Line data Source code
1 : /* Copyright (C) 2004 The PARI group.
2 :
3 : This file is part of the PARI/GP package.
4 :
5 : PARI/GP is free software; you can redistribute it and/or modify it under the
6 : terms of the GNU General Public License as published by the Free Software
7 : Foundation; either version 2 of the License, or (at your option) any later
8 : version. It is distributed in the hope that it will be useful, but WITHOUT
9 : ANY WARRANTY WHATSOEVER.
10 :
11 : Check the License for details. You should have received a copy of it, along
12 : with the package; see the file 'COPYING'. If not, write to the Free Software
13 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
14 :
15 : BEGINEXTERN
16 :
17 : #define uel(a,i) (((ulong*)(a))[i])
18 : #define ucoeff(a,i,j) (((ulong**)(a))[j][i])
19 : #define umael(a,i,j) (((ulong**)(a))[i][j])
20 : #define umael2(a,i,j) (((ulong**)(a))[i][j])
21 : #define umael3(a,i,j,k) (((ulong***)(a))[i][j][k])
22 : #define umael4(a,i,j,k,l) (((ulong****)(a))[i][j][k][l])
23 : #define umael5(a,i,j,k,l,m) (((ulong*****)(a))[i][j][k][l][m])
24 :
25 : #define numberof(x) (sizeof(x) / sizeof((x)[0]))
26 :
27 : /* to manipulate 'blocs' */
28 : #define BL_HEAD 8
29 : #define bl_base(x) (void*)((x) - BL_HEAD)
30 : #define bl_height(x) (((GEN)x)[-8])
31 : #define bl_left(x) (((GEN*)x)[-7])
32 : #define bl_right(x) (((GEN*)x)[-6])
33 : #define bl_size(x) (((GEN)x)[-5])
34 : #define bl_refc(x) (((GEN)x)[-4])
35 : #define bl_next(x) (((GEN*)x)[-3])
36 : #define bl_prev(x) (((GEN*)x)[-2])
37 : #define bl_num(x) (((GEN)x)[-1])
38 :
39 : void clone_lock(GEN C);
40 : void clone_unlock(GEN C);
41 : void clone_unlock_deep(GEN C);
42 :
43 : /* swap */
44 : #define lswap(x,y) {long _z=x; x=y; y=_z;}
45 : #define pswap(x,y) {GEN *_z=x; x=y; y=_z;}
46 : #define swap(x,y) {GEN _z=x; x=y; y=_z;}
47 : #define dswap(x,y) { double _t=x; x=y; y=_t; }
48 : #define swapspec(x,y, nx,ny) {swap(x,y); lswap(nx,ny);}
49 :
50 : /* loops */
51 : GEN incloop(GEN a);
52 : GEN resetloop(GEN a, GEN b);
53 : GEN setloop(GEN a);
54 :
55 : /* parser */
56 :
57 : /* GP control structures */
58 : #define EXPR_WRAP(code, call) \
59 : { GEN z; GEN __E = code; \
60 : push_lex(gen_0, __E); z = call; pop_lex(1); return z; }
61 : #define EXPRVOID_WRAP(code, call) \
62 : { GEN __E = code; \
63 : push_lex(gen_0, __E); call; pop_lex(1); }
64 : #define EXPR_ARG __E, &gp_eval
65 : #define EXPR_ARGPREC __E, &gp_evalprec
66 : #define EXPR_ARGUPTO __E, &gp_evalupto
67 : #define EXPR_ARGBOOL __E, &gp_evalbool
68 : #define EXPR_ARGVOID __E, &gp_evalvoid
69 :
70 : GEN andpari(GEN a, GEN b);
71 : GEN orpari(GEN a, GEN b);
72 : void ifpari_void(GEN g, GEN a, GEN b);
73 : GEN ifpari_multi(GEN g, GEN a);
74 :
75 : GEN gadde(GEN *x, GEN y);
76 : GEN gadd1e(GEN *x);
77 : GEN gdive(GEN *x, GEN y);
78 : GEN gdivente(GEN *x, GEN y);
79 : GEN gdivrounde(GEN *x, GEN y);
80 : GEN gmode(GEN *x, GEN y);
81 : GEN gmule(GEN *x, GEN y);
82 : GEN gshiftle(GEN *x, long n);
83 : GEN gshiftre(GEN *x, long n);
84 : GEN gsube(GEN *x, GEN y);
85 : GEN gsub1e(GEN *x);
86 : GEN gshift_right(GEN x, long n);
87 :
88 : GEN derivfun0(GEN args, GEN def, GEN code, long k, long prec);
89 : GEN direuler_bad(void *E, GEN (*eval)(void *, GEN, long), GEN a, GEN b, GEN c, GEN Sbad);
90 : GEN vecexpr0(GEN nmax, GEN code, GEN pred);
91 : GEN vecexpr1(GEN nmax, GEN code, GEN pred);
92 :
93 : /* mt */
94 : void mt_sigint(void);
95 : void mt_err_recover(long er);
96 : void mt_break_recover(void);
97 : void mt_export_add(const char *str, GEN val);
98 : void mt_export_del(const char *str);
99 : void mt_init_stack(size_t s);
100 : int mt_is_thread(void);
101 : void mt_thread_init(void);
102 :
103 : GEN eisker_worker(GEN Ei, GEN M, GEN D, GEN co, GEN CD);
104 : GEN pareval_worker(GEN code);
105 : GEN parfor_worker(GEN i, GEN C);
106 : GEN parvector_worker(GEN i, GEN C);
107 : GEN polmodular_worker(GEN pt, ulong L, GEN hilb, GEN factu,
108 : GEN vne, GEN vinfo, long compute_derivs, GEN j_powers, GEN G_surface,
109 : GEN G_floor, GEN fdb);
110 : GEN polclass_worker(GEN p, GEN G, GEN db);
111 : GEN nf_L2_bound(GEN nf, GEN den, GEN *pL);
112 : GEN nmV_polint_center_tree_worker(GEN Va, GEN T, GEN R, GEN xa, GEN m2);
113 : GEN nmV_chinese_center_tree_seq(GEN A, GEN P, GEN T, GEN R);
114 : GEN nxMV_polint_center_tree_worker(GEN Va, GEN T, GEN R, GEN xa, GEN m2);
115 : GEN nxMV_chinese_center_tree_seq(GEN A, GEN P, GEN T, GEN R);
116 : GEN F2xq_log_Coppersmith_worker(GEN u, long i, GEN V, GEN R);
117 : GEN Flxq_log_Coppersmith_worker(GEN u, long i, GEN V, GEN R);
