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 : /* for qsort */
18 : typedef int (*QSCOMP)(const void *, const void *);
19 :
20 : #define uel(a,i) (((ulong*)(a))[i])
21 : #define ucoeff(a,i,j) (((ulong**)(a))[j][i])
22 : #define umael(a,i,j) (((ulong**)(a))[i][j])
23 : #define umael2(a,i,j) (((ulong**)(a))[i][j])
24 : #define umael3(a,i,j,k) (((ulong***)(a))[i][j][k])
25 : #define umael4(a,i,j,k,l) (((ulong****)(a))[i][j][k][l])
26 : #define umael5(a,i,j,k,l,m) (((ulong*****)(a))[i][j][k][l][m])
27 :
28 : #define numberof(x) (sizeof(x) / sizeof((x)[0]))
29 :
30 : /* to manipulate 'blocs' */
31 : #define BL_HEAD 8
32 : #define bl_base(x) (void*)((x) - BL_HEAD)
33 : #define bl_height(x) (((GEN)x)[-8])
34 : #define bl_left(x) (((GEN*)x)[-7])
35 : #define bl_right(x) (((GEN*)x)[-6])
36 : #define bl_size(x) (((GEN)x)[-5])
37 : #define bl_refc(x) (((GEN)x)[-4])
38 : #define bl_next(x) (((GEN*)x)[-3])
39 : #define bl_prev(x) (((GEN*)x)[-2])
40 : #define bl_num(x) (((GEN)x)[-1])
41 :
42 : void clone_lock(GEN C);
43 : void clone_unlock(GEN C);
44 : void clone_unlock_deep(GEN C);
45 :
46 : /* swap */
47 : #define lswap(x,y) {long _z=x; x=y; y=_z;}
48 : #define pswap(x,y) {GEN *_z=x; x=y; y=_z;}
49 : #define swap(x,y) {GEN _z=x; x=y; y=_z;}
50 : #define dswap(x,y) { double _t=x; x=y; y=_t; }
51 : #define pdswap(x,y) { double* _t=x; x=y; y=_t; }
52 : #define swapspec(x,y, nx,ny) {swap(x,y); lswap(nx,ny);}
53 :
54 : /* loops */
55 : GEN incloop(GEN a);
56 : GEN resetloop(GEN a, GEN b);
57 : GEN setloop(GEN a);
58 :
59 : /* parser */
60 :
61 : /* GP control structures */
62 : #define EXPR_WRAP(code, call) \
63 : { GEN z; GEN __E = code; \
64 : push_lex(gen_0, __E); z = call; pop_lex(1); return z; }
65 : #define EXPRVOID_WRAP(code, call) \
66 : { GEN __E = code; \
67 : push_lex(gen_0, __E); call; pop_lex(1); }
68 : #define EXPR_ARG __E, &gp_eval
69 : #define EXPR_ARGPREC __E, &gp_evalprec
70 : #define EXPR_ARGUPTO __E, &gp_evalupto
71 : #define EXPR_ARGBOOL __E, &gp_evalbool
72 : #define EXPR_ARGVOID __E, &gp_evalvoid
73 :
74 : GEN dirpowerssum0(GEN N, GEN s, GEN f, long both, long prec);
75 : GEN iferrpari(GEN a, GEN b, GEN c);
76 : void forfactored(GEN a, GEN b, GEN code);
77 : void forpari(GEN a, GEN b, GEN node);
78 : void foreachpari(GEN a, GEN node);
79 : void forsquarefree(GEN a, GEN b, GEN code);
80 : void untilpari(GEN a, GEN b);
81 : void whilepari(GEN a, GEN b);
82 : GEN ifpari(GEN g, GEN a, GEN b);
83 : GEN andpari(GEN a, GEN b);
84 : GEN orpari(GEN a, GEN b);
85 : void ifpari_void(GEN g, GEN a, GEN b);
86 : GEN ifpari_multi(GEN g, GEN a);
87 : GEN geval_gp(GEN x, GEN t);
88 :
89 : GEN gadde(GEN *x, GEN y);
90 : GEN gadd1e(GEN *x);
91 : GEN gdive(GEN *x, GEN y);
92 : GEN gdivente(GEN *x, GEN y);
93 : GEN gdivrounde(GEN *x, GEN y);
94 : GEN gmode(GEN *x, GEN y);
95 : GEN gmule(GEN *x, GEN y);
96 : GEN gshiftle(GEN *x, long n);
97 : GEN gshiftre(GEN *x, long n);
98 : GEN gsube(GEN *x, GEN y);
99 : GEN gsub1e(GEN *x);
100 : GEN gshift_right(GEN x, long n);
101 :
102 : GEN asympnum0(GEN u, GEN alpha, long prec);
103 : GEN asympnumraw0(GEN u, long LIM, GEN alpha, long prec);
104 : GEN derivnum0(GEN a, GEN code, GEN ind, long prec);
105 : GEN derivfun0(GEN args, GEN def, GEN code, long k, long prec);
106 : GEN direuler0(GEN a, GEN b, GEN code, GEN c);
107 : GEN direuler_bad(void *E, GEN (*eval)(void *, GEN, long), GEN a, GEN b, GEN c, GEN Sbad);
108 : void forcomposite(GEN a, GEN b, GEN code);
109 : void fordiv(GEN a, GEN code);
110 : void fordivfactored(GEN a, GEN code);
111 : void forell0(long a, long b, GEN code, long flag);
112 : void forperm0(GEN k, GEN code);
113 : void forprime(GEN a, GEN b, GEN code);
114 : void forprimestep(GEN a, GEN b, GEN q, GEN code);
115 : void forstep(GEN a, GEN b, GEN s, GEN code);
116 : void forsubgroup0(GEN cyc, GEN bound, GEN code);
117 : void forsubset0(GEN nk, GEN code);
118 : void forvec(GEN x, GEN code, long flag);
119 : void forpart0(GEN k, GEN code , GEN nbound, GEN abound);
