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/* $Id: paripriv.h 8483 2007-03-29 08:58:00Z kb $
Copyright (C) 2004 The PARI group.
This file is part of the PARI/GP package.
PARI/GP is free software; you can redistribute it and/or modify it under the
terms of the GNU General Public License as published by the Free Software
Foundation. It is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY WHATSOEVER.
Check the License for details. You should have received a copy of it, along
with the package; see the file 'COPYING'. If not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
BEGINEXTERN
/* for qsort */
typedef int (*QSCOMP)(const void *, const void *);
/* swap */
#define lswap(x,y) {long _z=x; x=y; y=_z;}
#define pswap(x,y) {GEN *_z=x; x=y; y=_z;}
#define swap(x,y) {GEN _z=x; x=y; y=_z;}
#define dswap(x,y) { double _t=x; x=y; y=_t; }
#define pdswap(x,y) { double* _t=x; x=y; y=_t; }
#define swapspec(x,y, nx,ny) {swap(x,y); lswap(nx,ny);}
/* */
#define both_odd(x,y) ((x)&(y)&1)
/* unused */
GEN ellheightoo(GEN e, GEN z, long prec);
void ellprint(GEN e);
GEN mpinv(GEN b);
/* generic */
GEN arith_proto(long f(GEN), GEN x, int do_error);
GEN arith_proto2(long f(GEN,GEN), GEN x, GEN n);
GEN arith_proto2gs(long f(GEN,long), GEN x, long y);
GEN gassoc_proto(GEN f(GEN,GEN),GEN,GEN);
GEN garith_proto(GEN f(GEN), GEN x, int do_error);
GEN garith_proto2gs(GEN f(GEN,long), GEN x, long y);
GEN trans_fix_arg(long *prec, GEN *s0, GEN *sig, pari_sp *av, GEN *res);
GEN transc(GEN (*f) (GEN, long), GEN x, long prec);
GEN sort_factor(GEN y, int (*cmp)(GEN,GEN));
GEN sort_factor_gen(GEN y, int (*cmp)(GEN,GEN));
GEN sort_factor_gen_aux(GEN y, void *data, int (*cmp)(void *,GEN,GEN));
GEN sort_vecpol(GEN a, int (*cmp)(GEN,GEN));
/* loops */
GEN incloop(GEN a);
GEN resetloop(GEN a, GEN b);
GEN setloop(GEN a);
/* multiprecision */
GEN icopy_spec(GEN x, long nx);
GEN addrex01(GEN x);
GEN addumului(ulong a, ulong b, GEN Y);
void affr_fixlg(GEN z, GEN y);
GEN cxnorm(GEN x);
int lgcdii(ulong* d, ulong* d1, ulong* u, ulong* u1, ulong* v, ulong* v1, ulong vmax);
ulong rgcduu(ulong d, ulong d1, ulong vmax, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
ulong xgcduu(ulong d, ulong d1, int f, ulong* v, ulong* v1, long *s);
GEN quadnorm(GEN x);
ulong xxgcduu(ulong d, ulong d1, int f, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
GEN divgsns(GEN x, long i);
GEN divrsns(GEN x, long i);
GEN init_remiimul(GEN M);
GEN ishiftr_lg(GEN x, long lx, long n);
GEN logagmcx(GEN q, long prec);
GEN muliispec(GEN x, GEN y, long nx, long ny);
GEN padic_to_Fp(GEN x, GEN Y);
ulong padic_to_Fl(GEN x, ulong p);
GEN red_montgomery(GEN T, GEN N, ulong inv);
GEN remiimul(GEN x, GEN sy);
GEN sqrispec(GEN x, long nx);
GEN subrex01(GEN x);
GEN mulcxI(GEN x);
GEN mulcxmI(GEN x);
int approx_0(GEN x, GEN y);
GEN bernfrac_using_zeta(long n);
int OK_bern(long nb, long prec);
/* FIXME: adapt/use mpn_[lr]shift instead */
#define shift_left(z2,z1,imin,imax,f, sh) {\
register const ulong _m = BITS_IN_LONG - (sh);\
shift_left2((z2),(z1),(imin),(imax),(f),(sh),(_m)); }
#define shift_right(z2,z1,imin,imax,f, sh) {\
register const ulong _m = BITS_IN_LONG - (sh);\
shift_right2((z2),(z1),(imin),(imax),(f),(sh),(_m)); }
/* powers */