118 : GEN Fp_log_sieve_worker(long a, long prmax, GEN C, GEN c, GEN Ci, GEN ci, GEN pr, GEN sz);
119 : GEN QM_charpoly_ZX_worker(GEN P, GEN M, GEN dM);
120 : GEN QXQ_div_worker(GEN P, GEN A, GEN B, GEN C);
121 : GEN QXQ_inv_worker(GEN P, GEN A, GEN B);
122 : GEN RgM_ZM_mul_worker(GEN y, GEN x);
123 : GEN ZX_resultant_worker(GEN P, GEN A, GEN B, GEN dB);
124 : GEN ZXQX_resultant_worker(GEN P, GEN A, GEN B, GEN T, GEN dB);
125 : GEN ZX_ZXY_resultant_worker(GEN P, GEN A, GEN B, GEN dB, GEN v);
126 : GEN ZX_composedsum_worker(GEN P, GEN A, GEN B);
127 : GEN ZXQX_composedsum_worker(GEN P, GEN A, GEN B, GEN C);
128 : GEN ZX_gcd_worker(GEN P, GEN A, GEN B, GEN g);
129 : GEN ZXQ_minpoly_worker(GEN P, GEN A, GEN B, long d);
130 : GEN ZM_det_worker(GEN P, GEN A);
131 : GEN ZM_inv_worker(GEN P, GEN A);
132 : GEN ZM_ker_worker(GEN P, GEN A);
133 : GEN ZM_mul_worker(GEN P, GEN A, GEN B);
134 : GEN ZM_sqr_worker(GEN P, GEN A);
135 : GEN ZM_gauss_worker(GEN P, GEN A, GEN B);
136 : GEN ZabM_inv_worker(GEN P, GEN A, GEN Q);
137 : GEN aprcl_step4_worker(ulong q, GEN pC, GEN N, GEN v);
138 : GEN aprcl_step6_worker(GEN r, long t, GEN N, GEN N1, GEN et);
139 : GEN ecpp_sqrt_worker(GEN g, GEN N, GEN p);
140 : GEN ecpp_ispsp_worker(GEN N);
141 : GEN ecpp_step2_worker(GEN S, GEN HD, GEN primelist, long dbg);
142 : GEN primecertisvalid_ecpp_worker(GEN certi);
143 : GEN lfuninit_worker(long r, GEN K, GEN L, GEN peh2d, GEN vroots, GEN dr, GEN di, GEN an, GEN bn);
144 : GEN lfuninit_theta2_worker(long r, GEN L, GEN qk, GEN a, GEN di, GEN an, GEN bn);
145 : GEN gen_parapply(GEN worker, GEN D);
146 : GEN gen_parapply_percent(GEN worker, GEN D, long percent);
147 : GEN parapply_slice_worker(GEN worker, GEN D);
148 : GEN gen_parapply_slice(GEN worker, GEN D, long mmin);
149 : GEN gen_crt(const char *str, GEN worker, forprime_t *S, GEN dB, ulong bound, long mmin, GEN *pt_mod,
150 : GEN crt(GEN, GEN, GEN*), GEN center(GEN, GEN, GEN));
151 : void gen_inccrt(const char *str, GEN worker, GEN dB, long n, long mmin,
152 : forprime_t *S, GEN *pt_H, GEN *pt_mod, GEN crt(GEN, GEN, GEN*),
153 : GEN center(GEN, GEN, GEN));
154 : void gen_inccrt_i(const char *str, GEN worker, GEN dB, long n, long mmin,
155 : forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
156 : GEN center(GEN, GEN, GEN));
157 : GEN direllnf_worker(GEN P, ulong X, GEN E);
158 : GEN dirartin_worker(GEN P, ulong X, GEN nf, GEN G, GEN V, GEN aut);
159 : GEN direllsympow_worker(GEN P, ulong X, GEN E, ulong m);
160 : GEN dirgenus2_worker(GEN P, ulong X, GEN Q);
161 : GEN dirhgm_worker(GEN P, ulong X, GEN hgm, GEN t);
162 : GEN pardireuler(GEN worker, GEN a, GEN b, GEN c, GEN Sbad);
163 : GEN FpM_ratlift_worker(GEN A, GEN mod, GEN B);
164 : GEN ellQ_factorback_worker(GEN P, GEN E, GEN A, GEN L, ulong l);
165 : GEN chinese_unit_worker(GEN P, GEN A, GEN U, GEN B, GEN D, GEN C);
166 : GEN partmap_reverse_frac_worker(GEN t, GEN a, GEN b, GEN la, GEN lb, long v);
167 : GEN parsqf_worker(GEN gk, GEN vR, GEN data);
168 : GEN parsum_slice_worker(GEN a, GEN b, GEN m, GEN worker);
169 : GEN parsumprimefun_worker(GEN gk, GEN s, GEN zerf, GEN data, GEN vW, GEN f);
170 : GEN lerch_worker(GEN t, GEN E);
171 : GEN ramanujantau_worker(GEN gt, GEN p2_7, GEN p_9, GEN p);
172 : GEN taugen_n_worker(GEN t, GEN pol, GEN p4);
173 : GEN serh_worker(GEN gk, GEN V, GEN a, GEN ns, GEN gprec);
174 :
175 : /* Relative number fields */
176 : enum { rnf_NFABS = 1, rnf_MAPS };
177 :
178 : /* Finite fields */
179 : enum { t_FF_FpXQ = 0, t_FF_Flxq = 1, t_FF_F2xq = 2 };
180 : GEN FF_ellinit(GEN E, GEN fg);
181 : GEN FF_elldata(GEN E, GEN fg);
182 :
183 : /* L functions */
184 : enum { t_LFUN_GENERIC, t_LFUN_ZETA, t_LFUN_NF, t_LFUN_ELL, t_LFUN_KRONECKER,
185 : t_LFUN_CHIZ, t_LFUN_CHIGEN, t_LFUN_ETA,
186 : t_LFUN_DIV, t_LFUN_MUL, t_LFUN_CONJ,
187 : t_LFUN_SYMPOW_ELL, t_LFUN_QF, t_LFUN_ARTIN, t_LFUN_MFCLOS,
188 : t_LFUN_GENUS2, t_LFUN_TWIST, t_LFUN_CLOSURE0, t_LFUN_SHIFT,
189 : t_LFUN_HGM, t_LFUN_HECKE,t_LFUN_ABELREL};
190 : enum { t_LDESC_INIT, t_LDESC_THETA, t_LDESC_PRODUCT };
191 :
192 : /* Elliptic curves */
193 : /* common to Q and Rg */
194 : enum { R_PERIODS = 1, R_ETA, R_ROOTS, R_AB };
195 :
196 : enum { Qp_ROOT = 1, Qp_TATE };
197 : enum { Q_GROUPGEN = 5, Q_GLOBALRED, Q_ROOTNO, Q_MINIMALMODEL };
198 : enum { NF_MINIMALMODEL = 1, NF_GLOBALRED, NF_MINIMALPRIMES, NF_ROOTNO, NF_NF };
199 :
200 : /* common to Fp and Fq */
201 : enum { FF_CARD = 1, FF_GROUP, FF_GROUPGEN, FF_O };
202 :
203 : /* for Buchall_param */
204 : enum { fupb_NONE = 0, fupb_RELAT, fupb_LARGE, fupb_PRECI };
205 :
206 : /* Represents the data in the equation(s)
207 : * 4p = t^2 - v^2 D = t^2 - v^2 u^2 D_K = w^2 D_K.