120 : GEN intcirc0(GEN a, GEN R, GEN code, GEN tab, long prec);
121 : GEN intfuncinit0(GEN a, GEN b, GEN code, long m, long prec);
122 : GEN intnum0(GEN a, GEN b, GEN code, GEN tab, long prec);
123 : GEN intnumgauss0(GEN a, GEN b, GEN code, GEN tab, long prec);
124 : GEN intnumosc0(GEN a, GEN H, GEN code, long flag, GEN tab, long prec);
125 : GEN intnumromb0_bitprec(GEN a, GEN b, GEN code, long flag, long bit);
126 : GEN laurentseries0(GEN f, long M, long v, long prec);
127 : GEN limitnum0(GEN u, GEN alpha, long prec);
128 : GEN matrice(GEN nlig, GEN ncol, GEN code);
129 : void pariplot0(GEN a, GEN b, GEN code, GEN ysmlu, GEN ybigu, long prec);
130 : GEN prodeuler0(GEN a, GEN b, GEN code, long prec);
131 : GEN prodinf0(GEN a, GEN code, long flag, long prec);
132 : GEN produit(GEN a, GEN b, GEN code, GEN x);
133 : GEN somme(GEN a, GEN b, GEN code, GEN x);
134 : GEN sumalt0(GEN a, GEN code,long flag, long prec);
135 : GEN sumdivexpr(GEN num, GEN code);
136 : GEN sumdivmultexpr0(GEN num, GEN code);
137 : GEN suminf0_bitprec(GEN a, GEN code, long bit);
138 : GEN sumnum0(GEN a, GEN code, GEN tab, long prec);
139 : GEN sumnumap0(GEN a, GEN code, GEN tab, long prec);
140 : GEN sumnumlagrange0(GEN a, GEN code, GEN tab, long prec);
141 : GEN sumnummonien0(GEN a, GEN code, GEN tab, long prec);
142 : GEN sumnumsidi0(GEN a, GEN code, long safe, long prec);
143 : GEN sumpos0(GEN a, GEN code, long flag,long prec);
144 : GEN vecexpr0(GEN nmax, GEN code, GEN pred);
145 : GEN vecexpr1(GEN nmax, GEN code, GEN pred);
146 : GEN vecteursmall(GEN nmax, GEN code);
147 : GEN vecteur(GEN nmax, GEN n);
148 : GEN vvecteur(GEN nmax, GEN n);
149 : GEN zbrent0(GEN a, GEN b, GEN code, long prec);
150 : GEN solvestep0(GEN a, GEN b, GEN step, GEN code, long flag, long prec);
151 :
152 : GEN ploth0(GEN a, GEN b, GEN code, long flag, long n, long prec);
153 : GEN plothexport0(GEN fmt, GEN a, GEN b, GEN code, long flags, long n, long prec);
154 : GEN psploth0(GEN a,GEN b,GEN code,long flag,long n,long prec);
155 : GEN plotrecth0(long ne,GEN a,GEN b,GEN code,ulong flags,long n,long prec);
156 :
157 : GEN listcreate_gp(long n);
158 :
159 : /* mt */
160 : void mt_sigint(void);
161 : void mt_err_recover(long er);
162 : void mt_break_recover(void);
163 : void mt_export_add(const char *str, GEN val);
164 : void mt_export_del(const char *str);
165 : void mt_init_stack(size_t s);
166 : int mt_is_thread(void);
167 : void mt_thread_init(void);
168 :
169 : GEN eisker_worker(GEN Ei, GEN M, GEN D, GEN co, GEN CD);
170 : GEN pareval_worker(GEN code);
171 : void parfor0(GEN a, GEN b, GEN code, GEN code2);
172 : void parforstep0(GEN a, GEN b, GEN s, GEN code, GEN code2);
173 : GEN parfor_worker(GEN i, GEN C);
174 : void parforeach0(GEN x, GEN code, GEN code2);
175 : void parforprime0(GEN a, GEN b, GEN code, GEN code2);
176 : void parforprimestep0(GEN a, GEN b, GEN q, GEN code, GEN code2);
177 : void parforvec0(GEN a, GEN code, GEN code2, long flag);
178 : GEN parvector_worker(GEN i, GEN C);
179 : GEN polmodular_worker(GEN pt, ulong L, GEN hilb, GEN factu,
180 : GEN vne, GEN vinfo, long compute_derivs, GEN j_powers, GEN G_surface,
181 : GEN G_floor, GEN fdb);
182 : GEN polclass_worker(GEN p, GEN G, GEN db);
183 : GEN nf_L2_bound(GEN nf, GEN den, GEN *pL);
184 : GEN nmV_polint_center_tree_worker(GEN Va, GEN T, GEN R, GEN xa, GEN m2);
185 : GEN nmV_chinese_center_tree_seq(GEN A, GEN P, GEN T, GEN R);
186 : GEN nxMV_polint_center_tree_worker(GEN Va, GEN T, GEN R, GEN xa, GEN m2);
187 : GEN nxMV_chinese_center_tree_seq(GEN A, GEN P, GEN T, GEN R);
188 : GEN F2xq_log_Coppersmith_worker(GEN u, long i, GEN V, GEN R);
189 : GEN Flxq_log_Coppersmith_worker(GEN u, long i, GEN V, GEN R);
190 : GEN Fp_log_sieve_worker(long a, long prmax, GEN C, GEN c, GEN Ci, GEN ci, GEN pr, GEN sz);
191 : GEN QM_charpoly_ZX_worker(GEN P, GEN M, GEN dM);
192 : GEN QXQ_div_worker(GEN P, GEN A, GEN B, GEN C);
193 : GEN QXQ_inv_worker(GEN P, GEN A, GEN B);
194 : GEN RgM_ZM_mul_worker(GEN y, GEN x);
