Annotation of OpenXM_contrib/pari/src/headers/paridecl.h, Revision 1.1.1.1
1.1 maekawa 1: /*******************************************************************/
2: /* */
3: /* Fichier Include PARI */
4: /* declarations generales */
5: /* */
6: /*******************************************************************/
7: /* $Id: paridecl.h,v 1.6 1999/09/23 17:07:01 karim Exp $ */
8:
9: /* alglin1.c */
10:
11: GEN concat(GEN x, GEN y);
12: GEN concatsp(GEN x, GEN y);
13: GEN deplin(GEN x);
14: GEN det(GEN a);
15: GEN det0(GEN a,long flag);
16: GEN det2(GEN a);
17: GEN dethnf(GEN x);
18: GEN dethnf_i(GEN mat);
19: GEN detint(GEN x);
20: GEN diagonal(GEN x);
21: GEN eigen(GEN x, long prec);
22: GEN extract(GEN x, GEN l);
23: GEN extract0(GEN x, GEN l1, GEN l2);
24: GEN gaddmat(GEN x, GEN y);
25: GEN gauss(GEN a, GEN b);
26: GEN gaussmodulo(GEN M, GEN D, GEN Y);
27: GEN gaussmodulo2(GEN M, GEN D, GEN Y);
28: GEN gscalcol(GEN x, long n);
29: GEN gscalcol_i(GEN x, long n);
30: GEN gscalcol_proto(GEN z, GEN myzero, long n);
31: GEN gscalmat(GEN x, long n);
32: GEN gscalsmat(long x, long n);
33: GEN gtomat(GEN x);
34: GEN gtrans(GEN x);
35: GEN hnfadd(GEN mit,GEN perm,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
36: GEN hnfspec(long** mat,GEN perm,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
37: GEN idmat(long n);
38: GEN idmat_intern(long n,GEN myun,GEN myzero);
39: GEN image(GEN x);
40: GEN image2(GEN x);
41: GEN image_mod_p(GEN x, GEN p);
42: GEN imagecompl(GEN x);
43: GEN imagereel(GEN x, long prec);
44: GEN indexrank(GEN x);
45: GEN inverseimage(GEN mat, GEN y);
46: long isdiagonal(GEN x);
47: GEN ker(GEN x);
48: GEN ker_mod_p(GEN x, GEN p);
49: GEN keri(GEN x);
50: GEN matextract(GEN x, GEN l1, GEN l2);
51: GEN matimage0(GEN x,long flag);
52: GEN matker0(GEN x, long flag);
53: GEN matmuldiagonal(GEN x, GEN d);
54: GEN matmultodiagonal(GEN x, GEN y);
55: GEN matsolvemod0(GEN M, GEN D, GEN Y,long flag);
56: GEN mattodiagonal(GEN m);
57: long rank(GEN x);
58: long rank_mod_p(GEN x, GEN p);
59: GEN suppl(GEN x);
60: GEN suppl_intern(GEN x, GEN myid);
61: GEN zerocol(long n);
62:
63: /* alglin2.c */
64:
65: GEN adj(GEN x);
66: GEN assmat(GEN x);
67: GEN caract(GEN x, int v);
68: GEN caract2(GEN p, GEN x, int v);
69: GEN caradj(GEN x, long v, GEN *py);
70: GEN caradj0(GEN x, long v);
71: GEN carhess(GEN x, long v);
72: GEN charpoly0(GEN x, int v,long flag);
73: GEN conjvec(GEN x,long prec);
74: GEN gconj(GEN x);
75: GEN gnorm(GEN x);
76: GEN gnorml2(GEN x);
77: GEN gtrace(GEN x);
78: GEN hess(GEN x);
79: GEN hnf(GEN x);
80: GEN hnfall(GEN x);
81: GEN hnfhavas(GEN x);
82: GEN hnflll(GEN x);
83: GEN hnfmod(GEN x, GEN detmat);
84: GEN hnfmodid(GEN x,GEN p);
85: GEN hnfperm(GEN x);
86: GEN intersect(GEN x, GEN y);
87: GEN jacobi(GEN a, long prec);
88: GEN matrixqz(GEN x, GEN pp);
89: GEN matrixqz0(GEN x, GEN pp);
90: GEN matrixqz2(GEN x);
91: GEN matrixqz3(GEN x);
92: GEN signat(GEN a);
93: GEN smith(GEN x);
94: GEN smith2(GEN x);
95: GEN smithclean(GEN z);
96: GEN sqred(GEN a);
97: GEN sqred1(GEN a);
98: GEN sqred1intern(GEN a, long flag);
99: GEN sqred3(GEN a);
100:
101: /* anal.c */
102:
103: entree *fetch_named_var(char *s, int doerr);
104: entree *gp_variable(char *s);
105: void delete_named_var(entree *ep);
106: long delete_var(void);
107: long fetch_user_var(char *s);
108: long fetch_var(void);
109: GEN flisexpr(char *t);
110: void freeep(entree *ep);
111: long hashvalue(char *s);
112: entree* install(void *f, char *name, char *code);
113: GEN lisexpr(char *t);
114: GEN lisseq(char *t);
115: long manage_var(long n, entree *ep);
116: void name_var(long n, char *s);
117: GEN readseq(char *c, int strict);
118: GEN strtoGENstr(char *s, long flag);
119:
120: /* arith1.c */
121:
122: GEN bestappr(GEN x, GEN k);
123: GEN bezout(GEN a, GEN b, GEN *u, GEN *v);
124: GEN binaire(GEN x);
125: long bittest(GEN x, long n);
126: long carrecomplet(GEN x, GEN *pt);
127: long cbezout(long a,long b,long *uu,long *vv);
128: long cgcd(long a,long b);
129: GEN chinois(GEN x, GEN y);
130: GEN classno(GEN x);
131: GEN classno2(GEN x);
132: GEN fibo(long n);
133: GEN fundunit(GEN x);
134: GEN gbittest(GEN x, GEN n);
135: GEN gboundcf(GEN x, long k);
136: GEN gcarrecomplet(GEN x, GEN *pt);
137: GEN gcarreparfait(GEN x);
138: GEN gcf(GEN x);
139: GEN gcf2(GEN b, GEN x);
140: GEN gener(GEN m);
141: GEN gfundunit(GEN x);
142: GEN ggener(GEN m);
143: GEN gisfundamental(GEN x);
144: GEN gisprime(GEN x);
145: GEN gispsp(GEN x);
146: GEN gkrogs(GEN x, long y);
147: GEN gkronecker(GEN x, GEN y);
148: GEN gmillerrabin(GEN n, long k);
149: GEN gnextprime(GEN n);
150: GEN gprecprime(GEN n);
151: GEN gracine(GEN a);
152: GEN gregula(GEN x, long prec);
153: GEN hclassno(GEN x);
154: long hil(GEN x, GEN y, GEN p);
155: long hil0(GEN x, GEN y, GEN p);
156: long isfundamental(GEN x);
157: long isprime(GEN x);
158: long ispsp(GEN x);
159: long krogs(GEN x, long y);
160: long kronecker(GEN x, GEN y);
161: long krosg(long s, GEN x);
162: long kross(long x, long y);
163: void lucas(long n, GEN *ln, GEN *ln1);
164: long millerrabin(GEN n, long k);
165: GEN mpfact(long n);
166: GEN mpfactr(long n, long prec);
167: GEN mpinvmod(GEN a, GEN m);
168: GEN mppgcd(GEN a, GEN b);
169: GEN mpsqrtmod(GEN a, GEN p);
170: GEN order(GEN x);
171: GEN pnqn(GEN x);
172: GEN powmodulo(GEN a, GEN n, GEN m);
173: GEN qfbclassno0(GEN x,long flag);
174: GEN quaddisc(GEN x);
175: GEN racine(GEN a);
176: GEN regula(GEN x, long prec);
177: GEN sfcont(GEN x, GEN x1, long k);