#define sqrs(b) mulss((b),(b))
#define sqru(b) muluu((b),(b))
GEN rpowuu(ulong a, ulong n, long prec);
GEN powrshalf(GEN x, long s);
GEN powrfrac(GEN x, long n, long d);
ulong u_pow10(int n);
/* floats */
double dabs(double s, double t);
long dblexpo(double x);
ulong dblmantissa(double x);
void dcxlog(double s, double t, double *a, double *b);
double dnorm(double s, double t);
double dbllog2(GEN z);
ulong usqrtsafe(ulong a);
/* "abs" routines for t_REAL ( disregard sign ) */
int absrnz_egal1(GEN x);
int absrnz_egal2n(GEN x);
GEN exp1r_abs(GEN x);
GEN logagmr_abs(GEN q);
GEN logr_abs(GEN x);
GEN sqrtr_abs(GEN x);
/* hnf */
GEN gauss_triangle_i(GEN A, GEN B,GEN t);
GEN hnfadd(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
GEN hnfadd_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,GEN extramat,GEN extraC);
GEN hnf_gauss(GEN A, GEN B);
GEN hnf_invimage(GEN A, GEN b);
GEN hnfmerge_get_1(GEN A, GEN B);
GEN hnfperm_i(GEN A, GEN *ptU, GEN *ptperm);
GEN hnfspec_i(long** m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
GEN hnfspec(long** m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
GEN mathnfspec(GEN x, GEN *ptperm, GEN *ptdep, GEN *ptB, GEN *ptC);
/* LLL */
GEN lllint_fp_ip(GEN x, long D);
GEN lllfp_marked(long *M, GEN x, long D, long flag, long prec, int gram);
GEN lllint_marked(long *M, GEN x, long D, int g, GEN *h, GEN *f, GEN *B);
GEN LLL_check_progress(GEN Bnorm, long n0, GEN m, int final, long *ti_LLL);
GEN extendedgcd(GEN A);
GEN sqred1intern(GEN a);
GEN lllgramintern(GEN x, long alpha, long flag, long prec);
GEN lllintern(GEN x, long D, long flag, long prec);
/* miscellaneous linear algebra */
GEN diagonal_i(GEN x);
GEN F2V_red_ip(GEN v);
GEN gauss_realimag(GEN x, GEN y);
GEN imagecomplspec(GEN x, long *nlze);
GEN R_from_QR(GEN x, long prec);
void rowselect_p(GEN A, GEN B, GEN p, long init);
GEN split_realimag(GEN x, long r1, long r2);
GEN sqred1_from_QR(GEN x, long prec);
GEN supnorm(GEN L, long prec);
GEN znstar_hnf_elts(GEN Z, GEN H);
GEN ZV_lincomb(GEN u, GEN v, GEN X, GEN Y);
GEN vec_setconst(GEN v, GEN x);
GEN GS_norms(GEN B, long prec);
GEN dim1proj(GEN prh);
GEN detcyc(GEN cyc, long *L);
GEN close_modinvertible(GEN x, GEN y);
GEN colreducemodHNF(GEN x, GEN y, GEN *Q);
GEN col_to_ff(GEN x, long v);
/* famat */
GEN factorback_i(GEN fa, GEN e, GEN nf, int red);
GEN factorbackprime(GEN nf, GEN L, GEN e);
GEN famat_inv(GEN f);
GEN famat_makecoprime(GEN nf, GEN g, GEN e, GEN pr, GEN prk, GEN EX);
GEN famat_mul(GEN f, GEN g);
GEN famat_pow(GEN f, GEN n);
GEN famat_reduce(GEN fa);
GEN famat_to_arch(GEN nf, GEN fa, long prec);
GEN famat_to_nf_modideal_coprime(GEN nf, GEN g, GEN e, GEN id, GEN EX);
GEN famat_to_nf_modidele(GEN nf, GEN g, GEN e, GEN bid);
GEN merge_factor_i(GEN f, GEN g);
GEN to_famat_all(GEN x, GEN y);
GEN to_famat(GEN g, GEN e);
GEN trivfact(void);
/* integer factorization / discrete log */
int BSW_isprime(GEN x);
int BSW_isprime_small(GEN x);
GEN coprime_part(GEN x, GEN f);
GEN Z_factor_limit(GEN n, GEN limit);
GEN Fp_PHlog(GEN a, GEN g, GEN p, GEN ord);
GEN Fp_shanks(GEN x,GEN g0,GEN p, GEN q);
ulong is_kth_power(GEN x, ulong p, GEN *pt, byteptr d);
long ifac_decomp_break(GEN n, long (*B)(GEN,GEN,GEN,GEN), GEN s, long hint);
