz_vec_clear(g, 2 * a - 1);
_fmpz_vec_clear(t, 2 * a - 1);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 7 {Norm} *****************************************************/
/*
Computes the matrix for $q^{-1} F_q$ at $t = t_1$ as the
product $F \sigma(F) \dotsm \sigma^{a-1}(F)$ up appropriate
transpositions because our convention of columns vs rows is
the opposite of that used by Gerkmann.
Note that, in any case, transpositions do not affect
the characteristic polynomial.
*/
c0 = clock();
{
const long N = prec->N1 - a * vF1;
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
fmpz_pow_ui(pN, p, N);
fmpz_poly_mat_frobenius(T, F1, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
for (i = 2; i < a; i++)
{
fmpz_poly_mat_frobenius(T, T, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
}
vF1 = a * vF1;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Norm:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
/* Step 8 {Reverse characteristic polynomial} ****************************/
c0 = clock();
deformation_revcharpoly(cp, F1, vF1, n, d, prec->N0, prec->r, prec->s, Qq);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Reverse characteristic polynomial:\n");
printf(" p(T) = "), fmpz_poly_print_pretty(cp, "T"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Clean up **************************************************************/
padic_mat_clear(F0);
mat_clear(M, ctxFracQt);
free(bR);
free(bC);
fmpz_poly_clear(r);
fmpz_poly_mat_clear(C);
fmpz_poly_mat_clear(Cinv);
fmpz_poly_mat_clear(F);
fmpz_poly_mat_clear(F1);
fmpz_poly_clear(cp);
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("resultant_div....");
fflush(stdout);
for (i = 0; i < 50; i++)
{
fmpq_poly_t f, g, h, p;
fmpq_t x, y, z, zz;
fmpz_t den;
slong nbits;
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(p);
fmpq_poly_init(h);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
fmpq_init(zz);
fmpz_init(den);
fmpq_poly_randtest(f, state, n_randint(state, 50), 100);
fmpq_poly_randtest(g, state, n_randint(state, 50), 100);
fmpq_poly_randtest(h, state, n_randint(state, 50), 100);
fmpz_set(den, fmpq_poly_denref(f));
fmpq_poly_scalar_mul_fmpz(f, f, den);
fmpz_set(den, fmpq_poly_denref(g));
fmpq_poly_scalar_mul_fmpz(g, g, den);
fmpz_set(den, fmpq_poly_denref(h));
fmpq_poly_scalar_mul_fmpz(h, h, den);
fmpq_poly_mul(p, f, g);
fmpq_poly_resultant(x, f, h);
if (!fmpz_is_one(fmpq_denref(x)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("f = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(y, g, h);
if (!fmpz_is_one(fmpq_denref(y)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("h = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("z = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(z, p, h);
if (!fmpz_is_one(fmpq_denref(z)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("p = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
if (fmpq_is_zero(z))
{
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
continue;
}
nbits = (slong)fmpz_bits(fmpq_numref(y)) + 1;
fmpq_poly_resultant_div(z, p, h, fmpq_numref(x), nbits);
fmpq_poly_resultant(zz, p, h);
result = fmpq_equal(z, y);
if (!result)
{
flint_printf("FAIL (res(p, g)/div == res(p, g)/div:\n");
flint_printf("p = "), fmpq_poly_print_pretty(p, "x"), flint_printf("\n\n");
flint_printf("h = "), fmpq_poly_print_pretty(h, "x"), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(zz), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(x), flint_printf(" * "), fmpq_print(y), flint_printf("\n\n");
flint_printf("supplied divisor = "), fmpq_print(x), flint_printf("\n\n");
flint_printf("nbits = %wu\n\n", nbits);
flint_printf("divisor found = "), fmpq_print(z), flint_printf("\n\n");
flint_printf("correct result = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
arf_root(arf_ptr z, arf_srcptr x, ulong k, slong prec, arf_rnd_t rnd)
{
mp_size_t xn, zn, val;
mp_srcptr xptr;
mp_ptr tmp, zptr;
mpfr_t xf, zf;
fmpz_t q, r;
int inexact;
if (k == 0)
{
arf_nan(z);
return 0;
}
if (k == 1)
return arf_set_round(z, x, prec, rnd);
if (k == 2)
return arf_sqrt(z, x, prec, rnd);
if (arf_is_special(x))
{
if (arf_is_neg_inf(x))
arf_nan(z);
else
arf_set(z, x);
return 0;
}
if (ARF_SGNBIT(x))
{
arf_nan(z);
return 0;
}
fmpz_init(q);
fmpz_init(r);
/* x = m * 2^e where e = qk + r */
/* x^(1/k) = (m * 2^(qk+r))^(1/k) */
/* x^(1/k) = (m * 2^r)^(1/k) * 2^q */
fmpz_set_ui(r, k);
fmpz_fdiv_qr(q, r, ARF_EXPREF(x), r);
ARF_GET_MPN_READONLY(xptr, xn, x);
zn = (prec + FLINT_BITS - 1) / FLINT_BITS;
zf->_mpfr_d = tmp = flint_malloc(zn * sizeof(mp_limb_t));
zf->_mpfr_prec = prec;
zf->_mpfr_sign = 1;
zf->_mpfr_exp = 0;
xf->_mpfr_d = (mp_ptr) xptr;
xf->_mpfr_prec = xn * FLINT_BITS;
xf->_mpfr_sign = 1;
xf->_mpfr_exp = fmpz_get_ui(r);
inexact = mpfr_root(zf, xf, k, arf_rnd_to_mpfr(rnd));
inexact = (inexact != 0);
val = 0;
while (tmp[val] == 0)
val++;
ARF_GET_MPN_WRITE(zptr, zn - val, z);
flint_mpn_copyi(zptr, tmp + val, zn - val);
fmpz_add_si(ARF_EXPREF(z), q, zf->_mpfr_exp);
flint_free(tmp);
fmpz_clear(q);
fmpz_clear(r);
return inexact;
}
int main()
{
slong iter, iter2;
flint_rand_t state;
flint_printf("mul_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arf_t x, z, v;
fmpz_t y;
slong prec, r1, r2;
arf_rnd_t rnd;
arf_init(x);
arf_init(z);
arf_init(v);
fmpz_init(y);
for (iter2 = 0; iter2 < 100; iter2++)
{
arf_randtest_special(x, state, 2000, 10);
fmpz_randtest(y, state, 2000);
prec = 2 + n_randint(state, 2000);
if (n_randint(state, 10))
prec = ARF_PREC_EXACT;
switch (n_randint(state, 5))
{
case 0: rnd = ARF_RND_DOWN; break;
case 1: rnd = ARF_RND_UP; break;
case 2: rnd = ARF_RND_FLOOR; break;
case 3: rnd = ARF_RND_CEIL; break;