178: GEN sfcont0(GEN x, GEN b, long flag);
179: GEN znstar(GEN x);
180:
181: /* arith2.c */
182:
183: GEN Qfb0(GEN x, GEN y, GEN z, GEN d, long prec);
184: GEN addprimes(GEN primes);
185: GEN auxdecomp(GEN n, long all);
186: long bigomega(GEN n);
187: GEN boundfact(GEN n, long lim);
188: GEN compimag(GEN x, GEN y);
189: GEN compimagraw(GEN x, GEN y);
190: GEN compraw(GEN x, GEN y);
191: GEN compreal(GEN x, GEN y);
192: GEN comprealraw(GEN x, GEN y);
193: GEN core(GEN n);
194: GEN core0(GEN n,long flag);
195: GEN core2(GEN n);
196: GEN coredisc(GEN n);
197: GEN coredisc0(GEN n,long flag);
198: GEN coredisc2(GEN n);
199: GEN decomp(GEN n);
200: GEN divisors(GEN n);
201: GEN factorint(GEN n, long flag);
202: GEN gbigomega(GEN n);
203: GEN gboundfact(GEN n, long lim);
204: GEN gissquarefree(GEN x);
205: GEN gmu(GEN n);
206: GEN gnumbdiv(GEN n);
207: GEN gomega(GEN n);
208: GEN gphi(GEN n);
209: GEN gsumdiv(GEN n);
210: GEN gsumdivk(GEN n,long k);
211: byteptr initprimes(long maxnum);
212: long issquarefree(GEN x);
213: long mu(GEN n);
214: GEN nucomp(GEN x, GEN y, GEN l);
215: GEN nudupl(GEN x, GEN l);
216: GEN numbdiv(GEN n);
217: GEN nupow(GEN x, GEN n);
218: long omega(GEN n);
219: GEN phi(GEN n);
220: GEN powraw(GEN x, long n);
221: GEN powrealraw(GEN x, long n);
222: GEN prime(long n);
223: GEN primeform(GEN x, GEN p, long prec);
224: GEN primes(long n);
225: GEN qfbred0(GEN x, long flag, GEN D, GEN isqrtD, GEN sqrtD);
226: GEN qfi(GEN x, GEN y, GEN z);
227: GEN qfr(GEN x, GEN y, GEN z, GEN d);
228: GEN redimag(GEN x);
229: GEN redreal(GEN x);
230: GEN redrealnod(GEN x, GEN isqrtD);
231: GEN removeprimes(GEN primes);
232: GEN rhoreal(GEN x);
233: GEN rhorealnod(GEN x, GEN isqrtD);
234: GEN smallfact(GEN n);
235: GEN sqcompimag(GEN x);
236: GEN sqcompreal(GEN x);
237: GEN sumdiv(GEN n);
238: GEN sumdivk(GEN n,long k);
239:
240: /* base1.c */
241:
242: GEN bnfnewprec(GEN nf, long prec);
243: void check_pol_int(GEN x);
244: GEN check_units(GEN x, char *f);
245: void checkbid(GEN bid);
246: GEN checkbnf(GEN bnf);
247: void checkbnr(GEN bnr);
248: void checkbnrgen(GEN bnr);
249: void checkid(GEN x, long N);
250: GEN checknf(GEN nf);
251: void checkprhall(GEN prhall);
252: void checkprimeid(GEN bid);
253: void checkrnf(GEN rnf);
254: GEN differente(GEN nf, GEN premiers);
255: GEN galois(GEN x, long prec);
256: GEN galoisapply(GEN nf, GEN aut, GEN x);
257: GEN get_bnf(GEN x,int *t);
258: GEN get_nf(GEN x,int *t);
259: GEN get_primeid(GEN x);
260: GEN glambdak(GEN nfz, GEN s, long prec);
261: int gpolcomp(GEN p1, GEN p2);
262: GEN gsmith(GEN x);
263: GEN gsmith2(GEN x);
264: GEN gzetak(GEN nfz, GEN s, long prec);
265: GEN gzetakall(GEN nfz, GEN s, long flag, long prec);
266: GEN initalg(GEN x, long prec);
267: GEN initalgred(GEN x, long prec);
268: GEN initalgred2(GEN x, long prec);
269: GEN initzeta(GEN pol, long prec);
270: GEN mathnf0(GEN x,long flag);
271: GEN matsnf0(GEN x,long flag);
272: GEN nfinit0(GEN x,long flag, long prec);
273: GEN nfnewprec(GEN nf, long prec);
274: GEN rootsof1(GEN x);
275: GEN tschirnhaus(GEN x);
276:
277: /* base2.c */
278:
279: GEN allbase4(GEN f, long code, GEN *y, GEN *ptw);
280: GEN base(GEN x, GEN *y);
281: GEN base2(GEN x, GEN *y);
282: GEN compositum(GEN pol1, GEN pol2);
283: GEN compositum2(GEN pol1, GEN pol2);
284: GEN discf(GEN x);
285: GEN discf2(GEN x);
286: GEN factcp(GEN p,GEN f,GEN beta);
287: GEN factoredbase(GEN x, GEN p, GEN *y);
288: GEN factoreddiscf(GEN x, GEN p);
289: GEN gcdpm(GEN f1,GEN f2,GEN pm);
290: long idealval(GEN nf,GEN ix,GEN vp);
291: GEN nfbasis(GEN x, GEN *y,long flag,GEN p);
292: GEN nfbasis0(GEN x,long flag,GEN p);
293: GEN nfdiscf0(GEN x,long flag, GEN p);
294: GEN nfreducemodideal(GEN nf,GEN x,GEN ideal);
295: GEN nfreducemodpr(GEN nf, GEN x, GEN prhall);
296: GEN nfreducemodpr2(GEN nf, GEN x, GEN prhall);
297: GEN polcompositum0(GEN pol1, GEN pol2,long flag);
298: GEN primedec(GEN nf,GEN p);
299: GEN rnfbasis(GEN bnf, GEN order);
300: GEN rnfdet(GEN nf, GEN order);
301: GEN rnfdet0(GEN nf, GEN x, GEN y);
302: GEN rnfdet2(GEN nf, GEN A, GEN I);
303: GEN rnfdiscf(GEN nf, GEN pol);
304: GEN rnfequation(GEN nf, GEN pol2);
305: GEN rnfequation2(GEN nf, GEN pol);
306: GEN rnfequation0(GEN nf, GEN pol2, long flall);
307: GEN rnfhermitebasis(GEN bnf, GEN order);
308: long rnfisfree(GEN bnf, GEN order);
309: GEN rnflllgram(GEN nf, GEN pol, GEN order,long prec);
310: GEN rnfpolred(GEN nf, GEN pol, long prec);
311: GEN rnfpolredabs(GEN nf, GEN pol, long flag, long prec);
312: GEN rnfpseudobasis(GEN nf, GEN pol);
313: GEN rnfsimplifybasis(GEN bnf, GEN order);
314: GEN rnfsteinitz(GEN nf, GEN order);
315: GEN smallbase(GEN x, GEN *y);
316: GEN smalldiscf(GEN x);
317: GEN subcyclo(GEN p, GEN d, int n);
318:
319: /* base3.c */
320:
321: GEN algtobasis(GEN nf, GEN x);
322: GEN algtobasis_intern(GEN nf,GEN x);
323: GEN basistoalg(GEN nf, GEN x);
324: GEN element_div(GEN nf, GEN x, GEN y);
325: GEN element_inv(GEN nf, GEN x);
326: GEN element_invmodideal(GEN nf, GEN x, GEN ideal);
327: GEN element_mul(GEN nf,GEN x,GEN y);
328: GEN element_mulid(GEN nf, GEN x, long i);
329: GEN element_mulvec(GEN nf, GEN x, GEN v);
330: GEN element_pow(GEN nf,GEN x,GEN k);
331: GEN element_pow_mod_p(GEN nf, GEN x, GEN n, GEN p);
332: GEN element_powmodideal(GEN nf,GEN x,GEN k,GEN ideal);
333: GEN element_powmodidele(GEN nf,GEN x,GEN k,GEN idele,GEN structarch);
334: GEN element_sqr(GEN nf,GEN x);
335: long element_val(GEN nf, GEN x, GEN vp);