195 : GEN ZX_resultant_worker(GEN P, GEN A, GEN B, GEN dB);
196 : GEN ZXQX_resultant_worker(GEN P, GEN A, GEN B, GEN T, GEN dB);
197 : GEN ZX_ZXY_resultant_worker(GEN P, GEN A, GEN B, GEN dB, GEN v);
198 : GEN ZX_composedsum_worker(GEN P, GEN A, GEN B);
199 : GEN ZXQX_composedsum_worker(GEN P, GEN A, GEN B, GEN C);
200 : GEN ZX_gcd_worker(GEN P, GEN A, GEN B, GEN g);
201 : GEN ZXQ_minpoly_worker(GEN P, GEN A, GEN B, long d);
202 : GEN ZM_det_worker(GEN P, GEN A);
203 : GEN ZM_inv_worker(GEN P, GEN A);
204 : GEN ZM_ker_worker(GEN P, GEN A);
205 : GEN ZM_mul_worker(GEN P, GEN A, GEN B);
206 : GEN ZM_gauss_worker(GEN P, GEN A, GEN B);
207 : GEN ZabM_inv_worker(GEN P, GEN A, GEN Q);
208 : GEN aprcl_step4_worker(ulong q, GEN pC, GEN N, GEN v);
209 : GEN aprcl_step6_worker(GEN r, long t, GEN N, GEN N1, GEN et);
210 : GEN ecpp_sqrt_worker(GEN g, GEN N, GEN p);
211 : GEN ecpp_ispsp_worker(GEN N);
212 : GEN ecpp_step2_worker(GEN S, GEN HD, GEN primelist, long dbg);
213 : GEN primecertisvalid_ecpp_worker(GEN certi);
214 : GEN lfuninit_worker(long r, GEN K, GEN L, GEN peh2d, GEN vroots, GEN dr, GEN di, GEN an, GEN bn);
215 : GEN lfuninit_theta2_worker(long r, GEN L, GEN qk, GEN a, GEN di, GEN an, GEN bn);
216 : GEN gen_parapply(GEN worker, GEN D);
217 : GEN gen_parapply_percent(GEN worker, GEN D, long percent);
218 : GEN parapply_slice_worker(GEN worker, GEN D);
219 : GEN gen_parapply_slice(GEN worker, GEN D, long mmin);
220 : GEN gen_crt(const char *str, GEN worker, forprime_t *S, GEN dB, ulong bound, long mmin, GEN *pt_mod,
221 : GEN crt(GEN, GEN, GEN*), GEN center(GEN, GEN, GEN));
222 : void gen_inccrt(const char *str, GEN worker, GEN dB, long n, long mmin,
223 : forprime_t *S, GEN *pt_H, GEN *pt_mod, GEN crt(GEN, GEN, GEN*),
224 : GEN center(GEN, GEN, GEN));
225 : void gen_inccrt_i(const char *str, GEN worker, GEN dB, long n, long mmin,
226 : forprime_t *S, GEN *pH, GEN *pmod, GEN crt(GEN, GEN, GEN*),
227 : GEN center(GEN, GEN, GEN));
228 : GEN direllnf_worker(GEN P, ulong X, GEN E);
229 : GEN dirartin_worker(GEN P, ulong X, GEN nf, GEN G, GEN V, GEN aut);
230 : GEN direllsympow_worker(GEN P, ulong X, GEN E, ulong m);
231 : GEN dirgenus2_worker(GEN P, ulong X, GEN Q);
232 : GEN dirhgm_worker(GEN P, ulong X, GEN hgm, GEN t);
233 : GEN pardireuler(GEN worker, GEN a, GEN b, GEN c, GEN Sbad);
234 : GEN FpM_ratlift_worker(GEN A, GEN mod, GEN B);
235 : GEN ellQ_factorback_worker(GEN P, GEN E, GEN A, GEN L, ulong l);
236 : GEN chinese_unit_worker(GEN P, GEN A, GEN U, GEN B, GEN D, GEN C);
237 : GEN partmap_reverse_frac_worker(GEN t, GEN a, GEN b, GEN la, GEN lb, long v);
238 : GEN parsum_slice_worker(GEN a, GEN b, GEN m, GEN worker);
239 :
240 : /* Relative number fields */
241 : enum { rnf_NFABS = 1, rnf_MAPS };
242 :
243 : /* Finite fields */
244 : enum { t_FF_FpXQ = 0, t_FF_Flxq = 1, t_FF_F2xq = 2 };
245 : GEN FF_ellinit(GEN E, GEN fg);
246 : GEN FF_elldata(GEN E, GEN fg);
247 :
248 : /* L functions */
249 : enum { t_LFUN_GENERIC, t_LFUN_ZETA, t_LFUN_NF, t_LFUN_ELL, t_LFUN_KRONECKER,
250 : t_LFUN_CHIZ, t_LFUN_CHIGEN, t_LFUN_ETA,
251 : t_LFUN_DIV, t_LFUN_MUL, t_LFUN_CONJ,
252 : t_LFUN_SYMPOW_ELL, t_LFUN_QF, t_LFUN_ARTIN, t_LFUN_MFCLOS,
253 : t_LFUN_GENUS2, t_LFUN_TWIST, t_LFUN_CLOSURE0, t_LFUN_SHIFT,
254 : t_LFUN_HGM, t_LFUN_HECKE,t_LFUN_ABELREL};
255 : enum { t_LDESC_INIT, t_LDESC_THETA, t_LDESC_PRODUCT };
256 :
257 : /* Elliptic curves */
258 : /* common to Q and Rg */
259 : enum { R_PERIODS = 1, R_ETA, R_ROOTS, R_AB };
260 :
261 : enum { Qp_ROOT = 1, Qp_TATE };
262 : enum { Q_GROUPGEN = 5, Q_GLOBALRED, Q_ROOTNO, Q_MINIMALMODEL };
263 : enum { NF_MINIMALMODEL = 1, NF_GLOBALRED, NF_MINIMALPRIMES, NF_ROOTNO, NF_NF };
264 :
265 : /* common to Fp and Fq */
266 : enum { FF_CARD = 1, FF_GROUP, FF_GROUPGEN, FF_O };
267 :
268 : /* for Buchall_param */
269 : enum { fupb_NONE = 0, fupb_RELAT, fupb_LARGE, fupb_PRECI };
270 :
271 : /* Represents the data in the equation(s)
272 : * 4p = t^2 - v^2 D = t^2 - v^2 u^2 D_K = w^2 D_K.
273 : * t is the absolute trace, so always > 0.