default: rnd = ARF_RND_NEAR; break;
}
switch (n_randint(state, 2))
{
case 0:
r1 = arf_mul_fmpz(z, x, y, prec, rnd);
r2 = arf_mul_fmpz_naive(v, x, y, prec, rnd);
if (!arf_equal(z, v) || r1 != r2)
{
flint_printf("FAIL!\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpz_print(y); flint_printf("\n\n");
flint_printf("z = "); arf_print(z); flint_printf("\n\n");
flint_printf("v = "); arf_print(v); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
default:
r2 = arf_mul_fmpz_naive(v, x, y, prec, rnd);
r1 = arf_mul_fmpz(x, x, y, prec, rnd);
if (!arf_equal(x, v) || r1 != r2)
{
flint_printf("FAIL (aliasing)!\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpz_print(y); flint_printf("\n\n");
flint_printf("v = "); arf_print(v); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
}
}
arf_clear(x);
arf_clear(z);
arf_clear(v);
fmpz_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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;
}
void
gamma_rising_fmprb_ui_delta(fmprb_t y, const fmprb_t x, ulong n, ulong m, long prec)
{
fmprb_ptr xs;
fmprb_t t, u, v;
ulong i, k, rem;
fmpz_t c, h;
fmpz *s, *d;
long wp;
if (n == 0)
{
fmprb_one(y);
return;
}
if (n == 1)
{
fmprb_set_round(y, x, prec);
return;
}
wp = FMPR_PREC_ADD(prec, FLINT_BIT_COUNT(n));
fmprb_init(t);
fmprb_init(u);
fmprb_init(v);
fmpz_init(c);
fmpz_init(h);
if (m == 0)
{
ulong m1, m2;
m1 = 0.2 * pow(wp, 0.4);
m2 = n_sqrt(n);
m = FLINT_MIN(m1, m2);
}
m = FLINT_MIN(m, n);
m = FLINT_MAX(m, 1);
xs = _fmprb_vec_init(m + 1);
d = _fmpz_vec_init(m * m);
s = _fmpz_vec_init(m + 1);
_fmprb_vec_set_powers(xs, x, m + 1, wp);
rising_difference_polynomial(s, d, m);
/* tail */
rem = m;
while (rem + m <= n)
rem += m;
fmprb_one(y);
for (k = rem; k < n; k++)
{
fmprb_add_ui(t, xs + 1, k, wp);
fmprb_mul(y, y, t, wp);
}
/* initial rising factorial */
fmprb_zero(t);
for (i = 1; i <= m; i++)
fmprb_addmul_fmpz(t, xs + i, s + i, wp);
fmprb_mul(y, y, t, wp);
/* the leading coefficient is always the same */
fmprb_mul_fmpz(xs + m - 1, xs + m - 1, d + m - 1 + 0, wp);
for (k = 0; k + 2 * m <= n; k += m)
{
for (i = 0; i < m - 1; i++)
{
fmpz_set_ui(h, k);
_fmpz_poly_evaluate_horner_fmpz(c, d + i * m, m - i, h);
if (i == 0)
fmprb_add_fmpz(t, t, c, wp);
else
fmprb_addmul_fmpz(t, xs + i, c, wp);
}
fmprb_add(t, t, xs + m - 1, wp);
fmprb_mul(y, y, t, wp);
}
fmprb_set_round(y, y, prec);
fmprb_clear(t);
fmprb_clear(u);
fmprb_clear(v);
_fmprb_vec_clear(xs, m + 1);
_fmpz_vec_clear(d, m * m);
_fmpz_vec_clear(s, m + 1);
fmpz_clear(c);
fmpz_clear(h);
}
int
_fmpz_mat_solve_cramer_3x3(fmpz_mat_t X, fmpz_t den,
const fmpz_mat_t A, const fmpz_mat_t B)
{
fmpz_t t15, t16, t17;
int success;
fmpz_init(t15);
fmpz_init(t16);
fmpz_init(t17);
fmpz_mul(t17, AA(1,0), AA(2,1));
fmpz_submul(t17, AA(1,1), AA(2,0));
fmpz_mul(t16, AA(1,2), AA(2,0));
fmpz_submul(t16, AA(1,0), AA(2,2));
fmpz_mul(t15, AA(1,1), AA(2,2));
fmpz_submul(t15, AA(1,2), AA(2,1));
fmpz_mul (den, t15, AA(0,0));
fmpz_addmul(den, t16, AA(0,1));
fmpz_addmul(den, t17, AA(0,2));
success = !fmpz_is_zero(den);
if (success)
{
fmpz_t t12, t13, t14, x0, x1, x2;
long i, n = fmpz_mat_ncols(B);
fmpz_init(t12);
fmpz_init(t13);
fmpz_init(t14);
fmpz_init(x0);
fmpz_init(x1);
fmpz_init(x2);
for (i = 0; i < n; i++)
{
fmpz_mul(t14, AA(2,0), BB(1,i));
fmpz_submul(t14, AA(1,0), BB(2,i));
fmpz_mul(t13, AA(2,1), BB(1,i));
fmpz_submul(t13, AA(1,1), BB(2,i));
fmpz_mul(t12, AA(2,2), BB(1,i));
fmpz_submul(t12, AA(1,2), BB(2,i));
fmpz_mul (x0, t15, BB(0,i));
fmpz_addmul(x0, t13, AA(0,2));
fmpz_submul(x0, t12, AA(0,1));
fmpz_mul (x1, t16, BB(0,i));
fmpz_addmul(x1, t12, AA(0,0));
fmpz_submul(x1, t14, AA(0,2));
fmpz_mul (x2, t17, BB(0,i));
fmpz_addmul(x2, t14, AA(0,1));
fmpz_submul(x2, t13, AA(0,0));
fmpz_swap(XX(0,i), x0);
fmpz_swap(XX(1,i), x1);
fmpz_swap(XX(2,i), x2);
}
fmpz_clear(t12);
fmpz_clear(t13);
fmpz_clear(t14);
fmpz_clear(x0);
fmpz_clear(x1);
fmpz_clear(x2);
}
fmpz_clear(t15);
fmpz_clear(t16);
fmpz_clear(t17);
return success;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("divexact_ui....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 100000; i++)
{
fmpz_t a, c;
mpz_t e, f, g;
ulong n;
fmpz_init(a);
fmpz_init(c);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
n = n_randtest_not_zero(state);
fmpz_mul_ui(c, a, n);
fmpz_get_mpz(e, c);
fmpz_divexact_ui(a, c, n);
mpz_divexact_ui(f, e, n);
fmpz_get_mpz(g, a);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
printf("FAIL1\n");
gmp_printf("n = %lu, e = %Zd, f = %Zd, g = %Zd\n", n, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(c);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Test aliasing of a and c */
for (i = 0; i < 100000; i++)
{
fmpz_t a, c;
mpz_t d, f, g;
ulong n;
fmpz_init(a);
fmpz_init(c);
mpz_init(d);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
n = n_randtest_not_zero(state);
fmpz_mul_ui(c, a, n);
fmpz_get_mpz(d, c);
fmpz_divexact_ui(c, c, n);
mpz_divexact_ui(f, d, n);
fmpz_get_mpz(g, c);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
printf("FAIL:\n");
gmp_printf("d = %Zd, n = %lu, f = %Zd, g = %Zd\n", d, n, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(f);
mpz_clear(g);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
void _fmpq_poly_divrem(fmpz * Q, fmpz_t q, fmpz * R, fmpz_t r,
const fmpz * A, const fmpz_t a, slong lenA,
const fmpz * B, const fmpz_t b, slong lenB, const fmpz_preinvn_t inv)
{
slong lenQ = lenA - lenB + 1;
slong lenR = lenB - 1;
ulong d;
const fmpz * lead = B + (lenB - 1);
if (lenB == 1)
{
_fmpq_poly_scalar_div_fmpq(Q, q, A, a, lenA, B, b);
fmpz_one(r);
return;
}
/*
From pseudo division over Z we have
lead^d * A = Q * B + R
and thus
{A, a} = {b * Q, a * lead^d} * {B, b} + {R, a * lead^d}.