208 : * t is the absolute trace, so always > 0.
209 : * T is a twisting parameter, which satisfies (T|p) == -1. */
210 : typedef struct {
211 : GEN faw; /* factor(u*v) */
212 : long D, t, u, v;
213 : ulong p, pi, s2, T;
214 : } norm_eqn_struct;
215 : typedef norm_eqn_struct norm_eqn_t[1];
216 : void norm_eqn_set(norm_eqn_t ne, long D,long t,long u,long v,GEN faw,ulong p);
217 :
218 : #define zv_to_longptr(v) (&((v)[1]))
219 : #define zv_to_ulongptr(v) ((ulong *)&((v)[1]))
220 :
221 : /* Modular invariants */
222 : #define INV_J 0
223 : #define INV_F 1
224 : #define INV_F2 2
225 : #define INV_F3 3
226 : #define INV_F4 4
227 : #define INV_G2 5
228 : #define INV_W2W3 6
229 : #define INV_F8 8
230 : #define INV_W3W3 9
231 : #define INV_W2W5 10
232 : #define INV_W2W7 14
233 : #define INV_W3W5 15
234 : #define INV_W3W7 21
235 : #define INV_W2W3E2 23
236 : #define INV_W2W5E2 24
237 : #define INV_W2W13 26
238 : #define INV_W2W7E2 27
239 : #define INV_W3W3E2 28
240 : #define INV_W5W7 35
241 : #define INV_W3W13 39
242 : #define INV_ATKIN3 103
243 : #define INV_ATKIN5 105
244 : #define INV_ATKIN7 107
245 : #define INV_LAST 107
246 :
247 : /* Get coefficient of x^d in f, assuming f is nonzero. */
248 16921335 : INLINE ulong Flx_coeff(GEN f, long d) { return f[d + 2]; }
249 : /* Return the root of f, assuming deg(f) = 1. */
250 296114 : INLINE ulong Flx_deg1_root(GEN f, ulong p) {
251 296114 : if (degpol(f) != 1) pari_err_BUG("Flx_deg1_root");
252 296105 : return Fl_div(Fl_neg(Flx_coeff(f, 0), p), Flx_coeff(f, 1), p);
253 : }
254 :
255 : /* Allocation / GC */
256 : long getdebugvar(void);
257 : void setdebugvar(long n);
258 : void debug_stack(void);
259 : void minim_alloc(long n, double ***q, GEN *x, double **y, double **z, double **v);
260 : int pop_entree_block(entree *ep, long loc);
261 : int pop_val_if_newer(entree *ep, long loc);
262 :
263 : /* general printing */
264 : void print_errcontext(PariOUT *out, const char *msg, const char *s, const char *entry);
265 : void print_prefixed_text(PariOUT *out, const char *s, const char *prefix, const char *str);
266 : INLINE void
267 76 : print_text(const char *s) { print_prefixed_text(pariOut, s,NULL,NULL); }
268 : INLINE void
269 5327 : out_print_text(PariOUT *out, const char *s) { print_prefixed_text(out, s,NULL,NULL); }
270 : INLINE long
271 2596314 : is_keyword_char(char c) { return (isalnum((unsigned char)c) || c=='_'); }
272 :
273 : /* Interfaces (GP, etc.) */
274 : hashtable *hash_from_link(GEN e, GEN names, int use_stack);
275 : void gen_relink(GEN x, hashtable *table);
276 : entree* do_alias(entree *ep);
277 : char* get_sep(const char *t);
278 : long get_int(const char *s, long dflt);
279 : void gp_initrc(pari_stack *p_A);
280 :
281 : void pari_sigint(const char *s);
282 : void* get_stack(double fraction, long min);
283 : void free_graph(void);
284 : void initout(int initerr);
285 : void resetout(int initerr);
286 : void init_linewrap(long w);
287 : void print_functions_hash(const char *s);
288 : GEN readbin(const char *name, FILE *f, int *vector);
289 : int term_height(void);
290 : int term_width(void);
291 : /* gp_colors */
292 : void decode_color(long n, long *c);
293 :
294 : /* defaults */
295 : extern long precreal;
296 :
297 : void gen_output(GEN x);
298 : void fputGEN_pariout(GEN x, pariout_t *T, FILE *out);
299 :
300 : void parsestate_reset(void);
301 : void parsestate_save(struct pari_parsestate *state);
302 : void parsestate_restore(struct pari_parsestate *state);
303 :
304 : void compilestate_reset(void);
305 : void compilestate_save(struct pari_compilestate *comp);
306 : void compilestate_restore(struct pari_compilestate *comp);
307 :
308 : void filestate_save(struct pari_filestate *file);
309 : void filestate_restore(struct pari_filestate *file);
310 : void tmp_restore(pariFILE *F);
311 :
312 : long evalstate_get_trace(void);
313 : void evalstate_set_trace(long lvl);
314 : void evalstate_clone(void);
315 : void evalstate_reset(void);
316 : void evalstate_restore(struct pari_evalstate *state);
317 : GEN evalstate_restore_err(struct pari_evalstate *state);
318 : void evalstate_save(struct pari_evalstate *state);
319 : void varstate_save(struct pari_varstate *s);
320 : void varstate_restore(struct pari_varstate *s);
321 :
322 : void mtstate_save(struct pari_mtstate *s);
323 : void mtstate_reset(void);
324 : void mtstate_restore(struct pari_mtstate *s);
325 :
326 : void debug_context(void);
327 :