274 : * T is a twisting parameter, which satisfies (T|p) == -1. */
275 : typedef struct {
276 : GEN faw; /* factor(u*v) */
277 : long D, t, u, v;
278 : ulong p, pi, s2, T;
279 : } norm_eqn_struct;
280 : typedef norm_eqn_struct norm_eqn_t[1];
281 : void norm_eqn_set(norm_eqn_t ne, long D,long t,long u,long v,GEN faw,ulong p);
282 :
283 : #define zv_to_longptr(v) (&((v)[1]))
284 : #define zv_to_ulongptr(v) ((ulong *)&((v)[1]))
285 :
286 : /* Modular invariants */
287 : #define INV_J 0
288 : #define INV_F 1
289 : #define INV_F2 2
290 : #define INV_F3 3
291 : #define INV_F4 4
292 : #define INV_G2 5
293 : #define INV_W2W3 6
294 : #define INV_F8 8
295 : #define INV_W3W3 9
296 : #define INV_W2W5 10
297 : #define INV_W2W7 14
298 : #define INV_W3W5 15
299 : #define INV_W3W7 21
300 : #define INV_W2W3E2 23
301 : #define INV_W2W5E2 24
302 : #define INV_W2W13 26
303 : #define INV_W2W7E2 27
304 : #define INV_W3W3E2 28
305 : #define INV_W5W7 35
306 : #define INV_W3W13 39
307 :
308 : /* Get coefficient of x^d in f, assuming f is nonzero. */
309 16891380 : INLINE ulong Flx_coeff(GEN f, long d) { return f[d + 2]; }
310 : /* Return the root of f, assuming deg(f) = 1. */
311 294124 : INLINE ulong Flx_deg1_root(GEN f, ulong p) {
312 294124 : if (degpol(f) != 1) pari_err_BUG("Flx_deg1_root");
313 294129 : return Fl_div(Fl_neg(Flx_coeff(f, 0), p), Flx_coeff(f, 1), p);
314 : }
315 :
316 : /* Allocation / gerepile */
317 : long getdebugvar(void);
318 : void setdebugvar(long n);
319 : void debug_stack(void);
320 : void minim_alloc(long n, double ***q, GEN *x, double **y, double **z, double **v);
321 : int pop_entree_block(entree *ep, long loc);
322 : int pop_val_if_newer(entree *ep, long loc);
323 :
324 : /* general printing */
325 : void print_errcontext(PariOUT *out, const char *msg, const char *s, const char *entry);
326 : void print_prefixed_text(PariOUT *out, const char *s, const char *prefix, const char *str);
327 : INLINE void
328 76 : print_text(const char *s) { print_prefixed_text(pariOut, s,NULL,NULL); }
329 : INLINE void
330 5327 : out_print_text(PariOUT *out, const char *s) { print_prefixed_text(out, s,NULL,NULL); }
331 : INLINE long
332 2392369 : is_keyword_char(char c) { return (isalnum((unsigned char)c) || c=='_'); }
333 :
334 : /* Interfaces (GP, etc.) */
335 : hashtable *hash_from_link(GEN e, GEN names, int use_stack);
336 : void gen_relink(GEN x, hashtable *table);
337 : entree* do_alias(entree *ep);
338 : char* get_sep(const char *t);
339 : long get_int(const char *s, long dflt);
340 : ulong get_uint(const char *s);
341 : void gp_initrc(pari_stack *p_A);
342 :
343 : void pari_sigint(const char *s);
344 : void* get_stack(double fraction, long min);
345 : void free_graph(void);
346 : void initout(int initerr);
347 : void resetout(int initerr);
348 : void init_linewrap(long w);
349 : void print_functions_hash(const char *s);
350 : GEN readbin(const char *name, FILE *f, int *vector);
351 : int term_height(void);
352 : int term_width(void);
353 : /* gp_colors */
354 : void decode_color(long n, long *c);
355 :
356 : /* defaults */
357 : extern long precreal;
358 :
359 : void lim_lines_output(char *s, long n, long max);
360 : int tex2mail_output(GEN z, long n);
361 : void gen_output(GEN x);
362 : void fputGEN_pariout(GEN x, pariout_t *T, FILE *out);
363 :
364 : void parsestate_reset(void);
365 : void parsestate_save(struct pari_parsestate *state);
366 : void parsestate_restore(struct pari_parsestate *state);
367 :
368 : void compilestate_reset(void);
369 : void compilestate_save(struct pari_compilestate *comp);
370 : void compilestate_restore(struct pari_compilestate *comp);
371 :
372 : void filestate_save(struct pari_filestate *file);
373 : void filestate_restore(struct pari_filestate *file);
374 : void tmp_restore(pariFILE *F);
375 :
376 : long evalstate_get_trace(void);
377 : void evalstate_set_trace(long lvl);
378 : void evalstate_clone(void);
379 : void evalstate_reset(void);
380 : void evalstate_restore(struct pari_evalstate *state);
381 : GEN evalstate_restore_err(struct pari_evalstate *state);
382 : void evalstate_save(struct pari_evalstate *state);
383 : void varstate_save(struct pari_varstate *s);
384 : void varstate_restore(struct pari_varstate *s);
385 :
386 : void mtstate_save(struct pari_mtstate *s);
387 : void mtstate_reset(void);
388 : void mtstate_restore(struct pari_mtstate *s);
389 :
390 : void debug_context(void);
391 :
392 : typedef struct {
393 : const char *s;
394 : size_t ls;
395 : char **dir;
396 : } forpath_t;
397 : void forpath_init(forpath_t *T, gp_path *path, const char *s);
398 : char *forpath_next(forpath_t *T);
399 :
400 : /* GP output && output format */
401 : void gpwritebin(const char *s, GEN x);
402 : extern char *current_logfile;
403 :
404 : /* colors */
405 : extern long gp_colors[];
406 : extern int disable_color;
407 :
408 : /* entrees */
409 : #define EpVALENCE(ep) ((ep)->valence & 0xFF)
410 : #define EpSTATIC(ep) ((ep)->valence & 0x100)
411 : #define EpSETSTATIC(ep) ((ep)->valence |= 0x100)
412 : enum { EpNEW = 100, EpALIAS, EpVAR, EpINSTALL };
413 : #define initial_value(ep) ((ep)+1)
414 :
415 : /* functions lists */
416 : extern const long functions_tblsz; /* hashcodes table size */
417 : extern entree **functions_hash; /* functions hashtable */
418 : extern entree **defaults_hash; /* defaults hashtable */