long ifac_moebius(GEN n, long hint);
long ifac_issquarefree(GEN n, long hint);
long ifac_omega(GEN n, long hint);
long ifac_bigomega(GEN n, long hint);
GEN ifac_totient(GEN n, long hint);
GEN ifac_numdiv(GEN n, long hint);
GEN ifac_sumdiv(GEN n, long hint);
GEN ifac_sumdivk(GEN n, long k, long hint);
int miller(GEN n, long k);
GEN mpqs(GEN N);
ulong ugcd(ulong x, ulong y);
long Z_lvalrem_stop(GEN n, ulong p, int *stop);
/* quadratic forms, quadratic numbers */
long cornacchia(GEN d, GEN p, GEN *px, GEN *py);
long cornacchia2(GEN d, GEN p, GEN *px, GEN *py);
GEN primeform_u(GEN x, ulong p);
GEN qf_disc(GEN x);
void qfb_comp(GEN z,GEN x,GEN y);
GEN qfr_to_qfr5(GEN x, long prec);
GEN qfr3_comp(GEN x, GEN y, GEN D, GEN isqrtD);
GEN qfr3_pow(GEN x, GEN n, GEN D, GEN isqrtD);
GEN qfr3_red(GEN x, GEN D, GEN isqrtD);
GEN qfr3_rho(GEN x, GEN D, GEN isqrtD);
GEN qfr3_to_qfr(GEN x, GEN z);
GEN qfr5_dist(GEN e, GEN d, long prec);
GEN qfr5_comp(GEN x, GEN y, GEN D, GEN sqrtD, GEN isqrtD);
GEN qfr5_pow(GEN x, GEN n, GEN D, GEN sqrtD, GEN isqrtD);
GEN qfr5_red(GEN x, GEN D, GEN sqrtD, GEN isqrtD);
GEN qfr5_rho(GEN x, GEN D, GEN sqrtD, GEN isqrtD);
GEN qfr_pow(GEN x, GEN n);
GEN qfr_unit(GEN x);
GEN qfi_unit(GEN x);
GEN quad_polmod_conj(GEN x, GEN y);
GEN quad_polmod_norm(GEN x, GEN y);
/* Polynomials */
/* a) Arithmetic/conversions */
GEN addmulXn(GEN x, GEN y, long d);
GEN addshiftpol(GEN x, GEN y, long d);
GEN lift_if_rational(GEN x);
GEN monomial(GEN a, long degpol, long v);
GEN monomialcopy(GEN a, long degpol, long v);
GEN mulmat_pol(GEN A, GEN x);
long polegal_spec(GEN x, GEN y);
GEN polrecip_i(GEN x);
GEN pol_to_monic(GEN pol, GEN *lead);
GEN revpol(GEN x);
GEN ser2pol_i(GEN x, long lx);
GEN ser2rfrac_i(GEN x);
GEN shiftpol_i(GEN x, long v);
GEN swap_vars(GEN b0, long v);
GEN translate_pol(GEN P, GEN c);
/* b) Modular */
GEN bezout_lift_fact(GEN T, GEN Tmod, GEN p, long e);
GEN caractducos(GEN p, GEN x, long v);
GEN FpXQX_from_Kronecker(GEN z, GEN pol, GEN p);
GEN FpX_quad_root(GEN x, GEN p, int unknown);
long FpX_split_Berlekamp(GEN *t, GEN pp);
GEN FqX_split_all(GEN z, GEN T, GEN p);
long FqX_split_by_degree(GEN *pz, GEN u, GEN q, GEN T, GEN p);
long FqX_split_deg1(GEN *pz, GEN u, GEN q, GEN T, GEN p);
GEN FqX_split_roots(GEN z, GEN T, GEN p, GEN pol);
GEN polratlift(GEN P, GEN mod, GEN amax, GEN bmax, GEN denom);
GEN polsym_gen(GEN P, GEN y0, long n, GEN T, GEN N);
GEN ZX_caract_sqf(GEN A, GEN B, long *lambda, long v);
GEN ZX_disc_all(GEN,ulong);
long ZX_get_prec(GEN x);
GEN ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound);
GEN ZY_ZXY_resultant_all(GEN A, GEN B0, long *lambda, GEN *LPRS);
GEN ZY_ZXY_rnfequation(GEN A, GEN B0, long *lambda);
GEN RgXQ_u_pow(GEN x, ulong n, GEN T);
GEN RgX_gcd_simple(GEN x, GEN y);
GEN RgX_extgcd_simple(GEN a, GEN b, GEN *pu, GEN *pv);
GEN RgXQ_minpoly_naive(GEN y, GEN P);
GEN lift_intern0(GEN x,long v);
#define lift_intern(x) (lift_intern0((x),-1))
/* b') Chinese Remainder Theorem */
GEN ZM_init_CRT(GEN Hp, ulong p);
int ZM_incremental_CRT(GEN H, GEN Hp, GEN q, GEN qp, ulong p);
/* c) factorization */
double cauchy_bound(GEN p);
GEN chk_factors_get(GEN lt, GEN famod, GEN c, GEN T, GEN N);
int cmbf_precs(GEN q, GEN A, GEN B, long *a, long *b, GEN *qa, GEN *qb);