328 : typedef struct {
329 : const char *s;
330 : size_t ls;
331 : char **dir;
332 : } forpath_t;
333 : void forpath_init(forpath_t *T, gp_path *path, const char *s);
334 : char *forpath_next(forpath_t *T);
335 :
336 : /* GP output && output format */
337 : extern char *current_logfile;
338 :
339 : /* colors */
340 : extern long gp_colors[];
341 : extern int disable_color;
342 :
343 : /* entrees */
344 : #define EpVALENCE(ep) ((ep)->valence & 0xFF)
345 : #define EpSTATIC(ep) ((ep)->valence & 0x100)
346 : #define EpSETSTATIC(ep) ((ep)->valence |= 0x100)
347 : enum { EpNEW = 100, EpALIAS, EpVAR, EpINSTALL };
348 : #define initial_value(ep) ((ep)+1)
349 :
350 : /* functions lists */
351 : extern const long functions_tblsz; /* hashcodes table size */
352 : extern entree **functions_hash; /* functions hashtable */
353 : extern entree **defaults_hash; /* defaults hashtable */
354 :
355 : /* buffers */
356 : typedef struct Buffer {
357 : char *buf;
358 : ulong len;
359 : jmp_buf env;
360 : } Buffer;
361 : Buffer *new_buffer(void);
362 : void delete_buffer(Buffer *b);
363 : void fix_buffer(Buffer *b, long newlbuf);
364 :
365 : typedef struct {
366 : const char *s; /* source */
367 : char *t, *end; /* target, last char read */
368 : int in_string, in_comment, more_input, wait_for_brace;
369 : Buffer *buf;
370 : } filtre_t;
371 : void init_filtre(filtre_t *F, Buffer *buf);
372 : Buffer *filtered_buffer(filtre_t *F);
373 : void kill_buffers_upto_including(Buffer *B);
374 : void pop_buffer(void);
375 : void kill_buffers_upto(Buffer *B);
376 : int gp_read_line(filtre_t *F, const char *PROMPT);
377 : void parse_key_val(char *src, char **ps, char **pt);
378 : extern int (*cb_pari_get_line_interactive)(const char*, const char*, filtre_t *F);
379 : extern char *(*cb_pari_fgets_interactive)(char *s, int n, FILE *f);
380 : int get_line_from_file(const char *prompt, filtre_t *F, FILE *file);
381 : void pari_skip_space(char **s);
382 : void pari_skip_alpha(char **s);
383 : char *pari_translate_string(const char *src, char *s, char *entry);
384 :
385 : gp_data *default_gp_data(void);
386 :
387 : typedef char *(*fgets_t)(char *, int, void*);
388 :
389 : typedef struct input_method {
390 : /* optional */
391 : fgets_t myfgets; /* like libc fgets() but last argument is (void*) */
392 : /* mandatory */
393 : char * (*getline)(char**, int f, struct input_method*, filtre_t *F);
394 : int free; /* boolean: must we free the output of getline() ? */
395 : /* optional */
396 : const char *prompt, *prompt_cont;
397 : void *file; /* can be used as last argument for fgets() */
398 : } input_method;
399 :
400 : int input_loop(filtre_t *F, input_method *IM);
401 : char *file_input(char **s0, int junk, input_method *IM, filtre_t *F);
402 : char *file_getline(Buffer *b, char **s0, input_method *IM);
403 :
404 : /* readline */
405 : typedef struct {
406 : /* pointers to readline variables/functions */
407 : char **line_buffer;
408 : int *point;
409 : int *end;
410 : char **(*completion_matches)(const char *, char *(*)(const char*, int));
411 : char *(*filename_completion_function)(const char *, int);
412 : char *(*username_completion_function)(const char *, int);
413 : int (*insert)(int, int);
414 : int *completion_append_character;
415 :
416 : /* PARI-specific */
417 : int back; /* rewind the cursor by this number of chars */
418 : } pari_rl_interface;
419 :
420 : /* Code which wants to use readline needs to do the following:
421 :
422 : #include <readline/readline.h>
423 : #include <pari/paripriv.h>
424 : pari_rl_interface pari_rl;
425 : pari_use_readline(pari_rl);
426 :
427 : This will initialize the pari_rl structure. A pointer to this structure
428 : must be given as first argument to all PARI readline functions. */
429 :
430 : /* IMPLEMENTATION NOTE: this really must be a macro (not a function),
431 : * since we refer to readline symbols. */
432 : #define pari_use_readline(pari_rl) do {\
433 : (pari_rl).line_buffer = &rl_line_buffer; \
434 : (pari_rl).point = &rl_point; \
435 : (pari_rl).end = &rl_end; \
436 : (pari_rl).completion_matches = &rl_completion_matches; \
437 : (pari_rl).filename_completion_function = &rl_filename_completion_function; \
438 : (pari_rl).username_completion_function = &rl_username_completion_function; \
439 : (pari_rl).insert = &rl_insert; \
440 : (pari_rl).completion_append_character = &rl_completion_append_character; \
441 : (pari_rl).back = 0; } while(0)