336: long element_val2(GEN nf, GEN x, GEN d, GEN vp);
337: GEN ideallist(GEN nf,long bound);
338: GEN ideallist0(GEN nf,long bound, long flag);
339: GEN ideallistarch(GEN nf, GEN list, GEN arch);
340: GEN ideallistarch0(GEN nf, GEN list, GEN arch,long flag);
341: GEN ideallistarchgen(GEN nf, GEN list, GEN arch);
342: GEN ideallistunit(GEN nf,long bound);
343: GEN ideallistunitarch(GEN bnf,GEN list,GEN arch);
344: GEN ideallistunitarchgen(GEN bnf,GEN list,GEN arch);
345: GEN ideallistunitgen(GEN nf,long bound);
346: GEN ideallistzstar(GEN nf,long bound);
347: GEN ideallistzstargen(GEN nf,long bound);
348: GEN idealstar0(GEN nf, GEN x,long flag);
349: int isnfscalar(GEN x);
350: GEN lllreducemodmatrix(GEN x,GEN y);
351: GEN nfdiveuc(GEN nf, GEN a, GEN b);
352: GEN nfdivres(GEN nf, GEN a, GEN b);
353: GEN nfmod(GEN nf, GEN a, GEN b);
354: GEN nfreducemodidele(GEN nf,GEN g,GEN idele,GEN structarch);
355: GEN nfshanks(GEN nf,GEN x,GEN g0,GEN pr,GEN prhall);
356: GEN reducemodmatrix(GEN x, GEN y);
357: GEN zarchstar(GEN nf,GEN x,GEN arch,long nba);
358: GEN zideallog(GEN nf,GEN x,GEN bigideal);
359: GEN zidealstar(GEN nf, GEN x);
360: GEN zidealstarinit(GEN nf, GEN x);
361: GEN zidealstarinitall(GEN nf, GEN x,long flun);
362: GEN zidealstarinitgen(GEN nf, GEN x);
363: GEN zidealstarinitjoin(GEN nf, GEN bid1, GEN bid2);
364: GEN zidealstarinitjoinarch(GEN nf, GEN bid1, GEN arch, long nba);
365: GEN zidealstarinitjoinarchgen(GEN nf, GEN bid1, GEN arch, long nba);
366: GEN zidealstarinitjoingen(GEN nf, GEN bid1, GEN bid2);
367: GEN znlog(GEN x, GEN g);
368: GEN zsigne(GEN nf,GEN alpha,GEN arch);
369:
370: /* base4.c */
371:
372: GEN element_divmodpr(GEN nf, GEN x, GEN y, GEN prhall);
373: GEN element_invmodpr(GEN nf, GEN y, GEN prhall);
374: GEN element_mulmodpr2(GEN nf, GEN x, GEN y, GEN prhall);
375: GEN element_powmodpr(GEN nf, GEN x, GEN k, GEN prhall);
376: GEN element_reduce(GEN nf, GEN x, GEN ideal);
377: GEN ideal_two_elt(GEN nf, GEN ix);
378: GEN ideal_two_elt0(GEN nf, GEN ix, GEN a);
379: GEN ideal_two_elt2(GEN nf, GEN x, GEN a);
380: GEN idealadd(GEN nf, GEN x, GEN y);
381: GEN idealaddmultoone(GEN nf, GEN list);
382: GEN idealaddtoone(GEN nf, GEN x, GEN y);
383: GEN idealaddtoone0(GEN nf, GEN x, GEN y);
384: GEN idealappr(GEN nf, GEN x);
385: GEN idealappr0(GEN nf, GEN x, long fl);
386: GEN idealapprfact(GEN nf, GEN x);
387: GEN idealchinese(GEN nf, GEN x, GEN y);
388: GEN idealcoprime(GEN nf, GEN x, GEN y);
389: GEN idealdiv(GEN nf, GEN x, GEN y);
390: GEN idealdiv0(GEN nf, GEN x, GEN y,long flag);
391: GEN idealdivexact(GEN nf, GEN x, GEN y);
392: GEN idealfactor(GEN nf, GEN x);
393: GEN idealhermite(GEN nf, GEN x);
394: GEN idealhermite2(GEN nf, GEN a, GEN b);
395: GEN idealhnf0(GEN nf, GEN a, GEN b);
396: GEN idealintersect(GEN nf, GEN x, GEN y);
397: GEN idealinv(GEN nf, GEN ix);
398: GEN idealinv0(GEN nf, GEN ix,long flag);
399: GEN ideallllred(GEN nf,GEN ix,GEN vdir,long prec);
400: GEN ideallllredall(GEN nf, GEN ix, GEN vdir, long prec, long precint);
401: GEN idealmul(GEN nf, GEN ix, GEN iy);
402: GEN idealmul0(GEN nf, GEN ix, GEN iy, long flag, long prec);
403: GEN idealmulelt(GEN nf, GEN elt, GEN x);
404: GEN idealmulh(GEN nf, GEN ix, GEN iy);
405: GEN idealmulprime(GEN nf,GEN ix,GEN vp);
406: GEN idealmulred(GEN nf, GEN ix, GEN iy, long prec);
407: GEN idealnorm(GEN nf, GEN x);
408: GEN idealoplll(GEN op(GEN,GEN,GEN), GEN nf, GEN x, GEN y);
409: GEN idealpow(GEN nf, GEN ix, GEN n);
410: GEN idealpow0(GEN nf, GEN ix, GEN n, long flag, long prec);
411: GEN idealpowred(GEN nf, GEN ix, GEN n,long prec);
412: GEN idealpows(GEN nf, GEN ideal, long iexp);
413: GEN ideleaddone(GEN nf, GEN x, GEN idele);
414: int ishnfall(GEN x);
415: long isideal(GEN nf,GEN x);
416: long isinvector(GEN v, GEN x, long n);
417: GEN minideal(GEN nf,GEN ix,GEN vdir,long prec);
418: GEN nfdetint(GEN nf,GEN pseudo);
419: GEN nfhermite(GEN nf, GEN x);
420: GEN nfhermitemod(GEN nf, GEN x, GEN detmat);
421: GEN nfkermodpr(GEN nf, GEN x, GEN prhall);
422: GEN nfmodprinit(GEN nf, GEN pr);
423: GEN nfsmith(GEN nf, GEN x);
424: GEN nfsolvemodpr(GEN nf, GEN a, GEN b, GEN prhall);
425: GEN oldidealinv(GEN nf, GEN ix);
426: GEN prime_to_ideal(GEN nf, GEN vp);
427: GEN principalideal(GEN nf, GEN a);
428: GEN principalidele(GEN nf, GEN a, long prec);
429: GEN threetotwo(GEN nf, GEN a, GEN b, GEN c);
430: GEN threetotwo2(GEN nf, GEN a, GEN b, GEN c);
431: GEN twototwo(GEN nf, GEN a, GEN b);
432:
433: /* base5.c */
434:
435: GEN lift_to_pol(GEN x);
436: GEN matalgtobasis(GEN nf, GEN x);
437: GEN matbasistoalg(GEN nf, GEN x);
438: GEN rnfalgtobasis(GEN rnf, GEN x);
439: GEN rnfbasistoalg(GEN rnf, GEN x);
440: GEN rnfelementabstorel(GEN rnf, GEN x);
441: GEN rnfelementdown(GEN rnf, GEN x);
442: GEN rnfelementreltoabs(GEN rnf, GEN x);
443: GEN rnfelementup(GEN rnf, GEN x);
444: GEN rnfidealabstorel(GEN rnf, GEN x);
445: GEN rnfidealdown(GEN rnf, GEN x);
446: GEN rnfidealhermite(GEN rnf, GEN x);
447: GEN rnfidealmul(GEN rnf,GEN x,GEN y);
448: GEN rnfidealnormabs(GEN rnf, GEN x);
449: GEN rnfidealnormrel(GEN rnf, GEN x);
450: GEN rnfidealreltoabs(GEN rnf, GEN x);
451: GEN rnfidealtwoelement(GEN rnf,GEN x);
452: GEN rnfidealup(GEN rnf, GEN x);
453: GEN rnfinitalg(GEN nf,GEN pol,long prec);
454:
455: /* bibli1.c */
456:
457: GEN algdep(GEN x, long n, long prec);
458: GEN algdep0(GEN x, long n, long bit,long prec);
459: GEN algdep2(GEN x, long n, long bit);
460: GEN factoredpolred(GEN x, GEN p, long prec);
461: GEN factoredpolred2(GEN x, GEN p, long prec);