GEN ZX_DDF(GEN x, long hint);
GEN fact_from_DDF(GEN fa, GEN e, long n);
GEN initgaloisborne(GEN T, GEN dn, long prec, GEN *pL, GEN *pprep, GEN *pdis);
GEN logmax_modulus_bound(GEN p);
GEN polint_i(GEN xa, GEN ya, GEN x, long n, GEN *ptdy);
GEN quicktrace(GEN x, GEN sym);
GEN roots_to_pol_intern(GEN L, GEN a, long v, int plus);
GEN roots_to_pol_r1r2(GEN a, long r1, long v);
GEN special_pivot(GEN x);
GEN vandermondeinversemod(GEN L, GEN T, GEN den, GEN mod);
GEN ZX_monic_factorpadic(GEN f, GEN p, long prec);
#include "parinf.h"
/* Allocation / gerepile */
void debug_stack(void);
void fill_stack(void);
void init_dalloc();
double *dalloc(size_t n);
void gerepilecoeffs2(pari_sp av, GEN x, int n, GEN y, int o);
void minim_alloc(long n, double ***q, GEN *x, double **y, double **z, double **v);
int pop_entree_bloc(entree *ep, long loc);
int pop_val_if_newer(entree *ep, long loc);
void gclone_refc(GEN x);
void free_ep_args(entree *ep);
/* naive grow-arrays */
typedef struct {
void **v;
long len; /* len cells allocated */
long n; /* first n cells occupied */
} __pari_growarray;
typedef __pari_growarray growarray[1];
growarray *pari_get_modules();
growarray *pari_get_oldmodules();
void grow_append(growarray A, void *e);
void grow_copy(growarray A, growarray B);
void grow_init(growarray A);
void grow_kill(growarray A);
/* Interfaces (GP, etc.) */
void errcontext(char *msg, char *s, char *entry);
GEN geni(void);
void* get_stack(double fraction, long min);
GEN gpreadseq(char *c, int strict);
void initout(int initerr);
void init80col(long n);
char* itostr(GEN x, int minus);
void kill_from_hashlist(entree *ep, long n);
void member_err(char *s);
int pari_kernel_init(void);
int pari_last_was_newline(void);
void pari_set_last_newline(int last);
void print_functions_hash(const char *s);
void print_user_fun(entree *ep);
void print_user_member(entree *ep);
void print_all_user_fun(void);
void print_all_user_member(void);
void pop_val(entree *ep);
void push_val(entree *ep, GEN a);
GEN readbin(const char *name, FILE *f, int *vector);
void recover(int flag);
int term_height(void);
int term_width(void);
void var_make_safe();
void whatnow_new_syntax(char *f, long n);
/* defaults */
#define is_default(s) setdefault((s),"",d_EXISTS) == gen_1
enum { d_SILENT, d_ACKNOWLEDGE, d_INITRC, d_RETURN, d_EXISTS };
extern ulong precreal;
GEN sd_TeXstyle(const char *v, long flag);
GEN sd_colors(char *v, long flag);
GEN sd_compatible(const char *v, long flag);
GEN sd_datadir(char *v, long flag);
GEN sd_debug(const char *v, long flag);
GEN sd_debugfiles(const char *v, long flag);
GEN sd_debugmem(const char *v, long flag);
GEN sd_echo(const char *v, long flag);
GEN sd_factor_add_primes(char *v, long flag);
GEN sd_filename(const char *v, long flag, char *s, char **f);
GEN sd_format(const char *v, long flag);
GEN sd_help(char *v, long flag);
GEN sd_histsize(const char *v, long flag);
GEN sd_lines(const char *v, long flag);
GEN sd_log(const char *v, long flag);
GEN sd_logfile(const char *v, long flag);
GEN sd_new_galois_format(char *v, long flag);
GEN sd_output(const char *v, long flag);
GEN sd_parisize(const char *v, long flag);
GEN sd_path(char *v, long flag);
GEN sd_prettyprinter(char *v, long flag);