419 :
420 : /* buffers */
421 : typedef struct Buffer {
422 : char *buf;
423 : ulong len;
424 : jmp_buf env;
425 : } Buffer;
426 : Buffer *new_buffer(void);
427 : void delete_buffer(Buffer *b);
428 : void fix_buffer(Buffer *b, long newlbuf);
429 :
430 : typedef struct {
431 : const char *s; /* source */
432 : char *t, *end; /* target, last char read */
433 : int in_string, in_comment, more_input, wait_for_brace;
434 : Buffer *buf;
435 : } filtre_t;
436 : void init_filtre(filtre_t *F, Buffer *buf);
437 : Buffer *filtered_buffer(filtre_t *F);
438 : void kill_buffers_upto_including(Buffer *B);
439 : void pop_buffer(void);
440 : void kill_buffers_upto(Buffer *B);
441 : int gp_read_line(filtre_t *F, const char *PROMPT);
442 : void parse_key_val(char *src, char **ps, char **pt);
443 : extern int (*cb_pari_get_line_interactive)(const char*, const char*, filtre_t *F);
444 : extern char *(*cb_pari_fgets_interactive)(char *s, int n, FILE *f);
445 : int get_line_from_file(const char *prompt, filtre_t *F, FILE *file);
446 : void pari_skip_space(char **s);
447 : void pari_skip_alpha(char **s);
448 : char *pari_translate_string(const char *src, char *s, char *entry);
449 :
450 : gp_data *default_gp_data(void);
451 :
452 : typedef char *(*fgets_t)(char *, int, void*);
453 :
454 : typedef struct input_method {
455 : /* optional */
456 : fgets_t myfgets; /* like libc fgets() but last argument is (void*) */
457 : /* mandatory */
458 : char * (*getline)(char**, int f, struct input_method*, filtre_t *F);
459 : int free; /* boolean: must we free the output of getline() ? */
460 : /* optional */
461 : const char *prompt, *prompt_cont;
462 : void *file; /* can be used as last argument for fgets() */
463 : } input_method;
464 :
465 : int input_loop(filtre_t *F, input_method *IM);
466 : char *file_input(char **s0, int junk, input_method *IM, filtre_t *F);
467 : char *file_getline(Buffer *b, char **s0, input_method *IM);
468 :
469 : /* readline */
470 : typedef struct {
471 : /* pointers to readline variables/functions */
472 : char **line_buffer;
473 : int *point;
474 : int *end;
475 : char **(*completion_matches)(const char *, char *(*)(const char*, int));
476 : char *(*filename_completion_function)(const char *, int);
477 : char *(*username_completion_function)(const char *, int);
478 : int (*insert)(int, int);
479 : int *completion_append_character;
480 :
481 : /* PARI-specific */
482 : int back; /* rewind the cursor by this number of chars */
483 : } pari_rl_interface;
484 :
485 : /* Code which wants to use readline needs to do the following:
486 :
487 : #include <readline/readline.h>
488 : #include <pari/paripriv.h>
489 : pari_rl_interface pari_rl;
490 : pari_use_readline(pari_rl);
491 :
492 : This will initialize the pari_rl structure. A pointer to this structure
493 : must be given as first argument to all PARI readline functions. */
494 :
495 : /* IMPLEMENTATION NOTE: this really must be a macro (not a function),
496 : * since we refer to readline symbols. */
497 : #define pari_use_readline(pari_rl) do {\
498 : (pari_rl).line_buffer = &rl_line_buffer; \
499 : (pari_rl).point = &rl_point; \
500 : (pari_rl).end = &rl_end; \
501 : (pari_rl).completion_matches = &rl_completion_matches; \
502 : (pari_rl).filename_completion_function = &rl_filename_completion_function; \
503 : (pari_rl).username_completion_function = &rl_username_completion_function; \
504 : (pari_rl).insert = &rl_insert; \
505 : (pari_rl).completion_append_character = &rl_completion_append_character; \
506 : (pari_rl).back = 0; } while(0)
507 :
508 : /* FIXME: EXPORT AND DOCUMENT THE FOLLOWING */
509 :
510 : /* PROBABLY NOT IN THE RIGHT FILE, SORT BY THEME */
511 :
512 : /* multiprecision */
513 : GEN adduispec_offset(ulong s, GEN x, long offset, long nx);
514 : int lgcdii(ulong* d, ulong* d1, ulong* u, ulong* u1, ulong* v, ulong* v1, ulong vmax);
515 : ulong rgcduu(ulong d, ulong d1, ulong vmax, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
516 : ulong xgcduu(ulong d, ulong d1, int f, ulong* v, ulong* v1, long *s);
517 : ulong xxgcduu(ulong d, ulong d1, int f, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
518 : GEN muliispec(GEN x, GEN y, long nx, long ny);
519 : GEN red_montgomery(GEN T, GEN N, ulong inv);
520 : GEN sqrispec(GEN x, long nx);
521 : ulong *convi(GEN x, long *l);
522 :
523 : /* powers */
524 : GEN rpowuu(ulong a, ulong n, long prec);
525 :
526 : /* floats */
527 : double dabs(double s, double t);
528 : double darg(double s, double t);
529 : void dcxlog(double s, double t, double *a, double *b);
530 : double dnorm(double s, double t);
531 : double dbllog2(GEN z);
532 : double dbllambertW0(double a);
533 : double dbllambertW_1(double a);
534 :
535 : /* hnf */
536 : GEN hnfadd(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
537 : GEN hnfadd_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
538 : GEN hnfspec_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
539 : GEN hnfspec(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
540 : GEN mathnfspec(GEN x, GEN *ptperm, GEN *ptdep, GEN *ptB, GEN *ptC);
541 : GEN ZM_hnfmodall_i(GEN x, GEN dm, long flag);
542 :
543 : GEN LLL_check_progress(GEN Bnorm, long n0, GEN m, int final, long *ti_LLL);
544 :
545 : /* integer factorization / discrete log */