442 :
443 : /* FIXME: EXPORT AND DOCUMENT THE FOLLOWING */
444 :
445 : /* PROBABLY NOT IN THE RIGHT FILE, SORT BY THEME */
446 :
447 : /* multiprecision */
448 : GEN adduispec_offset(ulong s, GEN x, long offset, long nx);
449 : int lgcdii(ulong* d, ulong* d1, ulong* u, ulong* u1, ulong* v, ulong* v1, ulong vmax);
450 : ulong rgcduu(ulong d, ulong d1, ulong vmax, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
451 : ulong xgcduu(ulong d, ulong d1, int f, ulong* v, ulong* v1, long *s);
452 : ulong xxgcduu(ulong d, ulong d1, int f, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
453 : GEN muliispec(GEN x, GEN y, long nx, long ny);
454 : GEN red_montgomery(GEN T, GEN N, ulong inv);
455 : GEN sqrispec(GEN x, long nx);
456 : ulong *convi(GEN x, long *l);
457 :
458 : /* powers */
459 : GEN rpowuu(ulong a, ulong n, long prec);
460 :
461 : /* hnf */
462 : GEN hnfadd(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
463 : GEN hnfadd_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
464 : GEN hnfspec_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
465 : GEN hnfspec(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
466 : GEN mathnfspec(GEN x, GEN *ptperm, GEN *ptdep, GEN *ptB, GEN *ptC);
467 : GEN ZM_hnfmodall_i(GEN x, GEN dm, long flag);
468 :
469 : GEN LLL_check_progress(GEN Bnorm, long n0, GEN m, int final, long *ti_LLL);
470 :
471 : /* integer factorization / discrete log */
472 : ulong is_kth_power(GEN x, ulong p, GEN *pt);
473 : GEN mpqs(GEN N);
474 :
475 : /* Polynomials */
476 : /* a) Arithmetic/conversions */
477 : GEN lift_if_rational(GEN x);
478 : GEN monomial(GEN a, long degpol, long v);
479 : GEN monomialcopy(GEN a, long degpol, long v);
480 : GEN ser2pol_i(GEN x, long lx);
481 : GEN ser2pol_i_normalize(GEN x, long l, long *v);
482 : GEN ser2rfrac_i(GEN x);
483 : GEN swap_vars(GEN b0, long v, long vc);
484 : GEN RgX_recipspec_shallow(GEN x, long l, long n);
485 : GEN Xpm1_powu(long n, long s, long v);
486 :
487 : /* b) Modular */
488 : GEN bezout_lift_fact(GEN T, GEN Tmod, GEN p, long e);
489 : GEN polsym_gen(GEN P, GEN y0, long n, GEN T, GEN N);
490 : GEN ZXQ_charpoly_sqf(GEN A, GEN B, long *lambda, long v);
491 : GEN ZX_disc_all(GEN,ulong);
492 : GEN ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound);
493 : GEN ZX_ZXY_resultant_all(GEN A, GEN B, long *lambda, GEN *LPRS);
494 :
495 : GEN FlxqM_mul_Kronecker(GEN A, GEN B, GEN T, ulong p);
496 : GEN FqM_mul_Kronecker(GEN x, GEN y, GEN T, GEN p);
497 :
498 : /* c) factorization */
499 : GEN chk_factors_get(GEN lt, GEN famod, GEN c, GEN T, GEN N);
500 : long cmbf_maxK(long nb);
501 : GEN ZX_DDF(GEN x);
502 : GEN ZX_DDF_max(GEN x, long dmax);
503 : GEN initgaloisborne(GEN T, GEN dn, long prec, GEN *pL, GEN *pprep, GEN *pdis);
504 :
505 : /* number fields */
506 : GEN nflist_C3_worker(GEN gv, GEN T);
507 : GEN nflist_C4vec_worker(GEN gm, GEN X, GEN Xinf, GEN gs);
508 : GEN nflist_V4_worker(GEN D1, GEN X, GEN Xinf, GEN gs);
509 : GEN nflist_D4_worker(GEN D, GEN X, GEN Xinf, GEN listarch);
510 : GEN nflist_A4S4_worker(GEN P3, GEN X, GEN Xinf, GEN cards);
511 : GEN nflist_C5_worker(GEN N, GEN bnfC5);
512 : GEN nflist_CL_worker(GEN Fcond, GEN bnf, GEN ellprec);
513 : GEN nflist_DL_worker(GEN P2, GEN X1pow, GEN X0pow, GEN X, GEN Xinf, GEN ells);
514 : GEN nflist_Mgen_worker(GEN field, GEN X, GEN Xinf, GEN ella);
515 : GEN nflist_C6_worker(GEN P3, GEN X, GEN Xinf, GEN M, GEN T);
516 : GEN nflist_D612_worker(GEN P3, GEN X, GEN Xinf, GEN limd2s2);
517 : GEN nflist_A46S46P_worker(GEN P3, GEN Xinf, GEN sqX, GEN cards);
518 : GEN nflist_S46M_worker(GEN P3, GEN X, GEN Xinf, GEN gs);
519 : GEN nflist_A462_worker(GEN P3, GEN X, GEN Xinf, GEN listarch, GEN GAL);
520 : GEN nflist_S3C3_worker(GEN D2, GEN X, GEN Xinf);
521 : GEN nflist_S462_worker(GEN P3, GEN X, GEN Xinf, GEN listarch13, GEN GAL);
522 : GEN nflist_S36_worker(GEN pol, GEN X, GEN Xinf);
523 : GEN nflist_C32C4_worker(GEN P4, GEN X, GEN Xinf, GEN GAL);
524 : GEN nflist_C32D4_worker(GEN P, GEN X, GEN Xinf, GEN gs);
525 : GEN nflist_C9_worker(GEN P, GEN X, GEN Xinf);
526 : GEN nflist_C3C3_worker(GEN gi, GEN V3, GEN V3D, GEN X);
527 : GEN nflist_S3R_worker(GEN ga, GEN ALLCTS);
528 : GEN nflist_S3I_worker(GEN ga, GEN ALLCTS);
529 : GEN nflist_D9_worker(GEN P2, GEN X, GEN Xinf);
530 : GEN nflist_S32_worker(GEN all1, GEN X, GEN Xinf, GEN V3, GEN gs);
531 :
532 : /* pari_init / pari_close */
533 : void pari_close_compiler(void);