GEN sd_primelimit(const char *v, long flag);
GEN sd_prompt(const char *v, long flag);
GEN sd_prompt_cont(const char *v, long flag);
GEN sd_psfile(const char *v, long flag);
GEN sd_realprecision(const char *v, long flag);
GEN sd_rl(const char *v, long flag);
GEN sd_secure(const char *v, long flag);
GEN sd_seriesprecision(const char *v, long flag);
GEN sd_simplify(const char *v, long flag);
GEN sd_strictmatch(const char *v, long flag);
GEN sd_timer(const char *v, long flag);
GEN setdefault(const char *s, const char *v, long flag);
/* history */
typedef struct {
GEN *res; /* array of previous results, FIFO */
size_t size; /* # res */
ulong total; /* # of results computed since big bang */
} gp_hist;
/* prettyprinter */
typedef struct {
pariFILE *file;
char *cmd;
} gp_pp;
/* path */
typedef struct {
char *PATH;
char **dirs;
} gp_path;
/* for output */
typedef struct {
char format; /* e,f,g */
long fieldw; /* 0 (ignored) or field width */
long sigd; /* -1 (all) or number of significant digits printed */
int sp; /* 0 = suppress whitespace from output */
int prettyp; /* output style: raw, prettyprint, etc */
int TeXstyle;
} pariout_t;
char *GENtostr0(GEN x, pariout_t *T, void (*do_out)(GEN, pariout_t*));
void lim_lines_output(GEN z, pariout_t *fmt, long n, long max);
void gen_output(GEN x, pariout_t *T);
/* GP_DATA */
typedef struct {
ulong primelimit;
jmp_buf env;
gp_hist *hist;
gp_pp *pp;
gp_path *path;
pariout_t *fmt;
ulong flags, lim_lines;
char *help, *prompt, *prompt_cont;
pari_timer *T;
} gp_data;
/* GP_DATA->flags */
enum { QUIET=1, TEST=2, SIMPLIFY=4, CHRONO=8, ECHO=16, STRICTMATCH=32,
USE_READLINE=64, SECURE=128, EMACS=256, TEXMACS=512};
extern gp_data *GP_DATA;
typedef struct Buffer {
char *buf;
ulong len;
jmp_buf env;
} Buffer;
Buffer *new_buffer(void);
void delete_buffer(Buffer *b);
void fix_buffer(Buffer *b, long newlbuf);
typedef struct {
char *s, *t, *end; /* source, target, last char read */
int in_string, in_comment, more_input, wait_for_brace, downcase;
Buffer *buf;
} filtre_t;
void init_filtre(filtre_t *F, Buffer *buf);
char *filtre(char *s, int flag);
void check_filtre(filtre_t *F);
gp_data *default_gp_data(void);
GEN gp_history(gp_hist *H, long p, char *old, char *entry);
GEN set_hist_entry(gp_hist *H, GEN x);
void delete_dirs(gp_path *p);
void gp_expand_path(gp_path *p);
const char *pari_default_path();
char *expand_prompt(char *prompt, filtre_t *F);
typedef struct input_method {
/* mandatory */
char * (*fgets)(char *,int,FILE*);
char * (*getline)(char**, int f, struct input_method*, filtre_t *F);
int free; /* boolean: must we free the output of getline() ? */
/* for interactive methods */
char *prompt, *prompt_cont;
/* for non-interactive methods */
FILE *file;
} input_method;
int input_loop(filtre_t *F, input_method *IM);
char *file_input(char **s0, int junk, input_method *IM, filtre_t *F);
/* By files */
/* Flx.c */
GEN FlxX_recipspec(GEN x, long l, long n, long vs);
GEN FlxX_sub(GEN x, GEN y, ulong p);
GEN FlxX_subspec(GEN x, GEN y, ulong p, long lx, long ly);
GEN FlxX_swap(GEN x, long n, long ws);
GEN FlxX_to_Kronecker(GEN P, GEN Q);
GEN FlxX_to_Kronecker_spec(GEN P, long lp, GEN Q);
GEN Flx_addshift(GEN x, GEN y, ulong p, long d);
GEN Flx_addspec(GEN x, GEN y, ulong p, long lx, long ly);