546 : ulong is_kth_power(GEN x, ulong p, GEN *pt);
547 : GEN mpqs(GEN N);
548 :
549 : /* Polynomials */
550 : /* a) Arithmetic/conversions */
551 : GEN lift_if_rational(GEN x);
552 : GEN monomial(GEN a, long degpol, long v);
553 : GEN monomialcopy(GEN a, long degpol, long v);
554 : GEN ser2pol_i(GEN x, long lx);
555 : GEN ser2pol_i_normalize(GEN x, long l, long *v);
556 : GEN ser2rfrac_i(GEN x);
557 : GEN swap_vars(GEN b0, long v);
558 : GEN RgX_recipspec_shallow(GEN x, long l, long n);
559 :
560 : /* b) Modular */
561 : GEN bezout_lift_fact(GEN T, GEN Tmod, GEN p, long e);
562 : GEN polsym_gen(GEN P, GEN y0, long n, GEN T, GEN N);
563 : GEN ZXQ_charpoly_sqf(GEN A, GEN B, long *lambda, long v);
564 : GEN ZX_disc_all(GEN,ulong);
565 : GEN ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound);
566 : GEN ZX_ZXY_resultant_all(GEN A, GEN B, long *lambda, GEN *LPRS);
567 :
568 : GEN FlxqM_mul_Kronecker(GEN A, GEN B, GEN T, ulong p);
569 : GEN FqM_mul_Kronecker(GEN x, GEN y, GEN T, GEN p);
570 :
571 : /* c) factorization */
572 : GEN chk_factors_get(GEN lt, GEN famod, GEN c, GEN T, GEN N);
573 : long cmbf_maxK(long nb);
574 : GEN ZX_DDF(GEN x);
575 : GEN ZX_DDF_max(GEN x, long dmax);
576 : GEN initgaloisborne(GEN T, GEN dn, long prec, GEN *pL, GEN *pprep, GEN *pdis);
577 :
578 : /* number fields */
579 : GEN nflist_C3_worker(GEN gv, GEN T);
580 : GEN nflist_C4vec_worker(GEN gm, GEN X, GEN Xinf, GEN gs);
581 : GEN nflist_V4_worker(GEN D1, GEN X, GEN Xinf, GEN gs);
582 : GEN nflist_D4_worker(GEN D, GEN X, GEN Xinf, GEN listarch);
583 : GEN nflist_A4S4_worker(GEN P3, GEN X, GEN Xinf, GEN cards);
584 : GEN nflist_C5_worker(GEN N, GEN bnfC5);
585 : GEN nflist_CL_worker(GEN Fcond, GEN bnf, GEN ellprec);
586 : GEN nflist_DL_worker(GEN P2, GEN X1pow, GEN X0pow, GEN X, GEN Xinf, GEN ells);
587 : GEN nflist_Mgen_worker(GEN field, GEN X, GEN Xinf, GEN ella);
588 : GEN nflist_C6_worker(GEN P3, GEN X, GEN Xinf, GEN M, GEN T);
589 : GEN nflist_D612_worker(GEN P3, GEN X, GEN Xinf, GEN limd2s2);
590 : GEN nflist_A46S46P_worker(GEN P3, GEN Xinf, GEN sqX, GEN cards);
591 : GEN nflist_S46M_worker(GEN P3, GEN X, GEN Xinf, GEN gs);
592 : GEN nflist_A462_worker(GEN P3, GEN X, GEN Xinf, GEN listarch, GEN GAL);
593 : GEN nflist_S3C3_worker(GEN D2, GEN X, GEN Xinf);
594 : GEN nflist_S462_worker(GEN P3, GEN X, GEN Xinf, GEN listarch13, GEN GAL);
595 : GEN nflist_S36_worker(GEN pol, GEN X, GEN Xinf);
596 : GEN nflist_C32C4_worker(GEN P4, GEN X, GEN Xinf, GEN GAL);
597 : GEN nflist_C32D4_worker(GEN P, GEN X, GEN Xinf, GEN gs);
598 : GEN nflist_C9_worker(GEN P, GEN X, GEN Xinf);
599 : GEN nflist_C3C3_worker(GEN gi, GEN V3, GEN V3D, GEN X);
600 : GEN nflist_S3R_worker(GEN ga, GEN ALLCTS);
601 : GEN nflist_S3I_worker(GEN ga, GEN ALLCTS);
602 : GEN nflist_D9_worker(GEN P2, GEN X, GEN Xinf);
603 : GEN nflist_S32_worker(GEN all1, GEN X, GEN Xinf, GEN V3, GEN gs);
604 :
605 : /* pari_init / pari_close */
606 : void pari_close_compiler(void);
607 : void pari_close_evaluator(void);
608 : void pari_close_files(void);
609 : void pari_close_floats(void);
610 : void pari_close_homedir(void);
611 : void pari_close_parser(void);
612 : void pari_close_paths(void);
613 : void pari_close_primes(void);
614 : void pari_init_buffers(void);
615 : void pari_init_compiler(void);
616 : void pari_init_defaults(void);
617 : void pari_init_ellcondfile(void);
618 : void pari_init_evaluator(void);
619 : void pari_init_files(void);
620 : void pari_init_floats(void);
621 : void pari_close_hgm(void);
622 : void pari_init_hgm(void);
623 : void pari_init_homedir(void);
624 : void pari_init_graphics(void);
625 : void pari_init_parser(void);
626 : void pari_init_rand(void);
627 : void pari_init_paths(void);
628 : void pari_init_primetab(void);
629 : void pari_init_seadata(void);
630 : GEN pari_get_seadata(void);
631 : void pari_set_primetab(GEN global_primetab);
632 : void pari_set_seadata(GEN seadata);
633 : void pari_set_varstate(long *vp, struct pari_varstate *vs);
634 : void pari_thread_close_files(void);
635 :
636 : void export_add(const char *str, GEN val);
637 : void export_del(const char *str);
638 : GEN export_get(const char *str);
639 : void exportall(void);
640 : void unexportall(void);
641 :
642 : /* BY FILES */
643 :
644 : /* parinf.h */
645 :
646 : GEN coltoalg(GEN nf,GEN x);
647 : GEN fincke_pohst(GEN a,GEN BOUND,long stockmax,long PREC, FP_chk_fun *CHECK);
648 : void init_zlog(zlog_S *S, GEN bid);
649 : GEN log_gen_arch(zlog_S *S, long index);
650 : GEN log_gen_pr(zlog_S *S, long index, GEN nf, long e);
651 : GEN make_integral(GEN nf, GEN L0, GEN f, GEN listpr);
652 : GEN poltobasis(GEN nf,GEN x);
653 : GEN rnfdisc_get_T(GEN nf, GEN P, GEN *lim);
654 : GEN rnfallbase(GEN nf, GEN pol, GEN lim, GEN eq, GEN *pD, GEN *pfi, GEN *pdKP);
655 : GEN sprk_log_gen_pr(GEN nf, GEN sprk, long e);
656 : GEN sprk_log_gen_pr2(GEN nf, GEN sprk, long e);
657 : GEN sprk_log_prk1(GEN nf, GEN a, GEN sprk);
658 : GEN sprk_to_bid(GEN nf, GEN L, long flag);
659 : GEN subgroupcondlist(GEN cyc, GEN bound, GEN listKer);
660 :
661 : /* Qfb.c */
662 :
663 : GEN redimagsl2(GEN q, GEN *U);
664 :
665 : /* alglin1.c */
666 :
667 : typedef long (*pivot_fun)(GEN,GEN,long,GEN);
668 : GEN ZM_pivots(GEN x0, long *rr);
669 : GEN RgM_pivots(GEN x0, GEN data, long *rr, pivot_fun pivot);
