int main(void) { int i, result; flint_rand_t state; _randinit(state); { const char *str = "3 [5 0 0] [0 5 0] [0 0 5] (2 0 1)[1 1 3]"; const long n = atoi(str) - 1; mpoly_t P; ctx_t ctxFracQt; qadic_ctx_t Qq; fmpz_t p = {3L}; long d = 40; qadic_t t1; prec_t prec, prec_in; /* prec_in.N0 = 9; prec_in.N1 = 9; prec_in.N2 = 9; prec_in.N3 = 13; prec_in.N3i = 14; prec_in.N3w = 23; prec_in.N3iw = 22; prec_in.N4 = 18; prec_in.m = 29; prec_in.K = 178; prec_in.r = 0; prec_in.s = 0; */ ctx_init_fmpz_poly_q(ctxFracQt); qadic_ctx_init_conway(Qq, p, d, 1, 1, "X", PADIC_SERIES); qadic_init2(t1, 1); qadic_gen(t1, Qq); mpoly_init(P, n + 1, ctxFracQt); mpoly_set_str(P, str, ctxFracQt); frob(P, ctxFracQt, t1, Qq, &prec, NULL, 1); qadic_clear(t1); mpoly_clear(P, ctxFracQt); ctx_clear(ctxFracQt); qadic_ctx_clear(Qq); } _randclear(state); _fmpz_cleanup(); return EXIT_SUCCESS; }
int main(void) { int i, result; flint_rand_t state; _randinit(state); /* A generic sextic curve. */ { const char *str = "3 [6 0 0] [0 6 0] [0 0 6] " "(2 0 -1)[5 1 0] (2 0 7)[5 0 1] (2 0 2)[1 5 0] (2 0 1)[0 5 1] (2 0 2)[1 0 5] (2 0 1)[0 1 5] " "(2 0 2)[4 2 0] (2 0 2)[4 0 2] (2 0 3)[2 4 0] (2 0 1)[0 4 2] (2 0 3)[2 0 4] (2 0 1)[0 2 4] " "(2 0 3)[4 1 1] (2 0 3)[1 4 1] (2 0 1)[1 1 4] " "(2 0 -1)[3 3 0] (2 0 -2)[3 0 3] (2 0 4)[0 3 3] " "(2 0 2)[3 2 1] (2 0 1)[3 1 2] (2 0 -1)[2 3 1] (2 0 1)[1 3 2] (2 0 2)[2 1 3] (2 0 1)[1 2 3] " "(2 0 1)[2 2 2]"; const long n = atoi(str) - 1; mpoly_t P; ctx_t ctxFracQt; qadic_ctx_t Qq; fmpz_t p = {5L}; long d = 1; qadic_t t1; prec_t prec, prec_in; ctx_init_fmpz_poly_q(ctxFracQt); qadic_ctx_init_conway(Qq, p, d, 1, 1, "X", PADIC_SERIES); qadic_init2(t1, 1); qadic_set_ui(t1, 2, Qq); mpoly_init(P, n + 1, ctxFracQt); mpoly_set_str(P, str, ctxFracQt); frob(P, ctxFracQt, t1, Qq, &prec, NULL, 1); qadic_clear(t1); mpoly_clear(P, ctxFracQt); ctx_clear(ctxFracQt); qadic_ctx_clear(Qq); } _randclear(state); _fmpz_cleanup(); return EXIT_SUCCESS; }
int main(void) { int i, result; flint_rand_t state; _randinit(state); /* A quartic surface from Example 4.2.1 in [AKR]. TODO: This currently still fails! */ { const char *str = "4 (2 2 -1)[4 0 0 0] [0 4 0 0] [0 0 4 0] [0 0 0 4] " "(2 0 -1)[0 1 3 0] (2 0 1)[1 1 2 0] (2 0 1)[1 1 1 1] " "(2 0 1)[2 1 1 0] (2 0 -1)[2 1 0 1] (2 0 1)[1 0 3 0] (2 0 -1)[1 0 2 1]"; const long n = atoi(str) - 1; mpoly_t P; ctx_t ctxFracQt; qadic_ctx_t Qq; fmpz_t p = {3L}; long d = 2; qadic_t t1; prec_t prec, prec_in; ctx_init_fmpz_poly_q(ctxFracQt); qadic_ctx_init_conway(Qq, p, d, 1, 1, "X", PADIC_SERIES); qadic_init2(t1, 1); qadic_gen(t1, Qq); mpoly_init(P, n + 1, ctxFracQt); mpoly_set_str(P, str, ctxFracQt); frob(P, ctxFracQt, t1, Qq, &prec, NULL, 1); qadic_clear(t1); mpoly_clear(P, ctxFracQt); ctx_clear(ctxFracQt); qadic_ctx_clear(Qq); } _randclear(state); _fmpz_cleanup(); return EXIT_SUCCESS; }
int main(void) { int i, result; flint_rand_t state; _randinit(state); { const char *str = "4 [5 0 0 0] [0 5 0 0] [0 0 5 0] [0 0 0 5] (2 0 1)[2 1 1 1]"; const long n = atoi(str) - 1; mpoly_t P; ctx_t ctxFracQt; qadic_ctx_t Qq; fmpz_t p = {2L}; long d = 10; qadic_t t1; prec_t prec, prec_in; ctx_init_fmpz_poly_q(ctxFracQt); qadic_ctx_init_conway(Qq, p, d, 1, 1, "X", PADIC_SERIES); qadic_init2(t1, 1); qadic_gen(t1, Qq); mpoly_init(P, n + 1, ctxFracQt); mpoly_set_str(P, str, ctxFracQt); frob(P, ctxFracQt, t1, Qq, &prec, NULL, 1); qadic_clear(t1); mpoly_clear(P, ctxFracQt); ctx_clear(ctxFracQt); qadic_ctx_clear(Qq); } _randclear(state); _fmpz_cleanup(); 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; }
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; }