534 : void pari_close_evaluator(void);
535 : void pari_close_files(void);
536 : void pari_close_floats(void);
537 : void pari_close_homedir(void);
538 : void pari_close_parser(void);
539 : void pari_close_paths(void);
540 : void pari_close_primes(void);
541 : void pari_init_buffers(void);
542 : void pari_init_compiler(void);
543 : void pari_init_defaults(void);
544 : void pari_init_ellcondfile(void);
545 : void pari_init_evaluator(void);
546 : void pari_init_files(void);
547 : void pari_init_floats(void);
548 : void pari_close_hgm(void);
549 : void pari_init_hgm(void);
550 : void pari_init_homedir(void);
551 : void pari_init_graphics(void);
552 : void pari_init_parser(void);
553 : void pari_init_rand(void);
554 : void pari_init_paths(void);
555 : void pari_init_primetab(void);
556 : void pari_init_seadata(void);
557 : GEN pari_get_seadata(void);
558 : void pari_set_primetab(GEN global_primetab);
559 : void pari_set_seadata(GEN seadata);
560 : void pari_set_varstate(long *vp, struct pari_varstate *vs);
561 : void pari_thread_close_files(void);
562 :
563 : void export_add(const char *str, GEN val);
564 : void export_del(const char *str);
565 : GEN export_get(const char *str);
566 :
567 : /* BY FILES */
568 :
569 : /* parinf.h */
570 :
571 : GEN coltoalg(GEN nf,GEN x);
572 : GEN fincke_pohst(GEN a,GEN BOUND,long stockmax,long PREC, FP_chk_fun *CHECK);
573 : void init_zlog(zlog_S *S, GEN bid);
574 : GEN log_gen_arch(zlog_S *S, long index);
575 : GEN log_gen_pr(zlog_S *S, long index, GEN nf, long e);
576 : GEN make_integral(GEN nf, GEN L0, GEN f, GEN listpr);
577 : GEN poltobasis(GEN nf,GEN x);
578 : GEN rnfdisc_get_T(GEN nf, GEN P, GEN *lim);
579 : GEN rnfallbase(GEN nf, GEN pol, GEN lim, GEN eq, GEN *pD, GEN *pfi, GEN *pdKP);
580 : GEN sprk_log_gen_pr(GEN nf, GEN sprk, long e);
581 : GEN sprk_log_gen_pr2(GEN nf, GEN sprk, long e);
582 : GEN sprk_log_prk1(GEN nf, GEN a, GEN sprk);
583 : GEN sprk_to_bid(GEN nf, GEN L, long flag);
584 : GEN subgroupcondlist(GEN cyc, GEN bound, GEN listKer);
585 :
586 : /* Qfb.c */
587 :
588 : GEN redimagsl2(GEN q, GEN *U);
589 :
590 : /* alglin1.c */
591 :
592 : typedef long (*pivot_fun)(GEN,GEN,long,GEN);
593 : GEN ZM_pivots(GEN x0, long *rr);
594 : GEN RgM_pivots(GEN x0, long *rr, pivot_fun pivot, GEN data);
595 : void RgMs_structelim_col(GEN M, long nbcol, long nbrow, GEN A, GEN *p_col, GEN *p_lin);
596 :
597 : /* arith1.c */
598 :
599 : int is_gener_Fp(GEN x, GEN p, GEN p_1, GEN L);
600 : int is_gener_Fl(ulong x, ulong p, ulong p_1, GEN L);
601 :
602 : /* arith2.c */
603 :
604 : int divisors_init(GEN n, GEN *pP, GEN *pE);
605 : long set_optimize(long what, GEN g);
606 :
607 : /* base1.c */
608 :
609 : GEN zk_galoisapplymod(GEN nf, GEN z, GEN S, GEN p);
610 : int ZX_canon_neg(GEN z);
611 :
612 : /* base2.c */
613 :
614 : GEN gen_if_principal(GEN bnf, GEN x);
615 :
616 : /* base3.c */
617 :
618 : void check_nfelt(GEN x, GEN *den);
619 : GEN zk_ei_mul(GEN nf, GEN x, long i);
620 : GEN log_prk(GEN nf, GEN a, GEN sprk, GEN mod);
621 : GEN log_prk_units(GEN nf, GEN D, GEN sprk);
622 : GEN log_prk_units_init(GEN bnf);
623 : GEN veclog_prk(GEN nf, GEN v, GEN sprk);
624 : GEN log_prk_init(GEN nf, GEN pr, long k, GEN mod);
625 : GEN check_mod_factored(GEN nf, GEN ideal, GEN *fa, GEN *fa2, GEN *archp, GEN MOD);
626 : GEN sprk_get_cyc(GEN s);
627 : GEN sprk_get_expo(GEN s);
628 : GEN sprk_get_gen(GEN s);
629 : GEN sprk_get_prk(GEN s);
630 : GEN sprk_get_ff(GEN s);
631 : GEN sprk_get_pr(GEN s);
632 : void sprk_get_AgL2(GEN s, GEN *A, GEN *g, GEN *L2);
633 : void sprk_get_U2(GEN s, GEN *U1, GEN *U2);
634 : GEN famat_zlog_pr(GEN nf, GEN g, GEN e, GEN sprk, GEN mod);
635 :
636 : /* base4.c */
637 :
638 : GEN factorbackprime(GEN nf, GEN L, GEN e);
639 :
640 : /* base5.c */
641 :
642 : GEN condliftA4(GEN nf);
643 : GEN condliftA5(GEN nf);
644 : GEN condliftS4(GEN nf);
645 :
646 : /* bb_group.c */
647 :
648 : GEN producttree_scheme(long n);
649 :
650 : /* bern.c */
651 : long bernbitprec(long N);
652 :
653 : /* bibli2.c */
654 :
655 : GEN sort_factor_pol(GEN y, int (*cmp)(GEN,GEN));
656 :
657 : /* buch1.c */
658 :
659 : ulong bnf_increase_LIMC(ulong LIMC, ulong LIMCMAX);
660 :
661 : /* buch2.c */
662 :
663 : typedef struct GRHprime_t { ulong p; double logp; GEN dec; } GRHprime_t;
664 : typedef struct GRHcheck_t { double cD, cN; GRHprime_t *primes; long clone, nprimes, maxprimes; ulong limp; forprime_t P; } GRHcheck_t;