462: GEN fincke_pohst(GEN a, GEN borne, GEN stockmax, long flag, long prec, GEN (*check)(GEN));
463: GEN kerint(GEN x);
464: GEN kerint1(GEN x);
465: GEN kerint2(GEN x);
466: GEN lindep(GEN x, long prec);
467: GEN lindep0(GEN x, long flag,long prec);
468: GEN lindep2(GEN x, long bit);
469: GEN lll(GEN x, long prec);
470: GEN lll1(GEN x, long prec);
471: GEN lllgen(GEN x);
472: GEN lllgram(GEN x, long prec);
473: GEN lllgram1(GEN x, long prec);
474: GEN lllgramgen(GEN x);
475: GEN lllgramint(GEN x);
476: GEN lllgramintern(GEN x, long alpha, long flag, long prec);
477: GEN lllgramkerim(GEN x);
478: GEN lllgramkerimgen(GEN x);
479: GEN lllint(GEN x);
480: GEN lllintern(GEN x, long flag, long prec);
481: GEN lllintpartial(GEN mat);
482: GEN lllkerim(GEN x);
483: GEN lllkerimgen(GEN x);
484: GEN lllrat(GEN x);
485: GEN matkerint0(GEN x,long flag);
486: GEN minim(GEN a, GEN borne, GEN stockmax);
487: GEN minim0(GEN a, GEN borne, GEN stockmax,long flag, long prec);
488: GEN minim2(GEN a, GEN borne, GEN stockmax);
489: GEN ordred(GEN x, long prec);
490: GEN perf(GEN a);
491: GEN polred(GEN x, long prec);
492: GEN polred0(GEN x, long flag, GEN p, long prec);
493: GEN polred2(GEN x, long prec);
494: GEN polredabs(GEN x, long prec);
495: GEN polredabs0(GEN x, long flag, long prec);
496: GEN polredabs2(GEN x, long prec);
497: GEN polredabsall(GEN x, long flun, long prec);
498: GEN polredabsnored(GEN x, long prec);
499: GEN qflll0(GEN x, long flag, long prec);
500: GEN qflllgram0(GEN x, long flag, long prec);
501: GEN smallpolred(GEN x, long prec);
502: GEN smallpolred2(GEN x, long prec);
503:
504: /* bibli2.c */
505:
506: GEN binome(GEN x, long k);
507: int cmp_pol(GEN x, GEN y);
508: int cmp_prime_ideal(GEN x, GEN y);
509: int cmp_prime_over_p(GEN x, GEN y);
510: int cmp_vecint(GEN x, GEN y);
511: GEN convol(GEN x, GEN y);
512: GEN cyclo(long n, long v);
513: GEN dirdiv(GEN x, GEN y);
514: GEN dirmul(GEN x, GEN y);
515: GEN dirzetak(GEN nf, GEN b);
516: GEN gen_sort(GEN x, int flag, int (*cmp)(GEN,GEN));
517: GEN genrand(GEN N);
518: GEN getheap(void);
519: long getrand(void);
520: long getstack(void);
521: long gettime(void);
522: GEN gprec(GEN x, long l);
523: GEN gprec_w(GEN x, long pr);
524: GEN grando0(GEN x, long n, long do_clone);
525: GEN gtoset(GEN x);
526: GEN indexlexsort(GEN x);
527: GEN indexsort(GEN x);
528: GEN laplace(GEN x);
529: GEN legendre(long n, long v);
530: GEN lexsort(GEN x);
531: GEN mathilbert(long n);
532: GEN matqpascal(long n, GEN q);
533: long mymyrand(void);
534: int pari_compare_int(int *a,int *b);
535: int pari_compare_long(long *a,long *b);
536: GEN permute(long n, GEN x);
537: GEN permuteInv(GEN x);
538: GEN polint(GEN xa, GEN ya, GEN x, GEN *dy);
539: GEN polrecip(GEN x);
540: GEN polymodrecip(GEN x);
541: GEN setintersect(GEN x, GEN y);
542: long setisset(GEN x);
543: GEN setminus(GEN x, GEN y);
544: long setrand(long seed);
545: long setsearch(GEN x, GEN y, long flag);
546: GEN setunion(GEN x, GEN y);
547: GEN sindexlexsort(GEN x);
548: GEN sindexsort(GEN x);
549: GEN sort(GEN x);
550: long tablesearch(GEN T, GEN x, int (*cmp)(GEN,GEN));
551: GEN tayl(GEN x, long v, long precdl);
552: GEN tchebi(long n, long v);
553: GEN vecsort(GEN x, GEN k);
554: GEN vecsort0(GEN x, GEN k, long flag);
555:
556: /* buch1.c */
557:
558: GEN buchimag(GEN D, GEN gcbach, GEN gcbach2, GEN gCO);
559: GEN buchreal(GEN D, GEN gsens, GEN gcbach, GEN gcbach2, GEN gRELSUP, long prec);
560: GEN quadclassunit0(GEN x, long flag,GEN data, long prec);
561: GEN quadhilbert(GEN D, GEN flag, long prec);
562: GEN quadray(GEN bnf, GEN f, GEN flag, long prec);
563:
564:
565: /* buch2.c */
566:
567: GEN bnfclassunit0(GEN P,long flag,GEN data,long prec);
568: GEN bnfinit0(GEN P,long flag,GEN data,long prec);
569: GEN buchall(GEN P, GEN gcbach, GEN gcbach2, GEN gRELSUP, GEN gborne, long nbrelpid, long minsfb, long flun, long prec);
570: GEN buchfu(GEN bignf);
571: GEN classgrouponly(GEN P,GEN data,long prec);
572: GEN isprincipal(GEN bignf, GEN x);
573: GEN isprincipalall(GEN bignf, GEN x,long flall);
574: GEN isprincipalforce(GEN bignf,GEN x);
575: GEN isprincipalgen(GEN bignf, GEN x);
576: GEN isprincipalgenforce(GEN bignf,GEN x);
577: GEN isunit(GEN bignf, GEN x);
578: GEN bnfmake(GEN sbnf,long prec);
579: GEN regulator(GEN P,GEN data,long prec);
580: GEN signunits(GEN bignf);
581: GEN smallbuchinit(GEN pol,GEN gcbach,GEN gcbach2,GEN gRELSUP,GEN gborne,long nbrelpid,long minsfb,long prec);
582:
583: /* buch3.c */
584:
585: GEN bnrclass0(GEN bignf, GEN ideal, long flag, long prec);
586: GEN bnrconductor(GEN arg0,GEN arg1,GEN arg2,long all,long prec);
587: GEN bnrconductorofchar(GEN bnr,GEN chi,long prec);
588: GEN bnrdisc0(GEN arg0, GEN arg1, GEN arg2, long flag,long prec);
589: GEN bnrdisclist0(GEN bnf,GEN borne, GEN arch, long all);
590: GEN bnrinit0(GEN bignf,GEN ideal,long flag, long prec);
591: long bnrisconductor(GEN arg0,GEN arg1,GEN arg2,long prec);
592: GEN buchnarrow(GEN bignf);
593: GEN buchray(GEN bignf,GEN ideal,long prec);
594: GEN buchrayinit(GEN bignf,GEN ideal,long prec);
595: GEN buchrayinitgen(GEN bignf,GEN ideal,long prec);
596: long certifybuchall(GEN bnf);
597: GEN conductor(GEN bnr,GEN subgroup,long all,long prec);
598: GEN decodemodule(GEN nf, GEN fa);
599: GEN discrayabs(GEN bnr,GEN subgroup,long prec);
600: GEN discrayabscond(GEN bnr,GEN subgroup,long prec);
601: GEN discrayabslist(GEN bnf,GEN listes);
602: GEN discrayabslistarch(GEN bnf, GEN arch, long bound);
603: GEN discrayabslistlong(GEN bnf, long bound);