*/
_fmpz_poly_pseudo_divrem(Q, R, &d, A, lenA, B, lenB, inv);
/* Determine the actual length of R */
for ( ; lenR != 0 && fmpz_is_zero(R + (lenR - 1)); lenR--) ;
/* 1. lead^d == +-1. {Q, q} = {b Q, a}, {R, r} = {R, a} up to sign */
if (d == UWORD(0) || *lead == WORD(1) || *lead == WORD(-1))
{
fmpz_one(q);
_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, a);
fmpz_one(r);
if (lenR > 0)
_fmpq_poly_scalar_div_fmpz(R, r, R, r, lenR, a);
if (*lead == WORD(-1) && d % UWORD(2))
{
_fmpz_vec_neg(Q, Q, lenQ);
_fmpz_vec_neg(R, R, lenR);
}
}
/* 2. lead^d != +-1. {Q, q} = {b Q, a lead^d}, {R, r} = {R, a lead^d} */
else
{
/*
TODO: Improve this. Clearly we do not need to compute
den = a lead^d in many cases, but can determine the GCD from
lead alone already.
*/
fmpz_t den;
fmpz_init(den);
fmpz_pow_ui(den, lead, d);
fmpz_mul(den, a, den);
fmpz_one(q);
_fmpq_poly_scalar_mul_fmpz(Q, q, Q, q, lenQ, b);
_fmpq_poly_scalar_div_fmpz(Q, q, Q, q, lenQ, den);
fmpz_one(r);
if (lenR > 0)
_fmpq_poly_scalar_div_fmpz(R, r, R, r, lenR, den);
fmpz_clear(den);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("set_round_ui_2exp_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
slong prec, ret1, ret2;
fmpz_t man, exp;
fmpr_t x, y;
mp_limb_t lo;
fmpr_rnd_t rnd;
int negative;
fmpz_init(man);
fmpz_init(exp);
fmpr_init(x);
fmpr_init(y);
prec = 2 + n_randint(state, 1000);
if (n_randint(state, 10) == 0)
prec = FMPR_PREC_EXACT;
negative = n_randint(state, 2);
lo = n_randtest(state);
fmpz_randtest(exp, state, 1 + n_randint(state, 100));
if (negative)
fmpz_neg_ui(man, lo);
else
fmpz_set_ui(man, lo);
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
ret1 = fmpr_set_round_ui_2exp_fmpz(x, lo, exp, negative, prec, rnd);
fmpr_set_fmpz_2exp(y, man, exp);
ret2 = fmpr_set_round(y, y, prec, rnd);
if (!fmpr_equal(x, y) || ret1 != ret2 ||
!fmpr_check_ulp(x, ret1, prec) || !fmpr_check_ulp(y, ret2, prec))
{
flint_printf("FAIL\n\n");
flint_printf("prec: %wd\n", prec);
flint_printf("man = "); fmpz_print(man); flint_printf("\n\n");
flint_printf("exp = "); fmpz_print(exp); flint_printf("\n\n");
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("ret1 = %wd, ret2 = %wd\n\n", ret1, ret2);
abort();
}
fmpz_clear(man);
fmpz_clear(exp);
fmpr_clear(x);
fmpr_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
arb_get_unique_fmpz(fmpz_t z, const arb_t x)
{
if (!arb_is_finite(x))
{
return 0;
}
else if (arb_is_exact(x))
{
/* x = b*2^e, e >= 0 */
if (arf_is_int(arb_midref(x)))
{
/* arf_get_fmpz aborts on overflow */
arf_get_fmpz(z, arb_midref(x), ARF_RND_DOWN);
return 1;
}
else
{
return 0;
}
}
/* if the radius is >= 1, there are at least two integers */
else if (mag_cmp_2exp_si(arb_radref(x), 0) >= 0)
{
return 0;
}
/* there are 0 or 1 integers if the radius is < 1 */
else
{
fmpz_t a, b, exp;
int res;
/* if the midpoint is exactly an integer, it is what we want */
if (arf_is_int(arb_midref(x)))
{
/* arf_get_fmpz aborts on overflow */
arf_get_fmpz(z, arb_midref(x), ARF_RND_DOWN);
return 1;
}
fmpz_init(a);
fmpz_init(b);
fmpz_init(exp);
/* if the radius is tiny, it can't be an integer */
arf_bot(a, arb_midref(x));
if (fmpz_cmp(a, MAG_EXPREF(arb_radref(x))) > 0)
{
res = 0;
}
else
{
arb_get_interval_fmpz_2exp(a, b, exp, x);
if (COEFF_IS_MPZ(*exp))
{
flint_printf("arb_get_unique_fmpz: input too large\n");
abort();
}
if (*exp >= 0)
{
res = fmpz_equal(a, b);
if (res)
{
fmpz_mul_2exp(a, a, *exp);
fmpz_mul_2exp(b, b, *exp);
}
}
else
{
fmpz_cdiv_q_2exp(a, a, -(*exp));
fmpz_fdiv_q_2exp(b, b, -(*exp));
res = fmpz_equal(a, b);
}
if (res)
fmpz_set(z, a);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(exp);
return res;
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("is_int_2exp_si....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arf_t x, y;
fmpz_t t;
slong e;
int res1, res2;
arf_init(x);
arf_init(y);
fmpz_init(t);
arf_randtest_special(x, state, 2000, 100);
e = n_randtest(state);
arf_mul_2exp_si(y, x, e);
res1 = arf_is_int(x);
res2 = arf_is_int_2exp_si(y, e);
if (res1 != res2)
{
flint_printf("FAIL! (1)\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("res1 = %d, res2 = %d\n\n", res1, res2);
abort();
}
if (res1)
{
if (n_randint(state, 2))
arf_floor(y, x);
else
arf_ceil(y, x);
if (!arf_equal(x, y) || !arf_is_finite(x))
{
flint_printf("FAIL! (2)\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("res1 = %d\n\n", res1);
abort();
}
}
if (arf_is_finite(x) && !arf_is_zero(x))
{
arf_bot(t, x);
fmpz_neg(t, t);
arf_mul_2exp_fmpz(x, x, t);
res1 = arf_is_int(x);
arf_mul_2exp_si(y, x, -1);
res2 = arf_is_int(y);
if (!arf_is_int(x) || arf_is_int(y))
{
flint_printf("FAIL! (3)\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("res1 = %d, res2 = %d\n\n", res1, res2);
abort();
}
}
arf_clear(x);
arf_clear(y);
fmpz_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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;
}
static void
_qadic_exp_bsplit_series(fmpz *P, fmpz_t Q, fmpz *T,
const fmpz *x, slong len, slong lo, slong hi,
const fmpz *a, const slong *j, slong lena)
{
const slong d = j[lena - 1];
if (hi - lo == 1)
{
_fmpz_vec_set(P, x, len);
_fmpz_vec_zero(P + len, 2*d - 1 - len);
fmpz_set_si(Q, lo);
_fmpz_vec_set(T, P, 2*d - 1);
}
else if (hi - lo == 2)
{
_fmpz_poly_sqr(P, x, len);
_fmpz_vec_zero(P + (2*len - 1), d - (2*len - 1));
_fmpz_poly_reduce(P, 2*len - 1, a, j, lena);