665 : void free_GRHcheck(GRHcheck_t *S);
666 : void init_GRHcheck(GRHcheck_t *S, long N, long R1, double LOGD);
667 : void GRH_ensure(GRHcheck_t *S, long nb);
668 : ulong GRH_last_prime(GRHcheck_t *S);
669 : int GRHok(GRHcheck_t *S, double L, double SA, double SB);
670 : GEN extract_full_lattice(GEN x);
671 : GEN init_red_mod_units(GEN bnf, long prec);
672 : GEN isprincipalarch(GEN bnf, GEN col, GEN kNx, GEN e, GEN dx, long *pe);
673 : GEN red_mod_units(GEN col, GEN z);
674 :
675 : /* buch3.c */
676 :
677 : GEN minkowski_bound(GEN D, long N, long r2, long prec);
678 : int subgroup_conductor_ok(GEN H, GEN L);
679 : GEN subgrouplist_cond_sub(GEN bnr, GEN C, GEN bound);
680 :
681 : /* crvwtors.c */
682 :
683 : void random_curves_with_m_torsion(ulong *a4, ulong *a6, ulong *tx, ulong *ty, long ncurves, long m, ulong p, ulong pi);
684 :
685 : /* dirichlet.c */
686 :
687 : GEN direuler_factor(GEN s, long n);
688 :
689 : /* ellanal.c */
690 :
691 : GEN hnaive_max(GEN ell, GEN ht);
692 :
693 : /* elliptic.c */
694 :
695 : GEN ellQ_genreduce(GEN E, GEN G, GEN M, long prec);
696 : GEN ellQ_isdivisible(GEN E, GEN P, ulong l);
697 : GEN ellminimalbmodel(GEN E, GEN *ptv);
698 : GEN ellintegralbmodel(GEN e, GEN *pv);
699 : GEN ellnfembed(GEN E, long prec);
700 : void ellnfembed_free(GEN L);
701 : GEN ellpointnfembed(GEN E, GEN P, long prec);
702 : void ellprint(GEN e);
703 :
704 : /* ellrank.c */
705 :
706 : GEN ell2selmer_basis(GEN ell, GEN *cb, long prec);
707 :
708 : /* es.c */
709 :
710 : void killallfiles(void);
711 : pariFILE* newfile(FILE *f, const char *name, int type);
712 : int popinfile(void);
713 : pariFILE* try_pipe(const char *cmd, int flag);
714 :
715 : /* F2m.c */
716 :
717 : GEN F2m_gauss_pivot(GEN x, long *rr);
718 : GEN F2m_gauss_sp(GEN a, GEN b);
719 : GEN F2m_invimage_i(GEN A, GEN B);
720 :
721 : /* Fle.c */
722 :
723 : void FleV_add_pre_inplace(GEN P, GEN Q, GEN a4, ulong p, ulong pi);
724 : void FleV_dbl_pre_inplace(GEN P, GEN a4, ulong p, ulong pi);
725 : void FleV_mulu_pre_inplace(GEN P, ulong n, GEN a4, ulong p, ulong pi);
726 : void FleV_sub_pre_inplace(GEN P, GEN Q, GEN a4, ulong p, ulong pi);
727 :
728 : /* Flv.c */
729 :
730 : GEN Flm_gauss_sp(GEN a, GEN b, ulong *detp, ulong p);
731 : GEN Flm_invimage_i(GEN A, GEN B, ulong p);
732 : GEN Flm_inv_sp(GEN a, ulong *detp, ulong p);
733 : GEN Flm_pivots(GEN x, ulong p, long *rr, long inplace);
734 :
735 : /* Flxq_log.c */
736 :
737 : GEN Flxq_log_index(GEN a0, GEN b0, GEN m, GEN T0, ulong p);
738 : int Flxq_log_use_index(GEN m, GEN T0, ulong p);
739 :
740 : /* FlxqE.c */
741 :
742 : GEN ZpXQ_norm_pcyc(GEN x, GEN T, GEN q, GEN p);
743 : long zx_is_pcyc(GEN T);
744 :
745 : /* FpV.c */
746 :
747 : GEN FpMs_leftkernel_elt_col(GEN M, long nbcol, long nbrow, GEN p);
748 : GEN FpX_to_mod_raw(GEN z, GEN p);
749 :
750 : /* FpX.c */
751 :
752 : GEN ZlXQXn_expint(GEN h, long e, GEN T, GEN p, ulong pp);
753 :
754 : /* FpX_factor.c */
755 :
756 : GEN ddf_to_ddf2(GEN V);
757 : long ddf_to_nbfact(GEN D);
758 : GEN vddf_to_simplefact(GEN V, long d);
759 :
760 : /* FpXQX_factor.c */
761 :
762 : GEN FpXQX_factor_Berlekamp(GEN x, GEN T, GEN p);
763 :
764 : /* forprime.c*/
765 :
766 : void init_modular_big(forprime_t *S);
767 : void init_modular_small(forprime_t *S);
768 :
769 : /* galconj.c */
770 :
771 : GEN galoiscosets(GEN O, GEN perm);
772 : GEN galoisinitfromaut(GEN T, GEN aut, ulong l);
773 : GEN matrixnorm(GEN M, long prec);
774 :
775 : /* gen1.c */
776 :
777 : GEN gred_rfrac_simple(GEN n, GEN d);
778 : GEN sqr_ser_part(GEN x, long l1, long l2);
779 :
780 : /* hash.c */
781 :
782 : hashtable *hashstr_import_static(hashentry *e, ulong size);
783 :
784 : /* hyperell.c */
785 :
786 : GEN ZlXQX_hyperellpadicfrobenius(GEN H, GEN T, ulong p, long n);
787 : GEN hyperellextremalmodels(GEN F, long g, GEN p);
788 : GEN genus2_eulerfact(GEN P, GEN p, long ra, long rt);
789 : GEN genus2_eulerfact2(GEN F, GEN PQ);
790 :
791 : /* intnum.c */
792 :
793 : GEN contfraceval_inv(GEN CF, GEN tinv, long nlim);
794 : GEN contfracinit_i(GEN M, long n);
795 :
796 : /* lfunlarge.c */
797 :
798 : /* FIXME: delete */
799 : GEN lerchzetalarge(GEN s, GEN a, GEN lam, long prec);
800 : GEN lfunloglambdalarge(GEN CHI, GEN s, long bitprec);
801 : GEN lfunlambdalarge(GEN CHI, GEN s, long bitprec);
802 : GEN lfunlarge(GEN CHI, GEN s, long bitprec);
803 : GEN zetahurwitzlarge(GEN s, GEN a, long prec);
804 :
805 : /* mftrace.c */
806 :