604: GEN discrayrel(GEN bnr,GEN subgroup,long prec);
605: GEN discrayrelcond(GEN bnr,GEN subgroup,long prec);
606: GEN isprincipalray(GEN bignf, GEN x);
607: GEN isprincipalrayall(GEN bignf, GEN x,long flall);
608: GEN isprincipalraygen(GEN bignf, GEN x);
609: GEN rayclassno(GEN bignf,GEN ideal);
610: GEN rayclassnolist(GEN bnf,GEN listes);
611: GEN rnfconductor(GEN bnf, GEN polrel, long prec);
612: GEN rnfkummer(GEN bnr, GEN subgroup, long all, long prec);
613: GEN rnfnormgroup(GEN bnr, GEN polrel);
614: GEN subgrouplist0(GEN bnr, long indexbound, long all, long prec);
615:
616: /* buch4.c */
617:
618: GEN bnfisnorm(GEN bnf,GEN x,long flag,long PREC);
619: GEN rnfisnorm(GEN bnf,GEN ext,GEN x,long flag,long PREC);
620: GEN bnfissunit(GEN bnf,GEN suni,GEN x);
621: GEN bnfsunit(GEN bnf,GEN s,long PREC);
622: long nfhilbert(GEN bnf,GEN a,GEN b);
623: long nfhilbert0(GEN bnf,GEN a,GEN b,GEN p);
624: long nfhilbertp(GEN bnf,GEN a,GEN b,GEN p);
625: long qpsoluble(GEN pol,GEN p);
626: long qpsolublenf(GEN bnf,GEN pol,GEN p);
627: long zpsoluble(GEN pol,GEN p);
628: long zpsolublenf(GEN bnf,GEN pol,GEN p);
629:
630: /* elliptic.c */
631:
632: GEN addell(GEN e, GEN z1, GEN z2);
633: GEN akell(GEN e, GEN n);
634: GEN anell(GEN e, long n);
635: GEN apell(GEN e, GEN p);
636: GEN apell2(GEN e, GEN p);
637: GEN bilhell(GEN e, GEN z1, GEN z2, long prec);
638: GEN coordch(GEN e, GEN ch);
639: GEN ellap0(GEN e, GEN p, long flag);
640: GEN elleisnum(GEN om, long k, long flag, long prec);
641: GEN elleta(GEN om, long prec);
642: GEN ellheight0(GEN e, GEN a, long flag,long prec);
643: GEN ellinit0(GEN x,long flag,long prec);
644: long ellrootno(GEN e, GEN p);
645: GEN ellsigma(GEN om, GEN z, long flag, long prec);
646: GEN elltors0(GEN e, long flag);
647: GEN ellwp0(GEN e, GEN z, long flag, long prec, long PREC);
648: GEN ellzeta(GEN om, GEN z, long prec);
649: GEN ghell(GEN e, GEN a, long prec);
650: GEN ghell2(GEN e, GEN a, long prec);
651: GEN globalreduction(GEN e1);
652: GEN initell(GEN x, long prec);
653: GEN localreduction(GEN e, GEN p1);
654: GEN lseriesell(GEN e, GEN s, GEN A, long prec);
655: GEN mathell(GEN e, GEN x, long prec);
656: int oncurve(GEN e, GEN z);
657: GEN ordell(GEN e, GEN x, long prec);
658: GEN orderell(GEN e, GEN p);
659: GEN pointch(GEN x, GEN ch);
660: GEN pointell(GEN e, GEN z, long prec);
661: GEN powell(GEN e, GEN z, GEN n);
662: GEN smallinitell(GEN x);
663: GEN subell(GEN e, GEN z1, GEN z2);
664: GEN taniyama(GEN e);
665: GEN torsell(GEN e);
666: GEN weipell(GEN e, long precdl);
667: GEN zell(GEN e, GEN z, long prec);
668:
669: /* es.c */
670:
671: char* GENtostr(GEN x);
672: void brute(GEN g, char format, long dec);
673: void bruteall(GEN g, char format, long dec, long flbl);
674: void bruterr(GEN x,char format,long dec);
675: void ecrire(GEN x, char format, long dec, long chmp);
676: const char* eng_ord(long i);
677: void etatpile(unsigned int n);
678: char* expand_tilde(char *s);
679: char* filtre(char *s,int status);
680: void flusherr(void);
681: void fprintferr(char* pat, ...);
682: void killallfiles(int check);
683: int killfile(pariFILE *f);
684: GEN lisGEN(FILE *f);
685: void matbrute(GEN g, char format, long dec);
686: pariFILE* newfile(FILE *f, char *name, int type);
687: void outbeaut(GEN x);
688: void outbeauterr(GEN x);
689: void outbrute(GEN x);
690: void outerr(GEN x);
691: void outmat(GEN x);
692: void output(GEN x);
693: void outsor(GEN x);
694: void pari_fclose(pariFILE *f);
695: pariFILE* pari_fopen(char *s, char *mode);
696: char* pari_strdup(char *s);
697: char* pari_unique_filename(char *s);
698: char* pari_unique_filename(char *s);
699: void pari_unlink(char *s);
700: void pariflush(void);
701: void pariputc(char c);
702: void pariputs(char *s);
703: void pariputsf(char *format, ...);
704: int popinfile(void);
705: void sor(GEN g, char fo, long dd, long chmp);
706: void switchin(char *name);
707: void switchout(char *name);
708: void texe(GEN g, char format, long dec);
709: pariFILE* try_pipe(char *cmd, int flag);
710: char* type_name(long t);
711: void voir(GEN x, long nb);
712: void vpariputs(char* format, va_list args);
713:
714: /* galconj.c */
715:
716: GEN galoisconj(GEN nf);
717: GEN galoisconj0(GEN nf,long flag, GEN d, long prec);
718: GEN galoisconj2(GEN x, long nbmax, long prec);
719: GEN galoisconj4(GEN T, GEN den, long flag);
720: GEN galoisfixedfield(GEN gal, GEN v, GEN p);
721: GEN galoisinit(GEN nf, GEN den);
722: GEN galoispermtopol(GEN gal,GEN perm);
723: long numberofconjugates(GEN T, long pdepart);
724: GEN vandermondeinverse(GEN L, GEN T, GEN den);
725: /* gen1.c */
726:
727: GEN gadd(GEN x, GEN y);
728: GEN gdiv(GEN x, GEN y);
729: GEN gmul(GEN x, GEN y);
730: GEN gsub(GEN x, GEN y);
731:
732: /* gen2.c */
733: void gop1z(GEN (*f)(GEN), GEN x, GEN y);
734: void gop2z(GEN (*f)(GEN, GEN), GEN x, GEN y, GEN z);
735: GEN gopgs2(GEN (*f)(GEN, GEN), GEN y, long s);
736: void gops2gsz(GEN (*f)(GEN, long), GEN x, long s, GEN z);
737: void gops2sgz(GEN (*f)(long, GEN), long s, GEN y, GEN z);
738: void gops2ssz(GEN (*f)(long, long), long s, long y, GEN z);
739: GEN gopsg2(GEN (*f)(GEN, GEN), long s, GEN y);
740: void gopsg2z(GEN (*f)(GEN, GEN), long s, GEN y, GEN z);
741: long opgs2(int (*f)(GEN, GEN), GEN y, long s);
742:
743: GEN brutcopy(GEN x, GEN y);
744: GEN cgetp(GEN x);
745: GEN co8(GEN x, long l);
746: GEN cvtop(GEN x, GEN p, long l);
747: GEN dummyclone(GEN x);
748: GEN dummycopy(GEN x);
749: int egalii(GEN x, GEN y);