fmpz_set_si(Q, lo);
fmpz_mul_si(Q, Q, lo + 1);
_fmpz_vec_scalar_mul_si(T, x, len, lo + 1);
_fmpz_vec_zero(T + len, d - len);
_fmpz_vec_add(T, T, P, d);
}
else
{
const slong m = (lo + hi) / 2;
fmpz *PR, *TR, *W;
fmpz_t QR;
PR = _fmpz_vec_init(2*d - 1);
TR = _fmpz_vec_init(2*d - 1);
W = _fmpz_vec_init(2*d - 1);
fmpz_init(QR);
_qadic_exp_bsplit_series(P, Q, T, x, len, lo, m, a, j, lena);
_qadic_exp_bsplit_series(PR, QR, TR, x, len, m, hi, a, j, lena);
_fmpz_poly_mul(W, TR, d, P, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mul_fmpz(T, T, d, QR);
_fmpz_vec_add(T, T, W, d);
_fmpz_poly_mul(W, P, d, PR, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_swap(P, W, d);
fmpz_mul(Q, Q, QR);
_fmpz_vec_clear(PR, 2*d - 1);
_fmpz_vec_clear(TR, 2*d - 1);
_fmpz_vec_clear(W, 2*d - 1);
fmpz_clear(QR);
}
}
int
main(void)
{
int i, j, result;
ulong cflags = UWORD(0);
mpq_t n1, n2;
FLINT_TEST_INIT(state);
flint_printf("get/set_coeff_fmpz....");
fflush(stdout);
mpq_init(n1);
mpq_init(n2);
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpq_poly_t a;
fmpz_t x1, x2;
slong coeff, len;
fmpq_poly_init(a);
fmpz_init(x1);
fmpz_init(x2);
len = (slong) (n_randint(state, 100) + 1);
for (j = 0; j < 100; j++)
{
fmpz_randtest(x1, state, 200);
fmpz_get_mpz(mpq_numref(n1), x1);
flint_mpz_set_si(mpq_denref(n1), 1);
coeff = (slong) n_randint(state, len);
fmpq_poly_set_coeff_fmpz(a, coeff, x1);
fmpq_poly_get_coeff_mpq(n2, a, coeff);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
result = (mpq_equal(n1, n2) && !cflags);
if (!result)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "), fmpq_poly_debug(a), flint_printf("\n\n");
flint_printf("coeff = %wd\n\n", coeff);
flint_printf("len = %wd\n\n", len);
flint_printf("cflags = %wu\n\n", cflags);
gmp_printf("n1 = %Qd\n\n", n1);
gmp_printf("n2 = %Qd\n\n", n2);
abort();
}
}
fmpz_clear(x1);
fmpz_clear(x2);
fmpq_poly_clear(a);
}
mpq_clear(n1);
mpq_clear(n2);
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
_acb_poly_zeta_em_tail_naive(acb_ptr sum, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong d, slong prec)
{
acb_ptr u, term;
acb_t Na2, splus, rec;
arb_t x;
fmpz_t c;
int aint;
slong r;
BERNOULLI_ENSURE_CACHED(2 * M);
u = _acb_vec_init(d);
term = _acb_vec_init(d);
acb_init(splus);
acb_init(rec);
acb_init(Na2);
arb_init(x);
fmpz_init(c);
_acb_vec_zero(sum, d);
/* u = 1/2 * Nasx */
_acb_vec_scalar_mul_2exp_si(u, Nasx, d, -WORD(1));
/* term = u * (s+x) / (N+a) */
_acb_poly_mullow_cpx(u, u, d, s, d, prec);
_acb_vec_scalar_div(term, u, d, Na, prec);
/* (N+a)^2 or 1/(N+a)^2 */
acb_mul(Na2, Na, Na, prec);
aint = acb_is_int(Na2);
if (!aint)
acb_inv(Na2, Na2, prec);
for (r = 1; r <= M; r++)
{
/* flint_printf("sum 2: %wd %wd\n", r, M); */
/* sum += bernoulli number * term */
arb_set_round_fmpz(x, fmpq_numref(bernoulli_cache + 2 * r), prec);
arb_div_fmpz(x, x, fmpq_denref(bernoulli_cache + 2 * r), prec);
_acb_vec_scalar_mul_arb(u, term, d, x, prec);
_acb_vec_add(sum, sum, u, d, prec);
/* multiply term by ((s+x)+2r-1)((s+x)+2r) / ((N+a)^2 * (2*r+1)*(2*r+2)) */
acb_set(splus, s);
arb_add_ui(acb_realref(splus), acb_realref(splus), 2*r-1, prec);
_acb_poly_mullow_cpx(term, term, d, splus, d, prec);
arb_add_ui(acb_realref(splus), acb_realref(splus), 1, prec);
_acb_poly_mullow_cpx(term, term, d, splus, d, prec);
/* TODO: combine with previous multiplication? */
if (aint)
{
arb_mul_ui(x, acb_realref(Na2), 2*r+1, prec);
arb_mul_ui(x, x, 2*r+2, prec);
_acb_vec_scalar_div_arb(term, term, d, x, prec);
}
else
{
fmpz_set_ui(c, 2*r+1);
fmpz_mul_ui(c, c, 2*r+2);
acb_div_fmpz(rec, Na2, c, prec);
_acb_vec_scalar_mul(term, term, d, rec, prec);
}
}
_acb_vec_clear(u, d);
_acb_vec_clear(term, d);
acb_clear(splus);
acb_clear(rec);
acb_clear(Na2);
arb_clear(x);
fmpz_clear(c);
}
/* evaluates the truncated Taylor series (assumes no aliasing) */
void
_arb_mat_exp_taylor(arb_mat_t S, const arb_mat_t A, slong N, slong prec)
{
if (N == 1)
{
arb_mat_one(S);
}
else if (N == 2)
{
arb_mat_one(S);
arb_mat_add(S, S, A, prec);
}
else if (N == 3)
{
arb_mat_t T;
arb_mat_init(T, arb_mat_nrows(A), arb_mat_nrows(A));
arb_mat_mul(T, A, A, prec);
arb_mat_scalar_mul_2exp_si(T, T, -1);
arb_mat_add(S, A, T, prec);
arb_mat_one(T);
arb_mat_add(S, S, T, prec);
arb_mat_clear(T);
}
else
{
slong i, lo, hi, m, w, dim;
arb_mat_struct * pows;
arb_mat_t T, U;
fmpz_t c, f;
dim = arb_mat_nrows(A);
m = n_sqrt(N);
w = (N + m - 1) / m;
fmpz_init(c);
fmpz_init(f);
pows = flint_malloc(sizeof(arb_mat_t) * (m + 1));
arb_mat_init(T, dim, dim);
arb_mat_init(U, dim, dim);
for (i = 0; i <= m; i++)
{
arb_mat_init(pows + i, dim, dim);
if (i == 0)
arb_mat_one(pows + i);
else if (i == 1)
arb_mat_set(pows + i, A);
else
arb_mat_mul(pows + i, pows + i - 1, A, prec);
}
arb_mat_zero(S);
fmpz_one(f);
for (i = w - 1; i >= 0; i--)
{
lo = i * m;
hi = FLINT_MIN(N - 1, lo + m - 1);
arb_mat_zero(T);
fmpz_one(c);
while (hi >= lo)
{
arb_mat_scalar_addmul_fmpz(T, pows + hi - lo, c, prec);
if (hi != 0)
fmpz_mul_ui(c, c, hi);
hi--;
}
arb_mat_mul(U, pows + m, S, prec);
arb_mat_scalar_mul_fmpz(S, T, f, prec);
arb_mat_add(S, S, U, prec);
fmpz_mul(f, f, c);
}
arb_mat_scalar_div_fmpz(S, S, f, prec);
fmpz_clear(c);
fmpz_clear(f);
for (i = 0; i <= m; i++)
arb_mat_clear(pows + i);
flint_free(pows);
arb_mat_clear(T);
arb_mat_clear(U);
}
}
int main(void)
{
int i, result;
flint_rand_t state;
printf("sqrt... ");