GEN Flx_even_odd_comb(GEN P, ulong u, ulong v, ulong p);
GEN Flx_mulspec(GEN a, GEN b, ulong p, long na, long nb);
GEN Flx_negspec(GEN x, ulong p, long l);
GEN Flx_recipspec(GEN x, long l, long n);
GEN Flx_sqrspec(GEN a, ulong p, long na);
GEN Flx_subspec(GEN x, GEN y, ulong p, long lx, long ly);
GEN FlxqX_from_Kronecker(GEN z, GEN T, ulong p);
GEN FlxqX_invmontgomery(GEN T, GEN Q, ulong p);
GEN FlxqX_mulspec(GEN x, GEN y, GEN T, ulong p, long lx, long ly);
GEN FlxqX_rem_montgomery(GEN x, GEN mg, GEN T, GEN Q, ulong p);
/* Qfb.c */
GEN powimagraw(GEN x, long n);
GEN redimagsl2(GEN q, GEN *U);
GEN redrealsl2(GEN V);
GEN redrealsl2step(GEN A);
GEN sqcompimagraw(GEN x);
GEN sqcomprealraw(GEN x);
/* RgX.c */
GEN RgXQ_matrix_pow(GEN y, long n, long m, GEN P);
GEN RgX_copy_spec(GEN x, long nx);
GEN zx_copy_spec(GEN x, long nx);
/* alglin1.c */
GEN Flm_Fl_mul_inplace(GEN y, ulong x, ulong p);
GEN gauss_get_col(GEN a, GEN b, GEN p, long li);
GEN gauss_intern(GEN a, GEN b);
GEN matid_intern(long n,GEN myun,GEN myzero);
void vecselect_p(GEN A, GEN B, GEN p, long init, long lB);
/* alglin2.c */
GEN Frobeniusform(GEN V, long n);
GEN ZM_copy(GEN x);
GEN ZV_Z_mul(GEN X, GEN c);
GEN ZV_copy(GEN x);
void ZV_neg_ip(GEN M);
GEN hnf0(GEN A, int remove);
GEN hnf_special(GEN x, long remove);
GEN hnfall0(GEN A, long remove);
/* anal.c */
long unsigned int parse_option_string(char *arg, char *tmplate, long flag, char **failure, char **failure_arg);
GEN readexpr(char *t);
/* aprcl.c */
GEN aprcl(GEN N);
/* arith1.c */
GEN Z_chinese_coprime(GEN a, GEN b, GEN A, GEN B, GEN C);
GEN bestappr_mod(GEN x, GEN A, GEN B);
long hilii(GEN x, GEN y, GEN p);
long krouu_s(ulong x, ulong y, long s);
/* arith2.c */
GEN ibitand(GEN x, GEN y);
GEN ibitnegimply(GEN x, GEN y);
GEN ibitor(GEN x, GEN y);
GEN ibitxor(GEN x, GEN y);
byteptr initprimes0(ulong maxnum, long *lenp, ulong *lastp);
long set_optimize(long what, GEN g);
/* base1.c */
void nfbasic_init(GEN x, long flag, GEN fa, nfbasic_t *T);
GEN nffromhnfbasis(GEN nf, GEN x);
GEN nftohnfbasis(GEN nf, GEN x);
GEN polgaloisnames(long a, long b);
GEN primitive_pol_to_monic(GEN pol, GEN *ptlead);
/* base2.c */
long FpX_val(GEN x0, GEN t, GEN p, GEN *py);
GEN fast_respm(GEN f, GEN g, GEN p, long M);
GEN gen_if_principal(GEN bnf, GEN x);
int nfissquarefree(GEN nf, GEN x);
GEN nfreducemodpr_i(GEN x, GEN prh);
GEN polsymmodp(GEN g, GEN p);
GEN respm(GEN x, GEN y, GEN pm);
GEN rnfdet0(GEN nf, GEN x, GEN y);
/* base3.c */
GEN FpXQ_gener(GEN T, GEN p);
void check_nfelt(GEN x, GEN *den);
GEN ff_PHlog(GEN a, GEN g, GEN T, GEN p);
GEN nf_PHlog(GEN nf, GEN a, GEN g, GEN pr);
/* base4.c */
GEN arch_inv(GEN x);
GEN arch_pow(GEN x, GEN n);
void check_listpr(GEN x);
GEN factor_norm(GEN x);
GEN famat_to_nf(GEN nf, GEN f);
long val_norm(GEN x, GEN p, long *vz);
/* base5.c */
GEN check_and_build_nfabs(GEN rnf);
GEN check_and_build_norms(GEN rnf);
GEN checkrnfeq(GEN x);
GEN hnfcenter_ip(GEN M);
/* bibli1.c */
GEN gscal(GEN x, GEN y);
GEN lll_scaled(long MARKED, GEN X0, long D);
GEN lllall(GEN x, long D, int gram, long flag);
GEN lllintpartialall(GEN m, long flag);
GEN plindep(GEN x);
GEN pslq(GEN x);
GEN pslqL2(GEN x);
GEN sqscal(GEN x);
/* bibli2.c */