750: GEN forcecopy(GEN x);
751: GEN from_Kronecker(GEN z, GEN pol);
752: GEN gabs(GEN x, long prec);
753: void gaffect(GEN x, GEN y);
754: void gaffsg(long s, GEN x);
755: GEN gclone(GEN x);
756: int gcmp(GEN x, GEN y);
757: int gcmp0(GEN x);
758: int gcmp1(GEN x);
759: int gcmp_1(GEN x);
760: GEN gcopy(GEN x);
761: GEN gcopy_i(GEN x, long lx);
762: GEN gcvtop(GEN x, GEN p, long r);
763: int gegal(GEN x, GEN y);
764: long gexpo(GEN x);
765: long ggval(GEN x, GEN p);
766: long glength(GEN x);
767: GEN gmax(GEN x, GEN y);
768: GEN gmin(GEN x, GEN y);
769: GEN gneg(GEN x);
770: GEN gneg_i(GEN x);
771: GEN greffe(GEN x, long l, long use_stack);
772: int gsigne(GEN x);
773: long gsize(GEN x);
774: GEN gsqr(GEN x);
775: GEN gtolist(GEN x);
776: long gtolong(GEN x);
777: int lexcmp(GEN x, GEN y);
778: GEN listconcat(GEN list1, GEN list2);
779: GEN listcreate(long n);
780: GEN listinsert(GEN list, GEN object, long index);
781: void listkill(GEN list);
782: GEN listput(GEN list, GEN object, long index);
783: GEN listsort(GEN list, long flag);
784: GEN matsize(GEN x);
785: GEN normalize(GEN x);
786: GEN normalizepol(GEN x);
787: GEN normalizepol_i(GEN x, long lx);
788: long pvaluation(GEN x, GEN p, GEN *py);
789: long svaluation(ulong x, ulong p, long *py);
790: GEN realun(long prec);
791: GEN realzero(long prec);
792: long taille(GEN x);
793: long taille2(GEN x);
794: GEN vecmax(GEN x);
795: GEN vecmin(GEN x);
796:
797: /* gen3.c */
798:
799: GEN Mod0(GEN x, GEN y,long flag);
800: GEN centerlift(GEN x);
801: GEN centerlift0(GEN x,long v);
802: GEN compo(GEN x, long n);
803: long degree(GEN x);
804: GEN denom(GEN x);
805: GEN deriv(GEN x, long v);
806: GEN derivpol(GEN x);
807: GEN derivser(GEN x);
808: GEN gand(GEN x, GEN y);
809: GEN gceil(GEN x);
810: GEN gcvtoi(GEN x, long *e);
811: GEN gdivent(GEN x, GEN y);
812: GEN gdiventres(GEN x, GEN y);
813: GEN gdivgs(GEN x, long s);
814: GEN gdivmod(GEN x, GEN y, GEN *pr);
815: GEN gdivround(GEN x, GEN y);
816: GEN geq(GEN x, GEN y);
817: GEN geval(GEN x);
818: GEN gfloor(GEN x);
819: GEN gfrac(GEN x);
820: GEN gge(GEN x, GEN y);
821: GEN ggprecision(GEN x);
822: GEN ggt(GEN x, GEN y);
823: GEN gimag(GEN x);
824: GEN ginv(GEN x);
825: GEN gle(GEN x, GEN y);
826: GEN glt(GEN x, GEN y);
827: GEN gmod(GEN x, GEN y);
828: GEN gmodulcp(GEN x,GEN y);
829: GEN gmodulo(GEN x,GEN y);
830: GEN gmodulsg(long x, GEN y);
831: GEN gmodulss(long x, long y);
832: GEN gmul2n(GEN x, long n);
833: GEN gmulsg(long s, GEN y);
834: GEN gne(GEN x, GEN y);
835: GEN gnot(GEN x);
836: GEN gor(GEN x, GEN y);
837: GEN gpolvar(GEN y);
838: long gprecision(GEN x);
839: GEN gram_matrix(GEN M);
840: GEN greal(GEN x);
841: GEN grndtoi(GEN x, long *e);
842: GEN ground(GEN x);
843: GEN gshift(GEN x, long n);
844: GEN gsubst(GEN x, long v, GEN y);
845: GEN gtopoly(GEN x, long v);
846: GEN gtopolyrev(GEN x, long v);
847: GEN gtoser(GEN x, long v);
848: GEN gtovec(GEN x);
849: GEN gtrunc(GEN x);
850: int gvar(GEN x);
851: int gvar2(GEN x);
852: GEN hqfeval(GEN q, GEN x);
853: GEN integ(GEN x, long v);
854: int iscomplex(GEN x);
855: int isexactzero(GEN g);
856: int isinexactreal(GEN x);
857: int ismonome(GEN x);
858: GEN lift(GEN x);
859: GEN lift0(GEN x,long v);
860: GEN lift_intern0(GEN x,long v);
861: GEN mulmat_real(GEN x, GEN y);
862: GEN numer(GEN x);
863: long padicprec(GEN x, GEN p);
864: GEN polcoeff0(GEN x,long n,long v);
865: long poldegree(GEN x,long v);
866: GEN poleval(GEN x, GEN y);
867: GEN pollead(GEN x,long v);
868: long precision(GEN x);
869: GEN precision0(GEN x,long n);
870: GEN qf_base_change(GEN q, GEN M, int flag);
871: GEN qfeval(GEN q, GEN x);
872: GEN recip(GEN x);
873: GEN round0(GEN x, GEN *pte);
874: GEN scalarpol(GEN x, long v);
875: GEN scalarser(GEN x, long v, long prec);
876: GEN simplify(GEN x);
877: GEN truecoeff(GEN x, long n);
878: GEN trunc0(GEN x, GEN *pte);
879: GEN zeropol(long v);
880: GEN zeroser(long v, long prec);
881:
882: /* ifactor.c */
883: GEN nextprime(GEN n);
884: GEN precprime(GEN n);
885:
886: /* init.c */
887:
888: long allocatemoremem(ulong newsize);
889: GEN changevar(GEN x, GEN y);
890: void checkmemory(GEN x);
891: void disable_dbg(long val);
892: void freeall(void);
893: GEN gerepile(long ltop, long lbot, GEN q);
894: void gerepilemany(long av, GEN* g[], long n);
895: void gerepilemanycoeffs(long av, GEN x, long n);
896: void gerepilemanysp(long av, long tetpil, GEN* g[], long n);
897: void gerepilemanyvec(long av, long tetpil, long *g, long n);
898: GEN gerepileupto(long av, GEN q);
899: GEN gerepileuptoint(long av, GEN q);
900: GEN gerepileuptoleaf(long av, GEN q);
901: char* gpmalloc(size_t bytes);
902: char* gprealloc(void *pointer,size_t newsize,size_t oldsize);
903: void gunclone(GEN x);
904: void killbloc(GEN x);
905: void msgtimer(char *format, ...);
906: GEN newbloc(long n);
907: void pari_init(long parisize, long maxprime);
908: GEN reorder(GEN x);
909: void stackdummy(GEN x, long l);
910: stackzone* switch_stack(stackzone *z, long n);
911: long timer(void);
912: long timer2(void);
913:
914: BEGINEXTERN
915: VOLATILE void err(long numerr, ...);
916: ENDEXTERN
917:
918: /* mp.c ou mp.s */
919:
920: int absi_cmp(GEN x, GEN y);
921: int absi_equal(GEN x, GEN y);
922: int absr_cmp(GEN x, GEN y);
923: GEN addii(GEN x, GEN y);
924: GEN addir(GEN x, GEN y);
925: GEN addrr(GEN x, GEN y);
926: GEN addsi(long x, GEN y);
927: GEN addsr(long x, GEN y);
928: GEN addss(long x, long y);
929: void affir(GEN x, GEN y);
930: void affrr(GEN x, GEN y);