fflush(stdout);
flint_randinit(state);
/* PRIME p = 2 ***************************************************************/
/* Check aliasing: a = sqrt(a) */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
long N;
padic_ctx_t ctx;
int ans1, ans2;
padic_t a, d;
fmpz_init(p);
fmpz_set_ui(p, 2);
N = z_randint(state, 100);
padic_ctx_init(ctx, p, N, PADIC_SERIES);
padic_init(a, ctx);
padic_init(d, ctx);
padic_randtest(a, state, ctx);
ans1 = padic_sqrt(d, a, ctx);
ans2 = padic_sqrt(a, a, ctx);
result = ((ans1 == ans2) && (!ans1 || padic_equal(a, d, ctx)));
if (!result)
{
printf("FAIL (aliasing):\n\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("a = "), _padic_print(a, ctx), printf("\n");
printf("d = "), _padic_print(d, ctx), printf("\n");
abort();
}
padic_clear(a, ctx);
padic_clear(d, ctx);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
/* Test random elements */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
long N;
padic_ctx_t ctx;
int ans;
padic_t a, b, d;
fmpz_init(p);
fmpz_set_ui(p, 2);
N = z_randint(state, 100);
padic_ctx_init(ctx, p, N, PADIC_SERIES);
padic_init(a, ctx);
padic_init(b, ctx);
padic_init(d, ctx);
padic_randtest(a, state, ctx);
ans = padic_sqrt(b, a, ctx);
padic_mul(d, b, b, ctx);
if (ans && padic_val(a) < 0)
{
padic_ctx_t ctx2;
padic_t a2, d2;
padic_ctx_init(ctx2, p, N + padic_val(a), PADIC_SERIES);
padic_init(a2, ctx2);
padic_init(d2, ctx2);
padic_set(a2, a, ctx2);
padic_set(d2, d, ctx2);
padic_reduce(a2, ctx2);
padic_reduce(d2, ctx2);
result = (padic_equal(a2, d2, ctx2));
if (!result)
{
printf("FAIL (random elements):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("a2 = "), padic_print(a2, ctx2), printf("\n");
printf("d2 = "), padic_print(d2, ctx2), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
padic_clear(a2, ctx2);
padic_clear(d2, ctx2);
padic_ctx_clear(ctx2);
}
else
{
result = (!ans || padic_equal(a, d, ctx));
if (!result)
{
printf("FAIL (random elements):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
}
padic_clear(a, ctx);
padic_clear(b, ctx);
padic_clear(d, ctx);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
/* Test random squares */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
long N;
padic_ctx_t ctx;
int ans;
padic_t a, b, c, d;
fmpz_init(p);
fmpz_set_ui(p, 2);
N = z_randint(state, 100);
padic_ctx_init(ctx, p, N, PADIC_SERIES);
padic_init(a, ctx);
padic_init(b, ctx);
padic_init(c, ctx);
padic_init(d, ctx);
padic_randtest(b, state, ctx);
padic_mul(a, b, b, ctx);
ans = padic_sqrt(c, a, ctx);
padic_mul(d, c, c, ctx);
if (ans && padic_val(a) < 0)
{
padic_ctx_t ctx2;
padic_t a2, d2;
padic_ctx_init(ctx2, p, N + padic_val(a), PADIC_SERIES);
padic_init(a2, ctx2);
padic_init(d2, ctx2);
padic_set(a2, a, ctx2);
padic_set(d2, d, ctx2);
padic_reduce(a2, ctx2);
padic_reduce(d2, ctx2);
result = (padic_equal(a2, d2, ctx2));
if (!result)
{
printf("FAIL (random elements):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("c = "), padic_print(c, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("a2 = "), padic_print(a2, ctx2), printf("\n");
printf("d2 = "), padic_print(d2, ctx2), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
padic_clear(a2, ctx2);
padic_clear(d2, ctx2);
padic_ctx_clear(ctx2);
}
else
{
result = (ans && padic_equal(a, d, ctx));
if (!result)
{
printf("FAIL (random squares):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("c = "), padic_print(c, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
}
padic_clear(a, ctx);
padic_clear(b, ctx);
padic_clear(c, ctx);
padic_clear(d, ctx);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
/* PRIME p > 2 ***************************************************************/
/* Check aliasing: a = sqrt(a) */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
long N;
padic_ctx_t ctx;
int ans1, ans2;
padic_t a, d;
fmpz_init(p);
fmpz_set_ui(p, n_randprime(state, 5, 1));
N = z_randint(state, 100);
padic_ctx_init(ctx, p, N, PADIC_SERIES);
padic_init(a, ctx);
padic_init(d, ctx);
padic_randtest(a, state, ctx);
ans1 = padic_sqrt(d, a, ctx);
ans2 = padic_sqrt(a, a, ctx);
result = ((ans1 == ans2) && (!ans1 || padic_equal(a, d, ctx)));
if (!result)
{
printf("FAIL (aliasing):\n\n");
printf("a = "), _padic_print(a, ctx), printf("\n");
printf("d = "), _padic_print(d, ctx), printf("\n");
abort();
}
padic_clear(a, ctx);
padic_clear(d, ctx);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
/* Test random elements */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
long N;
padic_ctx_t ctx;
int ans;
padic_t a, b, d;
fmpz_init(p);
fmpz_set_ui(p, n_randprime(state, 5, 1));
N = z_randint(state, 100);
padic_ctx_init(ctx, p, N, PADIC_SERIES);
padic_init(a, ctx);
padic_init(b, ctx);
padic_init(d, ctx);
padic_randtest(a, state, ctx);
ans = padic_sqrt(b, a, ctx);
padic_mul(d, b, b, ctx);
if (ans && padic_val(a) < 0)
{
padic_ctx_t ctx2;
padic_t a2, d2;
padic_ctx_init(ctx2, p, N + padic_val(a), PADIC_SERIES);
padic_init(a2, ctx2);
padic_init(d2, ctx2);
padic_set(a2, a, ctx2);
padic_set(d2, d, ctx2);
padic_reduce(a2, ctx2);
padic_reduce(d2, ctx2);
result = (padic_equal(a2, d2, ctx2));
if (!result)
{
printf("FAIL (random elements):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("a2 = "), padic_print(a2, ctx2), printf("\n");
printf("d2 = "), padic_print(d2, ctx2), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
padic_clear(a2, ctx2);