long ZV_search(GEN x, GEN y);
GEN ZV_sort_uniq(GEN L);
GEN gen_vecsort(GEN x, GEN k, long flag);
/* buch1.c */
GEN buchquad(GEN D, double cbach, double cbach2, long RELSUP, long prec);
GEN form_to_ideal(GEN x);
GEN getallforms(GEN D, long *pth, GEN *ptz);
/* buch2.c */
GEN check_and_build_matal(GEN bnf);
GEN extract_full_lattice(GEN x);
GEN init_red_mod_units(GEN bnf, long prec);
GEN isprincipalarch(GEN bnf, GEN col, GEN kNx, GEN e, GEN dx, long *pe);
GEN red_mod_units(GEN col, GEN z, long prec);
int trunc_error(GEN x);
/* buch3.c */
GEN minkowski_bound(GEN D, long N, long r2, long prec);
/* elliptic.c */
GEN CM_CardEFp(GEN E, GEN p);
GEN CM_ellap(GEN E, GEN p);
GEN apell1(GEN e, GEN p);
void checkpt(GEN z);
GEN multi_invmod(GEN x, GEN p);
GEN ratroot(GEN p);
GEN weipell0(GEN e, long prec, long PREC);
/* es.c */
GEN Str0(GEN g, long flag);
void bruti(GEN g, pariout_t *T, int addsign);
const char * eng_ord(long i);
char * env_ok(char *s);
void matbruti(GEN g, pariout_t *T);
int pari_is_dir(char *name);
GEN readobj(FILE *f, int *ptc);
void sori(GEN g, pariout_t *T);
void texi(GEN g, pariout_t *T, int addsign);
void writeGEN(GEN x, FILE *f);
void writenamedGEN(GEN x, char *s, FILE *f);
/* galconj.c */
GEN fixedfieldfactmod(GEN Sp, GEN p, GEN Tmod);
GEN fixedfieldfactor(GEN L, GEN O, GEN perm, GEN M, GEN den, GEN mod, long x, long y);
GEN fixedfieldinclusion(GEN O, GEN PL);
GEN fixedfieldorbits(GEN O, GEN L);
GEN fixedfieldsympol(GEN O, GEN mod, GEN l, GEN p, long v);
GEN galoisconj2pol(GEN x, long nbmax, long prec);
GEN galoiscosets(GEN O, GEN perm);
long intheadlong(GEN x, GEN mod);
long isomborne(GEN P, GEN den, GEN p);
GEN listznstarelts(long m, long p);
GEN matheadlong(GEN W, GEN mod);
GEN matrixnorm(GEN M, long prec);
GEN monomorphismlift(GEN P, GEN S, GEN Q, GEN p, long e);
long polheadlong(GEN P, long n, GEN mod);
GEN sympol_aut_evalmod(GEN sym, long g, GEN sigma, GEN Tp, GEN p);
GEN sympol_eval(GEN v, GEN NS);
GEN vandermondeinverseprep(GEN L);
/* galois.c */
GEN partitions(long n);
GEN polgaloisnamesbig(long n, long k);
/* gen1.c */
int ff_poltype(GEN *x, GEN *p, GEN *pol);
GEN gred_frac2(GEN x1, GEN x2);
GEN gred_rfrac2(GEN x1, GEN x2);
GEN gred_rfrac_simple(GEN n, GEN d);
/* gen2.c */
void gopsg2z(GEN (*f) (GEN, GEN), long s, GEN y, GEN z);
/* gen3.c */
GEN gsubst_expr(GEN pol, GEN from, GEN to);
GEN inv_ser(GEN b);
GEN mul_real(GEN x, GEN y);
GEN poltoser(GEN x, long v, long prec);
GEN qfbeval(GEN q, GEN x, GEN y);
GEN rfractoser(GEN x, long v, long prec);
/* groupid.c */
long group_ident_i(GEN G, GEN S);
long group_ident_trans(GEN G, GEN S);
long groupelts_sumorders(GEN S);
GEN vecgroup_idxlist(GEN L, long order);
long vecgroup_sumorders(GEN L);
/* ifactor1.c */
GEN ellfacteur(GEN n, int insist);
long ifac_decomp(GEN n, long hint);
GEN ifac_primary_factor(GEN *partial, long *exponent);
void ifac_realloc(GEN *partial, GEN *where, long new_lg);
GEN ifac_start(GEN n, long moebius, long hint);
GEN pollardbrent(GEN n);
ulong snextpr(ulong p, byteptr *d, long *rcn, long *q, long k);
GEN squfof(GEN n);
/* init.c */
void err_recover(long numerr);
GEN gcopy_av(GEN x, GEN *AVMA);
int ok_gerepileupto(GEN x);
void pari_init_defaults(void);
/* nffactor.c */
long ZM_get_prec(GEN x);