931: void cgiv(GEN x);
932: int cmpii(GEN x, GEN y);
933: int cmprr(GEN x, GEN y);
934: int cmpsi(long x, GEN y);
935: GEN dbltor(double x);
936: void diviiz(GEN x, GEN y, GEN z);
937: GEN divir(GEN x, GEN y);
938: GEN divis(GEN y, long x);
939: GEN divri(GEN x, GEN y);
940: GEN divrr(GEN x, GEN y);
941: GEN divrs(GEN x, long y);
942: GEN divsi(long x, GEN y);
943: GEN divsr(long x, GEN y);
944: GEN dvmdii(GEN x, GEN y, GEN *z);
945: int invmod(GEN a, GEN b, GEN *res);
946: GEN modii(GEN x, GEN y);
947: void modiiz(GEN x, GEN y, GEN z);
948: GEN modiu(GEN y, ulong x);
949: GEN modsi(long x, GEN y);
950: GEN modss(long x, long y);
951: GEN modui(ulong x, GEN y);
952: void mpdivz(GEN x, GEN y, GEN z);
953: GEN mpent(GEN x);
954: GEN mptrunc(GEN x);
955: GEN mulii(GEN x, GEN y);
956: GEN mulir(GEN x, GEN y);
957: GEN mulrr(GEN x, GEN y);
958: GEN mulsi(long x, GEN y);
959: GEN mulsr(long x, GEN y);
960: GEN mulss(long x, long y);
961: GEN resss(long x, long y);
962: double rtodbl(GEN x);
963: GEN shifti(GEN x, long n);
964: long smodsi(long x, GEN y);
965: GEN sqri(GEN x);
966: GEN truedvmdii(GEN x, GEN y, GEN *z);
967: long vals(ulong x);
968:
969: /* nffactor.c */
970:
971: GEN nffactor(GEN nf,GEN x);
972: GEN nffactormod(GEN nf,GEN pol,GEN pr);
973: GEN nfroots(GEN nf,GEN pol);
974: GEN rnfcharpoly(GEN nf,GEN T,GEN alpha,int n);
975: GEN rnfdedekind(GEN nf,GEN T,GEN pr);
976: GEN unifpol(GEN nf,GEN pol,long flag);
977:
978: /* polarit1.c */
979:
980: GEN apprgen(GEN f, GEN a);
981: GEN apprgen9(GEN f, GEN a);
982: GEN factcantor(GEN x, GEN p);
983: GEN factmod(GEN f, GEN p);
984: GEN factmod9(GEN f, GEN p, GEN a);
985: GEN factormod0(GEN f, GEN p,long flag);
986: GEN factorpadic0(GEN f,GEN p,long r,long flag);
987: GEN factorpadic2(GEN x, GEN p, long r);
988: GEN factorpadic4(GEN x, GEN p, long r);
989: GEN factpol2(GEN x, long klim);
990: int gdivise(GEN x, GEN y);
991: GEN gred(GEN x);
992: GEN gred_rfrac(GEN x);
993: GEN incloop(GEN a);
994: int poldivis(GEN x, GEN y, GEN *z);
995: GEN poldivres(GEN x, GEN y, GEN *pr);
996: GEN rootmod(GEN f, GEN p);
997: GEN rootmod0(GEN f, GEN p,long flag);
998: GEN rootmod2(GEN f, GEN p);
999: GEN rootpadic(GEN f, GEN p, long r);
1000: GEN rootpadicfast(GEN f, GEN p, long r, long flall);
1001: GEN roots2(GEN pol,long PREC);
1002: GEN rootsold(GEN x, long l);
1003: GEN setloop(GEN a);
1004: GEN simplefactmod(GEN f, GEN p);
1005:
1006: /* polarit2.c */
1007:
1008: GEN bezoutpol(GEN a, GEN b, GEN *u, GEN *v);
1009: GEN centermod(GEN x, GEN p);
1010: GEN content(GEN x);
1011: GEN discsr(GEN x);
1012: GEN divide_conquer_prod(GEN x, GEN (*mul)(GEN,GEN));
1013: GEN factor(GEN x);
1014: GEN factor0(GEN x,long flag);
1015: GEN factorback(GEN fa,GEN nf);
1016: GEN factpol(GEN x, long klim, long hint);
1017: GEN gbezout(GEN x, GEN y, GEN *u, GEN *v);
1018: GEN gcd0(GEN x, GEN y,long flag);
1019: GEN gdivexact(GEN x, GEN y);
1020: GEN ggcd(GEN x, GEN y);
1021: GEN ginvmod(GEN x, GEN y);
1022: GEN gisirreducible(GEN x);
1023: GEN glcm(GEN x, GEN y);
1024: GEN newtonpoly(GEN x, GEN p);
1025: GEN nfisincl(GEN a, GEN b);
1026: GEN nfisisom(GEN a, GEN b);
1027: GEN poldisc0(GEN x, long v);
1028: GEN polfnf(GEN a, GEN t);
1029: GEN polresultant0(GEN x, GEN y,long v,long flag);
1030: GEN polsym(GEN x, long n);
1031: GEN quadgen(GEN x);
1032: GEN quadpoly(GEN x);
1033: GEN quadpoly0(GEN x, long v);
1034: GEN reduceddiscsmith(GEN pol);
1035: GEN resultant2(GEN x, GEN y);
1036: GEN resultantducos(GEN x, GEN y);
1037: GEN sort_factor(GEN y, int (*cmp)(GEN,GEN));
1038: GEN srgcd(GEN x, GEN y);
1039: long sturmpart(GEN x, GEN a, GEN b);
1040: GEN subresall(GEN u, GEN v, GEN *sol);
1041: GEN subresext(GEN x, GEN y, GEN *U, GEN *V);
1042: GEN sylvestermatrix(GEN x,GEN y);
1043: GEN vecbezout(GEN x, GEN y);
1044: GEN vecbezoutres(GEN x, GEN y);
1045:
1046: /* polarit3.c */
1047:
1048: GEN Fp_pol(GEN z, GEN p);
1049: GEN Fp_pol_extgcd(GEN x, GEN y, GEN p, GEN *ptu, GEN *ptv);
1050: GEN Fp_pol_gcd(GEN x, GEN y, GEN p);
1051: GEN Fp_pol_red(GEN z, GEN p);
1052: GEN Fp_pol_small(GEN z, GEN p, long l);
1053: GEN Fp_poldivres(GEN x, GEN y, GEN p, GEN *pr);
1054: GEN Fp_pow_mod_pol(GEN x, GEN n, GEN pol, GEN p);
1055: GEN Fp_vec(GEN z, GEN p);
1056: GEN Fp_vec_red(GEN z, GEN p);
1057: GEN modulargcd(GEN a,GEN b);
1058: GEN normalize_mod_p(GEN z, GEN p);
1059: GEN quickmul(GEN a, GEN b, long na, long nb);
1060: GEN quicksqr(GEN a, long na);
1061: GEN small_to_pol(GEN z, long l, long p);
1062: GEN stopoly(long m, long p, long v);
1063: GEN stopoly_gen(GEN m, GEN p, long v);
1064:
1065: /* rootpol.c */
1066:
1067: int isrealappr(GEN x, long l);
1068: GEN roots(GEN x,long l);
1069: GEN roots0(GEN x,long flag,long l);
1070:
1071: /* subfields.c */
1072:
1073: GEN ffinit(GEN p,long n, long v);
1074: GEN subfields(GEN nf,GEN d);
1075: GEN subfields0(GEN nf,GEN d);
1076: GEN conjugates(GEN pol);
1077:
1078: /* subgroup.c */
1079:
1080: void forsubgroup(entree *oep, GEN cyc, long bound, char *och);
1081: GEN subgrouplist(GEN cyc, long bound);
1082:
1083: /* stark.c */
1084:
1085: GEN bnrL1(GEN bnr, long flag, long prec);
1086: GEN bnrrootnumber(GEN bnr, GEN chi, long flag, long prec);
1087: GEN bnrstark(GEN bnr, GEN subgroup, long flag, long prec);
1088:
1089: /* sumiter.c */
1090:
1091: GEN direuler(entree *ep, GEN a, GEN b, char *ch);
1092: GEN divsum(GEN num,entree *ep, char *ch);
1093: void fordiv(GEN a, entree *ep, char *ch);
1094: void forpari(entree *ep, GEN a, GEN b, char *ch);