padic_clear(d2, ctx2);
padic_ctx_clear(ctx2);
}
else
{
result = (!ans || padic_equal(a, d, ctx));
if (!result)
{
printf("FAIL (random elements):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
}
padic_clear(a, ctx);
padic_clear(b, ctx);
padic_clear(d, ctx);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
/* Test random squares */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
long N;
padic_ctx_t ctx;
int ans;
padic_t a, b, c, d;
fmpz_init(p);
fmpz_set_ui(p, n_randprime(state, 5, 1));
N = z_randint(state, 100);
padic_ctx_init(ctx, p, N, PADIC_SERIES);
padic_init(a, ctx);
padic_init(b, ctx);
padic_init(c, ctx);
padic_init(d, ctx);
padic_randtest(b, state, ctx);
padic_mul(a, b, b, ctx);
ans = padic_sqrt(c, a, ctx);
padic_mul(d, c, c, ctx);
if (ans && padic_val(a) < 0)
{
padic_ctx_t ctx2;
padic_t a2, d2;
padic_ctx_init(ctx2, p, N + padic_val(a), PADIC_SERIES);
padic_init(a2, ctx2);
padic_init(d2, ctx2);
padic_set(a2, a, ctx2);
padic_set(d2, d, ctx2);
padic_reduce(a2, ctx2);
padic_reduce(d2, ctx2);
result = (padic_equal(a2, d2, ctx2));
if (!result)
{
printf("FAIL (random elements):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("c = "), padic_print(c, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("a2 = "), padic_print(a2, ctx2), printf("\n");
printf("d2 = "), padic_print(d2, ctx2), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
padic_clear(a2, ctx2);
padic_clear(d2, ctx2);
padic_ctx_clear(ctx2);
}
else
{
result = (ans && padic_equal(a, d, ctx));
if (!result)
{
printf("FAIL (random squares):\n\n");
printf("a = "), padic_print(a, ctx), printf("\n");
printf("b = "), padic_print(b, ctx), printf("\n");
printf("c = "), padic_print(c, ctx), printf("\n");
printf("d = "), padic_print(d, ctx), printf("\n");
printf("p = "), fmpz_print(p), printf("\n");
printf("ans = %d\n", ans);
abort();
}
}
padic_clear(a, ctx);
padic_clear(b, ctx);
padic_clear(c, ctx);
padic_clear(d, ctx);
fmpz_clear(p);
padic_ctx_clear(ctx);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("remove....");
fflush(stdout);
/* Compare with MPIR, random input */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c;
mpz_t d, e, f, g;
slong x, y;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest_not_zero(a, state, 200);
do {
fmpz_randtest_not_zero(b, state, 200);
fmpz_abs(b, b);
} while (fmpz_is_one(b));
fmpz_get_mpz(d, a);
fmpz_get_mpz(e, b);
x = fmpz_remove(c, a, b);
y = mpz_remove(f, d, e);
fmpz_get_mpz(g, c);
result = ((x == y) && (mpz_cmp(f, g) == 0));
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Compare with MPIR, random input but ensure that factors exist */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c, pow;
mpz_t d, e, f, g;
slong x, y;
ulong n;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
fmpz_init(pow);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest_not_zero(a, state, 200);
do {
fmpz_randtest_not_zero(b, state, 200);
fmpz_abs(b, b);
} while (fmpz_is_one(b));
n = n_randint(state, 10);
fmpz_pow_ui(pow, b, n);
fmpz_mul(a, a, pow);
fmpz_get_mpz(d, a);
fmpz_get_mpz(e, b);
x = fmpz_remove(c, a, b);
y = mpz_remove(f, d, e);
fmpz_get_mpz(g, c);
result = ((x == y) && (x >= n) && (mpz_cmp(f, g) == 0));
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
fmpz_clear(pow);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Check aliasing of a and b */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpz_t a, c;
slong x;
fmpz_init(a);
fmpz_init(c);
do {
fmpz_randtest_not_zero(a, state, 200);
fmpz_abs(a, a);
} while (fmpz_is_one(a));
x = fmpz_remove(c, a, a);
result = ((x == 1) && (fmpz_cmp_ui(c, 1) == 0));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_print(a), flint_printf("\n");
fmpz_print(c), flint_printf("\n");
abort();
}
fmpz_clear(a);
fmpz_clear(c);
}
/* Check aliasing of a and c */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c;
slong x, y;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
fmpz_randtest_not_zero(a, state, 200);
do {
fmpz_randtest_not_zero(b, state, 200);
fmpz_abs(b, b);
} while (fmpz_is_one(b));
x = fmpz_remove(c, a, b);
y = fmpz_remove(a, a, b);
result = ((x == y) && fmpz_equal(a, c));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_print(a), flint_printf("\n");
fmpz_print(b), flint_printf("\n");
fmpz_print(c), flint_printf("\n");
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
}
/* Check aliasing of b and c */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c;
slong x, y;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
fmpz_randtest_not_zero(a, state, 200);
do {
fmpz_randtest_not_zero(b, state, 200);
fmpz_abs(b, b);
} while (fmpz_is_one(b));
x = fmpz_remove(c, a, b);
y = fmpz_remove(b, a, b);
result = ((x == y) && fmpz_equal(b, c));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_print(a), flint_printf("\n");
fmpz_print(b), flint_printf("\n");
fmpz_print(c), flint_printf("\n");
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
~FlintZZ() { fmpz_clear(value); }
static void
bsplit_recursive_fmprb(fmprb_t P, fmprb_t Q, fmprb_t B, fmprb_t T,
const hypgeom_t hyp, long a, long b, int cont, long prec)
{
if (b - a < 4)
{
fmpz_t PP, QQ, BB, TT;
fmpz_init(PP);
fmpz_init(QQ);
fmpz_init(BB);
fmpz_init(TT);
bsplit_recursive_fmpz(PP, QQ, BB, TT, hyp, a, b, cont);
fmprb_set_fmpz(P, PP);
fmprb_set_fmpz(Q, QQ);
fmprb_set_fmpz(B, BB);
fmprb_set_fmpz(T, TT);