670 : void RgMs_structelim_col(GEN M, long nbcol, long nbrow, GEN A, GEN *p_col, GEN *p_lin);
671 :
672 : /* arith1.c */
673 :
674 : int is_gener_Fp(GEN x, GEN p, GEN p_1, GEN L);
675 : int is_gener_Fl(ulong x, ulong p, ulong p_1, GEN L);
676 :
677 : /* arith2.c */
678 :
679 : int divisors_init(GEN n, GEN *pP, GEN *pE);
680 : long set_optimize(long what, GEN g);
681 :
682 : /* base1.c */
683 :
684 : GEN zk_galoisapplymod(GEN nf, GEN z, GEN S, GEN p);
685 : int ZX_canon_neg(GEN z);
686 :
687 : /* base2.c */
688 :
689 : GEN dim1proj(GEN prh);
690 : GEN gen_if_principal(GEN bnf, GEN x);
691 :
692 : /* base3.c */
693 :
694 : void check_nfelt(GEN x, GEN *den);
695 : GEN zk_ei_mul(GEN nf, GEN x, long i);
696 : GEN log_prk(GEN nf, GEN a, GEN sprk, GEN mod);
697 : GEN log_prk_units(GEN nf, GEN D, GEN sprk);
698 : GEN log_prk_units_init(GEN bnf);
699 : GEN veclog_prk(GEN nf, GEN v, GEN sprk);
700 : GEN log_prk_init(GEN nf, GEN pr, long k, GEN mod);
701 : GEN check_mod_factored(GEN nf, GEN ideal, GEN *fa, GEN *fa2, GEN *archp, GEN MOD);
702 : GEN sprk_get_cyc(GEN s);
703 : GEN sprk_get_expo(GEN s);
704 : GEN sprk_get_gen(GEN s);
705 : GEN sprk_get_prk(GEN s);
706 : GEN sprk_get_ff(GEN s);
707 : GEN sprk_get_pr(GEN s);
708 : void sprk_get_AgL2(GEN s, GEN *A, GEN *g, GEN *L2);
709 : void sprk_get_U2(GEN s, GEN *U1, GEN *U2);
710 : GEN famat_zlog_pr(GEN nf, GEN g, GEN e, GEN sprk, GEN mod);
711 :
712 : /* base4.c */
713 :
714 : GEN factorbackprime(GEN nf, GEN L, GEN e);
715 :
716 : /* bb_group.c */
717 :
718 : GEN producttree_scheme(long n);
719 :
720 : /* bern.c */
721 : long bernbitprec(long N);
722 :
723 : /* bibli2.c */
724 :
725 : GEN sort_factor_pol(GEN y, int (*cmp)(GEN,GEN));
726 :
727 : /* buch1.c */
728 :
729 : ulong bnf_increase_LIMC(ulong LIMC, ulong LIMCMAX);
730 :
731 : /* buch2.c */
732 :
733 : typedef struct GRHprime_t { ulong p; double logp; GEN dec; } GRHprime_t;
734 : typedef struct GRHcheck_t { double cD, cN; GRHprime_t *primes; long clone, nprimes, maxprimes; ulong limp; forprime_t P; } GRHcheck_t;
735 : void free_GRHcheck(GRHcheck_t *S);
736 : void init_GRHcheck(GRHcheck_t *S, long N, long R1, double LOGD);
737 : void GRH_ensure(GRHcheck_t *S, long nb);
738 : ulong GRH_last_prime(GRHcheck_t *S);
739 : int GRHok(GRHcheck_t *S, double L, double SA, double SB);
740 : GEN extract_full_lattice(GEN x);
741 : GEN init_red_mod_units(GEN bnf, long prec);
742 : GEN isprincipalarch(GEN bnf, GEN col, GEN kNx, GEN e, GEN dx, long *pe);
743 : GEN red_mod_units(GEN col, GEN z);
744 :
745 : /* buch3.c */
746 :
747 : GEN minkowski_bound(GEN D, long N, long r2, long prec);
748 : int subgroup_conductor_ok(GEN H, GEN L);
749 : GEN subgrouplist_cond_sub(GEN bnr, GEN C, GEN bound);
750 :
751 : /* crvwtors.c */
752 :
753 : void random_curves_with_m_torsion(ulong *a4, ulong *a6, ulong *tx, ulong *ty, long ncurves, long m, ulong p, ulong pi);
754 :
755 : /* dirichlet.c */
756 :
757 : GEN direuler_factor(GEN s, long n);
758 :
759 : /* ellanal.c */
760 :
761 : GEN hnaive_max(GEN ell, GEN ht);
762 :
763 : /* elliptic.c */
764 :
765 : GEN ellQ_genreduce(GEN E, GEN G, GEN M, long prec);
766 : GEN ellQ_isdivisible(GEN E, GEN P, ulong l);
767 : GEN ellminimalbmodel(GEN E, GEN *ptv);
768 : GEN ellintegralbmodel(GEN e, GEN *pv);
769 : void ellprint(GEN e);
770 :
771 : /* ellrank.c */
772 :
773 : GEN ell2selmer_basis(GEN ell, GEN *cb, long prec);
774 :
775 : /* es.c */
776 :
777 : void killallfiles(void);
778 : pariFILE* newfile(FILE *f, const char *name, int type);
779 : int popinfile(void);
780 : pariFILE* try_pipe(const char *cmd, int flag);
781 :
782 : /* F2m.c */
783 :
784 : GEN F2m_gauss_pivot(GEN x, long *rr);
785 : GEN F2m_gauss_sp(GEN a, GEN b);
786 : GEN F2m_invimage_i(GEN A, GEN B);
787 :
788 : /* Fle.c */
789 :
790 : void FleV_add_pre_inplace(GEN P, GEN Q, GEN a4, ulong p, ulong pi);
791 : void FleV_dbl_pre_inplace(GEN P, GEN a4, ulong p, ulong pi);
792 : void FleV_mulu_pre_inplace(GEN P, ulong n, GEN a4, ulong p, ulong pi);
793 : void FleV_sub_pre_inplace(GEN P, GEN Q, GEN a4, ulong p, ulong pi);
794 :
795 : /* Flv.c */
796 :
797 : GEN Flm_gauss_sp(GEN a, GEN b, ulong *detp, ulong p);
798 : GEN Flm_invimage_i(GEN A, GEN B, ulong p);
799 : GEN Flm_inv_sp(GEN a, ulong *detp, ulong p);
800 : GEN Flm_pivots(GEN x, ulong p, long *rr, long inplace);
801 :
802 : /* Flxq_log.c */
803 :
804 : GEN Flxq_log_index(GEN a0, GEN b0, GEN m, GEN T0, ulong p);
805 : int Flxq_log_use_index(GEN m, GEN T0, ulong p);
806 :
807 : /* FlxqE.c */
808 :
809 : GEN ZpXQ_norm_pcyc(GEN x, GEN T, GEN q, GEN p);
810 : long zx_is_pcyc(GEN T);
811 :
812 : /* FpV.c */
813 :
814 : GEN FpMs_leftkernel_elt_col(GEN M, long nbcol, long nbrow, GEN p);
815 : GEN FpX_to_mod_raw(GEN z, GEN p);
816 :
817 : /* FpX.c */
818 :
819 : GEN ZlXQXn_expint(GEN h, long e, GEN T, GEN p, ulong pp);
820 :
821 : /* FpX_factor.c */
822 :
823 : GEN ddf_to_ddf2(GEN V);
824 : long ddf_to_nbfact(GEN D);
825 : GEN vddf_to_simplefact(GEN V, long d);
826 :
827 : /* FpXQX_factor.c */
828 :
829 : GEN FpXQX_factor_Berlekamp(GEN x, GEN T, GEN p);
830 :
831 : /* forprime.c*/
832 :
833 : void init_modular_big(forprime_t *S);
834 : void init_modular_small(forprime_t *S);
835 :
836 : /* galconj.c */
837 :
838 : GEN galoiscosets(GEN O, GEN perm);
839 : GEN galoisinitfromaut(GEN T, GEN aut, ulong l);