807 : void pari_close_mf(void);
808 : long polishomogeneous(GEN P);
809 : GEN sertocol(GEN S);
810 : GEN mfrhopol(long n);
811 : GEN mfrhopol_u_eval(GEN Q, ulong t2);
812 : GEN mfrhopol_eval(GEN Q, GEN t2);
813 :
814 : /* prime.c */
815 :
816 : long BPSW_psp_nosmalldiv(GEN N);
817 : int MR_Jaeschke(GEN n);
818 : long Z_isanypower_nosmalldiv(GEN N, ulong cutoff, GEN *px);
819 :
820 : /* perm.c */
821 :
822 : long cosets_perm_search(GEN C, GEN p);
823 : GEN perm_generate(GEN S, GEN H, long o);
824 : long perm_relorder(GEN p, GEN S);
825 : GEN vecperm_extendschreier(GEN C, GEN v, long n);
826 :
827 : /* polclass.c */
828 :
829 : GEN polclass0(long D, long inv, long vx, GEN *db);
830 :
831 : /* polmodular.c */
832 :
833 : GEN polmodular0_ZM(long L, long inv, GEN J, GEN Q, int compute_derivs, GEN *db);
834 : GEN Flm_Fl_polmodular_evalx(GEN phi, long L, ulong j, ulong p, ulong pi);
835 : GEN polmodular_db_init(long inv);
836 : void polmodular_db_clear(GEN db);
837 : void polmodular_db_add_level(GEN *db, long L, long inv);
838 : void polmodular_db_add_levels(GEN *db, long *levels, long k, long inv);
839 : GEN polmodular_db_for_inv(GEN db, long inv);
840 : GEN polmodular_db_getp(GEN fdb, long L, ulong p);
841 :
842 : long modinv_level(long inv);
843 : long modinv_degree(long *p1, long *p2, long inv);
844 : long modinv_ramified(long D, long inv, long *pN);
845 : long modinv_j_from_2double_eta(GEN F, long inv, ulong x0, ulong x1, ulong p, ulong pi);
846 : GEN double_eta_raw(long inv);
847 : ulong modfn_root(ulong j, norm_eqn_t ne, long inv);
848 : long modfn_unambiguous_root(ulong *r, long inv, ulong j0, norm_eqn_t ne, GEN jdb);
849 : GEN qfb_nform(long D, long n);
850 :
851 : /* Fle.c */
852 :
853 : ulong Flj_order_ufact(GEN P, ulong n, GEN F, ulong a4, ulong p, ulong pi);
854 :
855 : /* polarit3.c */
856 :
857 : GEN Flm_Frobenius_pow(GEN M, long d, GEN T, ulong p);
858 : GEN FpM_Frobenius_pow(GEN M, long d, GEN T, GEN p);
859 : GEN RgXQ_charpoly_i(GEN x, GEN T, long v);
860 : ulong ZX_ZXY_ResBound(GEN A, GEN B, GEN dB);
861 : GEN ffinit_Artin_Schreier(ulong p, long l);
862 : GEN ffinit_rand(GEN p, long n);
863 : GEN nf_direct_compositum(GEN nf, GEN A, GEN B);
864 :
865 : /* nflist.c */
866 :
867 : GEN veccond_to_A5(GEN L, long s);
868 : long ceilsqrtdiv(GEN x, GEN y);
869 :
870 : /* nflistQT.c */
871 :
872 : GEN nflistQT(long n, long k, long v);
873 :
874 : /* readline.c */
875 :
876 : char** pari_completion(pari_rl_interface *pari_rl, char *text, int START, int END);
877 : char** pari_completion_matches(pari_rl_interface *pari_rl, const char *s, long pos, long *wordpos);
878 :
879 : /* subcyclo.c */
880 :
881 : GEN galoiscyclo(long n, long v);
882 : long subcyclo_nH(const char *fun, GEN N, GEN *psg);
883 : GEN znstar_bits(long n, GEN H);
884 : long znstar_conductor(GEN H);
885 : long znstar_conductor_bits(GEN bits);
886 : GEN znstar_cosets(long n, long phi_n, GEN H);
887 : GEN znstar_elts(long n, GEN H);
888 : GEN znstar_generate(long n, GEN V);
889 : GEN znstar_hnf(GEN Z, GEN M);
890 : GEN znstar_hnf_elts(GEN Z, GEN H);
891 : GEN znstar_hnf_generators(GEN Z, GEN M);
892 : GEN znstar_reduce_modulus(GEN H, long n);
893 : GEN znstar_small(GEN zn);
894 :
895 : /* trans1.c */
896 :
897 : struct abpq { GEN *a, *b, *p, *q; };
898 : struct abpq_res { GEN P, Q, B, T; };
899 : void abpq_init(struct abpq *A, long n);
900 : void abpq_sum(struct abpq_res *r, long n1, long n2, struct abpq *A);
901 : GEN logagmcx(GEN q, long prec);
902 : GEN zellagmcx(GEN a0, GEN b0, GEN r, GEN t, long prec);
903 :
904 : /* trans2.c */
905 :
906 : GEN trans_fix_arg(long *prec, GEN *s0, GEN *sig, GEN *tau, pari_sp *av, GEN *res);
907 :
908 : /* trans3.c */
909 :
910 : GEN double_eta_quotient(GEN a, GEN w, GEN D, long p, long q, GEN pq, GEN sqrtD);
911 : GEN inv_szeta_euler(long n, long prec);
912 :
913 : /* volcano.c */
914 :
915 : long j_level_in_volcano(GEN phi, ulong j, ulong p, ulong pi, long L, long depth);
916 : ulong ascend_volcano(GEN phi, ulong j, ulong p, ulong pi, long level, long L, long depth, long steps);
917 : ulong descend_volcano(GEN phi, ulong j, ulong p, ulong pi, long level, long L, long depth, long steps);
918 : long next_surface_nbr(ulong *nJ, GEN phi, long L, long h, ulong J, const ulong *pJ, ulong p, ulong pi);
919 : GEN enum_roots(ulong j, norm_eqn_t ne, GEN fdb, GEN G, GEN vshape);
920 :
921 : ENDEXTERN
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