fmpz_clear(PP);
fmpz_clear(QQ);
fmpz_clear(BB);
fmpz_clear(TT);
}
else
{
long m;
fmprb_t P2, Q2, B2, T2;
m = (a + b) / 2;
fmprb_init(P2);
fmprb_init(Q2);
fmprb_init(B2);
fmprb_init(T2);
bsplit_recursive_fmprb(P, Q, B, T, hyp, a, m, 1, prec);
bsplit_recursive_fmprb(P2, Q2, B2, T2, hyp, m, b, 1, prec);
if (fmprb_is_one(B) && fmprb_is_one(B2))
{
fmprb_mul(T, T, Q2, prec);
fmprb_addmul(T, P, T2, prec);
}
else
{
fmprb_mul(T, T, B2, prec);
fmprb_mul(T, T, Q2, prec);
fmprb_mul(T2, T2, B, prec);
fmprb_addmul(T, P, T2, prec);
}
fmprb_mul(B, B, B2, prec);
fmprb_mul(Q, Q, Q2, prec);
if (cont)
fmprb_mul(P, P, P2, prec);
fmprb_clear(P2);
fmprb_clear(Q2);
fmprb_clear(B2);
fmprb_clear(T2);
}
}
int main(void)
{
int i, j, result;
ulong count = UWORD(0);
gmp_randstate_t st;
FLINT_TEST_INIT(state);
gmp_randinit_default(st);
flint_printf("factor_pp1....");
fflush(stdout);
for (i = 0; i < 50 * flint_test_multiplier(); i++) /* Test random numbers */
{
mp_bitcnt_t bits;
mpz_t m, n;
fmpz_t n1, n2, r;
mpz_init(n);
mpz_init(m);
fmpz_init(n1);
fmpz_init(n2);
fmpz_init(r);
do {
mpz_urandomb(n, st, n_randint(state, 128) + 2);
} while (flint_mpz_cmp_ui(n, 2) < 0);
do {
mpz_urandomb(m, st, n_randint(state, 50) + 2);
} while (!mpz_probab_prime_p(m, 20));
mpz_mul(n, n, m);
fmpz_set_mpz(n1, n);
bits = FLINT_MIN(fmpz_bits(n1), FLINT_BITS);
for (j = 0; j < 20; j++)
{
fmpz_factor_pp1(n2, n1, 10000, 10000, n_randbits(state, bits - 2) + 3);
if (fmpz_cmp_ui(n2, 1) > 0) break;
}
if (fmpz_cmp_ui(n2, 1) > 0)
{
count++;
fmpz_mod(r, n1, n2);
result = (fmpz_is_zero(r));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("n1 = ");
fmpz_print(n1);
flint_printf(", n2 = ");
fmpz_print(n2);
flint_printf("\n");
fmpz_print(r); flint_printf("\n");
abort();
}
}
fmpz_clear(n1);
fmpz_clear(n2);
fmpz_clear(r);
mpz_clear(m);
mpz_clear(n);
}
if (count < 49 * flint_test_multiplier())
{
flint_printf("FAIL:\n");
flint_printf("Only %wu numbers factored\n", count);
abort();
}
gmp_randclear(st);
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int j, i, result;
fq_zech_ctx_t ctx;
FLINT_TEST_INIT(state);
flint_printf("mul_fmpz... ");
fflush(stdout);
for (j = 0; j < 50; j++)
{
fq_zech_ctx_randtest(ctx, state);
for (i = 0; i < 200; i++)
{
fmpz_t x;
fq_nmod_t aa, bb;
fq_zech_t a, b, c;
fq_nmod_init(aa, ctx->fq_nmod_ctx);
fq_nmod_init(bb, ctx->fq_nmod_ctx);
fmpz_init(x);
fmpz_randtest_mod_signed(x, state, fq_zech_ctx_prime(ctx));
fq_nmod_randtest(aa, state, ctx->fq_nmod_ctx);
fq_zech_set_fq_nmod(a, aa, ctx);
fq_nmod_mul_fmpz(bb, aa, x, ctx->fq_nmod_ctx);
fq_zech_set_fq_nmod(b, bb, ctx);
fq_zech_mul_fmpz(c, a, x, ctx);
result = (fq_zech_equal(b, c, ctx));
if (!result)
{
flint_printf("FAIL:\n\n");
fq_zech_ctx_print(ctx);
flint_printf("\n");
flint_printf("aa = ");
fq_nmod_print_pretty(aa, ctx->fq_nmod_ctx);
flint_printf("\n");
flint_printf("a = ");
fq_zech_print_pretty(a, ctx);
flint_printf("\n");
flint_printf("b = ");
fq_zech_print_pretty(b, ctx);
flint_printf("\n");
flint_printf("c = ");
fq_zech_print_pretty(c, ctx);
flint_printf("\n");
abort();
}
fmpz_clear(x);
fq_nmod_clear(bb, ctx->fq_nmod_ctx);
fq_nmod_clear(aa, ctx->fq_nmod_ctx);
}
for (i = 0; i < 200; i++)
{
fmpz_t x;
fq_nmod_t aa, bb;
fq_zech_t a, b;
fq_nmod_init(aa, ctx->fq_nmod_ctx);
fq_nmod_init(bb, ctx->fq_nmod_ctx);
fmpz_init(x);
fmpz_randtest_mod_signed(x, state, fq_zech_ctx_prime(ctx));
fq_nmod_randtest(aa, state, ctx->fq_nmod_ctx);
fq_zech_set_fq_nmod(a, aa, ctx);
fq_nmod_mul_fmpz(bb, aa, x, ctx->fq_nmod_ctx);
fq_zech_set_fq_nmod(b, bb, ctx);
fq_zech_mul_fmpz(a, a, x, ctx);
result = (fq_zech_equal(b, a, ctx));
if (!result)
{
flint_printf("FAIL:\n\n");
fq_zech_ctx_print(ctx);
flint_printf("\n");
flint_printf("aa = ");
fq_nmod_print_pretty(aa, ctx->fq_nmod_ctx);
flint_printf("\n");
flint_printf("a = ");
fq_zech_print_pretty(a, ctx);
flint_printf("\n");
flint_printf("b = ");
fq_zech_print_pretty(b, ctx);
flint_printf("\n");
abort();
}
fmpz_clear(x);
fq_nmod_clear(bb, ctx->fq_nmod_ctx);
fq_nmod_clear(aa, ctx->fq_nmod_ctx);
}
fq_zech_ctx_clear(ctx);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
_fmpz_poly_resultant(fmpz_t res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2)
{
if (len2 == 1)
{
fmpz_pow_ui(res, poly2, len1 - 1);
}
else
{
fmpz_t a, b, g, h, t;
fmpz *A, *B, *W;
const long alloc = len1 + len2;
long sgn = 1;
fmpz_init(a);
fmpz_init(b);
fmpz_init(g);
fmpz_init(h);
fmpz_init(t);
A = W = _fmpz_vec_init(alloc);
B = W + len1;
_fmpz_poly_content(a, poly1, len1);
_fmpz_poly_content(b, poly2, len2);
_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, a);
_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, b);
fmpz_set_ui(g, 1);
fmpz_set_ui(h, 1);
fmpz_pow_ui(a, a, len2 - 1);
fmpz_pow_ui(b, b, len1 - 1);
fmpz_mul(t, a, b);
do
{
const long d = len1 - len2;
if (!(len1 & 1L) & !(len2 & 1L))
sgn = -sgn;
_fmpz_poly_pseudo_rem_cohen(A, A, len1, B, len2);
for (len1--; len1 >= 0 && !A[len1]; len1--) ;
len1++;
if (len1 == 0)
{
fmpz_zero(res);
goto cleanup;
}
{
fmpz * T;
long len;
T = A, A = B, B = T;
len = len1, len1 = len2, len2 = len;
}
fmpz_pow_ui(a, h, d);
fmpz_mul(b, g, a);
_fmpz_vec_scalar_divexact_fmpz(B, B, len2, b);
fmpz_pow_ui(g, A + (len1 - 1), d);
fmpz_mul(b, h, g);
fmpz_divexact(h, b, a);
fmpz_set(g, A + (len1 - 1));
} while (len2 > 1);
fmpz_pow_ui(g, h, len1 - 1);
fmpz_pow_ui(b, B + (len2 - 1), len1 - 1);