840 : GEN matrixnorm(GEN M, long prec);
841 :
842 : /* gen1.c */
843 :
844 : GEN gred_rfrac_simple(GEN n, GEN d);
845 : GEN sqr_ser_part(GEN x, long l1, long l2);
846 :
847 : /* hash.c */
848 :
849 : hashtable *hashstr_import_static(hashentry *e, ulong size);
850 :
851 : /* hyperell.c */
852 :
853 : GEN ZlXQX_hyperellpadicfrobenius(GEN H, GEN T, ulong p, long n);
854 :
855 : /* ifactor1.c */
856 :
857 : ulong snextpr(ulong p, byteptr *d, long *rcn, long *q, int (*ispsp)(ulong));
858 :
859 : /* intnum.c */
860 :
861 : GEN contfraceval_inv(GEN CF, GEN tinv, long nlim);
862 : GEN contfracinit_i(GEN M, long n);
863 :
864 : /* mftrace.c */
865 :
866 : void pari_close_mf(void);
867 : long polishomogeneous(GEN P);
868 : GEN sertocol(GEN S);
869 : GEN mfrhopol(long n);
870 : GEN mfrhopol_u_eval(GEN Q, ulong t2);
871 : GEN mfrhopol_eval(GEN Q, GEN t2);
872 :
873 : /* prime.c */
874 :
875 : long BPSW_psp_nosmalldiv(GEN N);
876 : int MR_Jaeschke(GEN n);
877 : long isanypower_nosmalldiv(GEN N, GEN *px);
878 : void prime_table_next_p(ulong a, byteptr *pd, ulong *pp, ulong *pn);
879 :
880 : /* perm.c */
881 :
882 : long cosets_perm_search(GEN C, GEN p);
883 : GEN perm_generate(GEN S, GEN H, long o);
884 : long perm_relorder(GEN p, GEN S);
885 : GEN vecperm_extendschreier(GEN C, GEN v, long n);
886 :
887 : /* polclass.c */
888 :
889 : GEN polclass0(long D, long inv, long vx, GEN *db);
890 :
891 : /* polmodular.c */
892 :
893 : GEN polmodular0_ZM(long L, long inv, GEN J, GEN Q, int compute_derivs, GEN *db);
894 : GEN Flm_Fl_polmodular_evalx(GEN phi, long L, ulong j, ulong p, ulong pi);
895 : GEN polmodular_db_init(long inv);
896 : void polmodular_db_clear(GEN db);
897 : void polmodular_db_add_level(GEN *db, long L, long inv);
898 : void polmodular_db_add_levels(GEN *db, long *levels, long k, long inv);
899 : GEN polmodular_db_for_inv(GEN db, long inv);
900 : GEN polmodular_db_getp(GEN fdb, long L, ulong p);
901 :
902 : long modinv_level(long inv);
903 : long modinv_degree(long *p1, long *p2, long inv);
904 : long modinv_ramified(long D, long inv, long *pN);
905 : long modinv_j_from_2double_eta(GEN F, long inv, ulong x0, ulong x1, ulong p, ulong pi);
906 : GEN double_eta_raw(long inv);
907 : ulong modfn_root(ulong j, norm_eqn_t ne, long inv);
908 : long modfn_unambiguous_root(ulong *r, long inv, ulong j0, norm_eqn_t ne, GEN jdb);
909 : GEN qfb_nform(long D, long n);
910 :
911 : /* Fle.c */
912 :
913 : ulong Flj_order_ufact(GEN P, ulong n, GEN F, ulong a4, ulong p, ulong pi);
914 :
915 : /* polarit3.c */
916 :
917 : GEN Flm_Frobenius_pow(GEN M, long d, GEN T, ulong p);
918 : GEN FpM_Frobenius_pow(GEN M, long d, GEN T, GEN p);
919 : GEN RgXQ_charpoly_i(GEN x, GEN T, long v);
920 : ulong ZX_ZXY_ResBound(GEN A, GEN B, GEN dB);
921 : GEN ffinit_Artin_Schreier(ulong p, long l);
922 : GEN ffinit_rand(GEN p, long n);
923 : GEN nf_direct_compositum(GEN nf, GEN A, GEN B);
924 :
925 : /* nflist.c */
926 :
927 : GEN veccond_to_A5(GEN L, long s);
928 : long ceilsqrtdiv(GEN x, GEN y);
929 :
930 : /* nflistQT.c */
931 :
932 : GEN nflistQT(long n, long k, long v);
933 :
934 : /* ramanujantau.c */
935 : GEN ramanujantau_worker(GEN gt, GEN p2_7, GEN p_9, GEN p);
936 : GEN taugen_n_worker(GEN t, GEN pol, GEN p4);
937 :
938 : /* readline.c */
939 :
940 : char** pari_completion(pari_rl_interface *pari_rl, char *text, int START, int END);
941 : char** pari_completion_matches(pari_rl_interface *pari_rl, const char *s, long pos, long *wordpos);
942 :
943 : /* subcyclo.c */
944 :
945 : GEN galoiscyclo(long n, long v);
946 : long subcyclo_nH(const char *fun, GEN N, GEN *psg);
947 : GEN znstar_bits(long n, GEN H);
948 : long znstar_conductor(GEN H);
949 : long znstar_conductor_bits(GEN bits);
950 : GEN znstar_cosets(long n, long phi_n, GEN H);
951 : GEN znstar_elts(long n, GEN H);
952 : GEN znstar_generate(long n, GEN V);
953 : GEN znstar_hnf(GEN Z, GEN M);
954 : GEN znstar_hnf_elts(GEN Z, GEN H);
955 : GEN znstar_hnf_generators(GEN Z, GEN M);
956 : GEN znstar_reduce_modulus(GEN H, long n);
957 : GEN znstar_small(GEN zn);
958 :
959 : /* trans1.c */
960 :
961 : struct abpq { GEN *a, *b, *p, *q; };
962 : struct abpq_res { GEN P, Q, B, T; };
963 : void abpq_init(struct abpq *A, long n);
964 : void abpq_sum(struct abpq_res *r, long n1, long n2, struct abpq *A);
965 : GEN logagmcx(GEN q, long prec);
966 : GEN zellagmcx(GEN a0, GEN b0, GEN r, GEN t, long prec);
967 :
968 : /* trans2.c */
969 :
970 : GEN trans_fix_arg(long *prec, GEN *s0, GEN *sig, GEN *tau, pari_sp *av, GEN *res);
971 :
972 : /* trans3.c */
973 :
974 : GEN double_eta_quotient(GEN a, GEN w, GEN D, long p, long q, GEN pq, GEN sqrtD);
975 : GEN inv_szeta_euler(long n, long prec);
976 : GEN lerch_worker(GEN t, GEN E);
977 :
978 : /* volcano.c */
979 :
980 : long j_level_in_volcano(GEN phi, ulong j, ulong p, ulong pi, long L, long depth);
981 : ulong ascend_volcano(GEN phi, ulong j, ulong p, ulong pi, long level, long L, long depth, long steps);
982 : ulong descend_volcano(GEN phi, ulong j, ulong p, ulong pi, long level, long L, long depth, long steps);
983 : long next_surface_nbr(ulong *nJ, GEN phi, long L, long h, ulong J, const ulong *pJ, ulong p, ulong pi);
984 : GEN enum_roots(ulong j, norm_eqn_t ne, GEN fdb, GEN G, GEN vshape);
985 :
986 : ENDEXTERN
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