1095: void forprime(entree *ep, GEN a, GEN b, char *ch);
1096: void forstep(entree *ep, GEN a, GEN b, GEN s, char *ch);
1097: void forvec(entree *ep, GEN x, char *ch, long flag);
1098: GEN intnum0(entree *ep, GEN a, GEN b, char *ch,long flag,long prec);
1099: GEN matrice(GEN nlig, GEN ncol,entree *ep1, entree *ep2, char *ch);
1100: GEN polzag(long n, long m);
1101: GEN polzagreel(long n, long m, long prec);
1102: GEN prodeuler(entree *ep, GEN a, GEN b, char *ch, long prec);
1103: GEN prodinf(entree *ep, GEN a, char *ch, long prec);
1104: GEN prodinf0(entree *ep, GEN a, char *ch, long flag, long prec);
1105: GEN prodinf1(entree *ep, GEN a, char *ch, long prec);
1106: GEN produit(entree *ep, GEN a, GEN b, char *ch, GEN x);
1107: GEN qromb(entree *ep, GEN a, GEN b, char *ch, long prec);
1108: GEN qromi(entree *ep, GEN a, GEN b, char *ch, long prec);
1109: GEN qromo(entree *ep, GEN a, GEN b, char *ch, long prec);
1110: GEN rombint(entree *ep, GEN a, GEN b, char *ch, long prec);
1111: GEN somme(entree *ep, GEN a, GEN b, char *ch, GEN x);
1112: GEN sumalt(entree *ep, GEN a, char *ch, long prec);
1113: GEN sumalt0(entree *ep, GEN a, char *ch,long flag, long prec);
1114: GEN sumalt2(entree *ep, GEN a, char *ch, long prec);
1115: GEN sumpos(entree *ep, GEN a, char *ch, long prec);
1116: GEN sumpos0(entree *ep, GEN a, char *ch, long flag,long prec);
1117: GEN sumpos2(entree *ep, GEN a, char *ch, long prec);
1118: GEN suminf(entree *ep, GEN a, char *ch, long prec);
1119: GEN vecteur(GEN nmax, entree *ep, char *ch);
1120: GEN vvecteur(GEN nmax, entree *ep, char *ch);
1121: GEN zbrent(entree *ep, GEN a, GEN b, char *ch, long prec);
1122:
1123: /* thue.c */
1124:
1125: GEN bnfisintnorm(GEN x, GEN y);
1126: GEN thue(GEN thueres, GEN rhs, GEN ne);
1127: GEN thueinit(GEN poly, long flag, long prec);
1128:
1129: /* trans1.c */
1130:
1131: void consteuler(long prec);
1132: void constpi(long prec);
1133: GEN gcos(GEN x, long prec);
1134: void gcosz(GEN x, GEN y);
1135: GEN gcotan(GEN x, long prec);
1136: GEN gexp(GEN x, long prec);
1137: void gexpz(GEN x, GEN y);
1138: GEN glog(GEN x, long prec);
1139: void glogz(GEN x, GEN y);
1140: GEN gpow(GEN x, GEN n, long prec);
1141: GEN gpowgs(GEN x, long n);
1142: GEN gsin(GEN x, long prec);
1143: void gsincos(GEN x, GEN *s, GEN *c, long prec);
1144: void gsinz(GEN x, GEN y);
1145: GEN gsqrt(GEN x, long prec);
1146: void gsqrtz(GEN x, GEN y);
1147: GEN gtan(GEN x, long prec);
1148: void gtanz(GEN x, GEN y);
1149: GEN log0(GEN x,long flag, long prec);
1150: GEN mpeuler(long prec);
1151: GEN mpexp(GEN x);
1152: GEN mpexp1(GEN x);
1153: GEN mplog(GEN x);
1154: GEN mppi(long prec);
1155: GEN mpsqrt(GEN x);
1156: GEN palog(GEN x);
1157: GEN powgi(GEN x, GEN n);
1158: GEN teich(GEN x);
1159: GEN transc(GEN (*f) (GEN, long), GEN x, long prec);
1160:
1161: /* trans2.c */
1162:
1163: GEN bernfrac(long n);
1164: GEN bernreal(long n, long prec);
1165: GEN bernvec(long nomb);
1166: GEN gach(GEN x, long prec);
1167: void gachz(GEN x, GEN y);
1168: GEN gacos(GEN x, long prec);
1169: void gacosz(GEN x, GEN y);
1170: GEN garg(GEN x, long prec);
1171: GEN gash(GEN x, long prec);
1172: void gashz(GEN x, GEN y);
1173: GEN gasin(GEN x, long prec);
1174: void gasinz(GEN x, GEN y);
1175: GEN gatan(GEN x, long prec);
1176: void gatanz(GEN x, GEN y);
1177: GEN gath(GEN x, long prec);
1178: void gathz(GEN x, GEN y);
1179: GEN gch(GEN x, long prec);
1180: void gchz(GEN x, GEN y);
1181: GEN ggamd(GEN x, long prec);
1182: void ggamdz(GEN x, GEN y);
1183: GEN ggamma(GEN x, long prec);
1184: void ggammaz(GEN x, GEN y);
1185: GEN glngamma(GEN x, long prec);
1186: void glngammaz(GEN x, GEN y);
1187: GEN gpsi(GEN x, long prec);
1188: void gpsiz(GEN x, GEN y);
1189: GEN gsh(GEN x, long prec);
1190: void gshz(GEN x, GEN y);
1191: GEN gth(GEN x, long prec);
1192: void gthz(GEN x, GEN y);
1193: void mpbern(long nomb, long prec);
1194: void mpgamdz(long s, GEN y);
1195:
1196: /* trans3.c */
1197:
1198: GEN agm(GEN x, GEN y, long prec);
1199: GEN dilog(GEN x, long prec);
1200: GEN eint1(GEN x, long prec);
1201: GEN eta(GEN x, long prec);
1202: GEN eta0(GEN x, long flag,long prec);
1203: GEN gerfc(GEN x, long prec);
1204: GEN glogagm(GEN x, long prec);
1205: GEN gpolylog(long m, GEN x, long prec);
1206: void gpolylogz(long m, GEN x, GEN y);
1207: GEN gzeta(GEN x, long prec);
1208: void gzetaz(GEN x, GEN y);
1209: GEN hyperu(GEN a, GEN b, GEN gx, long prec);
1210: GEN incgam(GEN a, GEN x, long prec);
1211: GEN incgam0(GEN a, GEN x, GEN z,long prec);
1212: GEN incgam1(GEN a, GEN x, long prec);
1213: GEN incgam2(GEN a, GEN x, long prec);
1214: GEN incgam3(GEN a, GEN x, long prec);
1215: GEN incgam4(GEN a, GEN x, GEN z, long prec);
1216: GEN jbesselh(GEN n, GEN z, long prec);
1217: GEN jell(GEN x, long prec);
1218: GEN kbessel(GEN nu, GEN gx, long prec);
1219: GEN kbessel0(GEN nu, GEN gx, long flag,long prec);
1220: GEN kbessel2(GEN nu, GEN x, long prec);
1221: GEN logagm(GEN q);
1222: GEN polylog(long m, GEN x, long prec);
1223: GEN polylog0(long m, GEN x, long flag, long prec);
1224: GEN polylogd(long m, GEN x, long prec);
1225: GEN polylogdold(long m, GEN x, long prec);
1226: GEN polylogp(long m, GEN x, long prec);
1227: GEN theta(GEN q, GEN z, long prec);
1228: GEN thetanullk(GEN q, long k, long prec);
1229: GEN trueeta(GEN x, long prec);
1230: GEN veceint1(GEN nmax, GEN C, long prec);
1231: GEN weber0(GEN x, long flag,long prec);
1232: GEN wf(GEN x, long prec);
1233: GEN wf2(GEN x, long prec);
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