fmpz_mul(a, h, b);
fmpz_divexact(h, a, g);
fmpz_mul(res, t, h);
if (sgn < 0)
fmpz_neg(res, res);
cleanup:
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(g);
fmpz_clear(h);
fmpz_clear(t);
_fmpz_vec_clear(W, alloc);
}
}
int main(void)
{
char *str; /* String for the input polynomial P */
mpoly_t P; /* Input polynomial P */
int n; /* Number of variables minus one */
long K; /* Required t-adic precision */
long N, Nw;
long b; /* Matrix dimensions */
long i, j, k;
mat_t M;
ctx_t ctxM;
mon_t *rows, *cols;
padic_mat_struct *C;
fmpz_t p;
fmpz_poly_mat_t B;
long vB;
printf("solve... \n");
fflush(stdout);
/* Example 3-1-1 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[1 1 1]"; */
/* Example 3-3-2 */
/* str = "3 [3 0 0] [0 3 0] [0 0 3] (2 0 1)[2 1 0] (2 0 1)[0 2 1] (2 0 1)[1 0 2]"; */
/* Example 4-4-2 */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[3 1 0 0] (2 0 1)[1 0 1 2] (2 0 1)[0 1 0 3]"; */
/* Example ... */
/* str = "4 [4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] (2 0 1)[1 1 1 1]"; */
/* Example from AKR */
str = "4 (1 3)[0 3 0 0] (2 0 3)[0 1 2 0] "
"(2 0 -1)[1 1 1 0] (2 0 3)[1 1 0 1] "
"(2 0 -1)[2 1 0 0] [0 0 3 0] (2 0 -1)[1 0 2 0] "
"(1 2)[0 0 0 3] [3 0 0 0]";
n = atoi(str) - 1;
K = 616;
N = 10;
Nw = 22;
fmpz_init(p);
fmpz_set_ui(p, 5);
ctx_init_fmpz_poly_q(ctxM);
ctxM->print = &__fmpz_poly_q_print_pretty;
mpoly_init(P, n + 1, ctxM);
mpoly_set_str(P, str, ctxM);
printf("P = "), mpoly_print(P, ctxM), printf("\n");
b = gmc_basis_size(n, mpoly_degree(P, -1, ctxM));
mat_init(M, b, b, ctxM);
fmpz_poly_mat_init(B, b, b);
vB = 0;
gmc_compute(M, &rows, &cols, P, ctxM);
mat_print(M, ctxM);
printf("\n");
gmde_solve(&C, K, p, N, Nw, M, ctxM);
gmde_convert_soln(B, &vB, C, K, p);
printf("Solution to (d/dt + M) C = 0:\n");
fmpz_poly_mat_print(B, "t");
printf("vB = %ld\n", vB);
gmde_check_soln(B, vB, p, N, K, M, ctxM);
mpoly_clear(P, ctxM);
mat_clear(M, ctxM);
free(rows);
free(cols);
fmpz_poly_mat_clear(B);
ctx_clear(ctxM);
fmpz_clear(p);
for (i = 0; i < K; i++)
padic_mat_clear(C + i);
free(C);
_fmpz_cleanup();
return EXIT_SUCCESS;
}
void
acb_pow_fmpz_binexp(acb_t y, const acb_t b, const fmpz_t e, long prec)
{
long i, wp, bits;
if (-2L <= *e && *e <= 4L)
{
if (*e == 0L)
{
acb_one(y);
}
else if (*e == 1L)
{
acb_set_round(y, b, prec);
}
else if (*e == -1L)
{
acb_inv(y, b, prec);
}
else if (*e == 2L)
{
acb_mul(y, b, b, prec);
}
else if (*e == 3L)
{
acb_cube(y, b, prec);
}
else if (*e == 4L)
{
acb_mul(y, b, b, prec);
acb_mul(y, y, y, prec);
}
else
{
acb_inv(y, b, prec);
acb_mul(y, y, y, prec);
}
return;
}
if (fmpz_sgn(e) < 0)
{
fmpz_t f;
fmpz_init(f);
fmpz_neg(f, e);
acb_pow_fmpz_binexp(y, b, f, prec + 2);
acb_inv(y, y, prec);
fmpz_clear(f);
return;
}
if (!COEFF_IS_MPZ(*e) && ((*e) % 3 == 0))
{
fmpz e3 = (*e) / 3;
acb_pow_fmpz_binexp(y, b, &e3, prec);
acb_cube(y, y, prec);
return;
}
if (y == b)
{
acb_t t;
acb_init(t);
acb_set(t, b);
acb_pow_fmpz_binexp(y, t, e, prec);
acb_clear(t);
return;
}
acb_set(y, b);
bits = fmpz_bits(e);
wp = ARF_PREC_ADD(prec, bits);
for (i = bits - 2; i >= 0; i--)
{
acb_mul(y, y, y, wp);
if (fmpz_tstbit(e, i))
acb_mul(y, y, b, wp);
}
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("pseudo_div....");
fflush(stdout);
/* Check r = a - q * b has small degree, no aliasing */
for (i = 0; i < 200 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, q, r, prod;
fmpz_t p;
ulong d;
fmpz_init(p);
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(q);
fmpz_poly_init(r);
fmpz_poly_init(prod);
fmpz_poly_randtest(a, state, n_randint(state, 100), 50);
fmpz_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1, 50);
fmpz_poly_pseudo_div(q, &d, a, b);
fmpz_poly_mul(prod, q, b);
fmpz_pow_ui(p, b->coeffs + b->length - 1, d);
fmpz_poly_scalar_mul_fmpz(a, a, p);
fmpz_poly_sub(r, a, prod);
result = (fmpz_poly_length(r) < fmpz_poly_length(b));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(a), flint_printf("\n\n");
fmpz_poly_print(prod), flint_printf("\n\n");
fmpz_poly_print(q), flint_printf("\n\n");
fmpz_poly_print(r), flint_printf("\n\n");
abort();
}
fmpz_clear(p);
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(q);
fmpz_poly_clear(r);
fmpz_poly_clear(prod);
}
/* Check q and a alias */
for (i = 0; i < 50 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, q;
ulong d;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(q);
fmpz_poly_randtest(a, state, n_randint(state, 100), 50);
fmpz_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1, 50);
fmpz_poly_pseudo_div(q, &d, a, b);
fmpz_poly_pseudo_div(a, &d, a, b);
result = (fmpz_poly_equal(a, q));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(a), flint_printf("\n\n");
fmpz_poly_print(q), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(q);
}
/* Check q and b alias */
for (i = 0; i < 50 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, q;
ulong d;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(q);
fmpz_poly_randtest(a, state, n_randint(state, 100), 50);
fmpz_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1, 50);
fmpz_poly_pseudo_div(q, &d, a, b);
fmpz_poly_pseudo_div(b, &d, a, b);
result = (fmpz_poly_equal(b, q));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(a), flint_printf("\n\n");
fmpz_poly_print(q), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(q);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