int nfissplit(GEN nf, GEN x);
/* perm.c */
long cosets_perm_search(GEN C, GEN p);
GEN group_export_GAP(GEN G);
GEN group_export_MAGMA(GEN G);
GEN perm_conj(GEN s, GEN t);
GEN perm_generate(GEN S, GEN H, long o);
long perm_relorder(GEN p, GEN S);
GEN perm_to_GAP(GEN p);
GEN quotient_subgroup_lift(GEN C, GEN H, GEN S);
/* polarit1.c */
GEN Flx_Berlekamp_ker(GEN u, ulong p);
GEN FpX_Berlekamp_ker(GEN u, GEN p);
GEN FpX_factcantor(GEN f, GEN pp, long flag);
GEN FqX_Berlekamp_ker(GEN u, GEN T, GEN q, GEN p);
GEN FqX_rand(long d1, long v, GEN T, GEN p);
long FqX_split_Berlekamp(GEN *t, GEN q, GEN T, GEN p);
GEN Zp_appr(GEN f, GEN a);
int cmp_padic(GEN x, GEN y);
GEN factcantor0(GEN f, GEN pp, long flag);
GEN zrhqr(GEN a, long prec);
/* polarit2.c */
GEN DDF_roots(GEN pol, GEN polp, GEN p);
GEN Q_divmuli_to_int(GEN x, GEN d, GEN n);
long checkdeflate(GEN x);
void factor_quad(GEN x, GEN res, long *ptcnt);
GEN factorback_aux(GEN fa, GEN e, GEN (*_mul) (void *, GEN, GEN), GEN (*_pow) (void *, GEN, GEN), void *data);
GEN matratlift(GEN M, GEN mod, GEN amax, GEN bmax, GEN denom);
GEN pseudodiv(GEN x, GEN y, GEN *ptr);
long s_centermod(long x, ulong pp, ulong pps2);
GEN sort_vecpol_gen(GEN a, int (*cmp) (GEN, GEN));
GEN sylvestermatrix_i(GEN x, GEN y);
/* polarit3.c */
GEN Flm_Frobenius_pow(GEN M, long d, GEN T, ulong p);
GEN Flxq_matrix_pow(GEN y, long n, long m, GEN P, ulong l);
GEN FpM_Frobenius_pow(GEN M, long d, GEN T, GEN p);
GEN FpXQ_sqrtl(GEN a, GEN l, GEN T, GEN p, GEN q, long e, GEN r, GEN y, GEN m);
GEN FpXYQQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p);
GEN FpX_compositum(GEN A, GEN B, GEN p);
GEN FpX_direct_compositum(GEN A, GEN B, GEN p);
GEN FpX_div_by_X_x(GEN a, GEN x, GEN p, GEN *r);
GEN FpX_gcd_check(GEN x, GEN y, GEN p);
GEN RgX_to_FpXQX(GEN x, GEN T, GEN p);
GEN Rg_to_FpXQ(GEN x, GEN T, GEN p);
int ZX_incremental_CRT(GEN *ptH, GEN Hp, GEN q, GEN qp, ulong p);
GEN ZX_init_CRT(GEN Hp, ulong p, long v);
ulong ZY_ZXY_ResBound(GEN A, GEN B, GEN dB);
int Z_incremental_CRT(GEN *H, ulong Hp, GEN q, GEN qp, ulong p);
GEN ffinit_Artin_Shreier(GEN ip, long l);
GEN ffinit_rand(GEN p, long n);
byteptr init_modular(ulong *p);
GEN polint_triv(GEN xa, GEN ya);
/* rootpol.c */
GEN FFT(GEN x, GEN Omega);
GEN FFTinit(long k, long prec);
/* subcyclo.c */
GEN bnr_to_znstar(GEN bnr, long *complex);
GEN galoiscyclo(long n, long v);
GEN subcyclo_complex_bound(pari_sp ltop, GEN V, long prec);
GEN subcyclo_complex_roots(long n, long real, long prec);
GEN subcyclo_cyclic(long n, long d, long m, long z, long g, GEN powz, GEN le);
GEN subcyclo_orbits(long n, GEN H, GEN O, GEN powz, GEN le);
GEN subcyclo_roots(long n, GEN zl);
GEN subcyclo_start(long n, long d, long o, GEN borne, long *ptr_val, long *ptr_l);
GEN znstar_bits(long n, GEN H);
long znstar_conductor(long n, GEN H);
GEN znstar_coset_bits(long n, GEN H, long c);
void znstar_coset_bits_inplace(long n, GEN H, GEN bits, long c);
void znstar_coset_func(long n, GEN H, void (*func) (void *, long), void *data, long c);
GEN znstar_cosets(long n, long phi_n, GEN H);
GEN znstar_elts(long n, GEN H);
GEN znstar_generate(long n, GEN V);
GEN znstar_hnf(GEN Z, GEN M);
GEN znstar_hnf_generators(GEN Z, GEN M);
GEN znstar_partial_bits(long n, GEN H, long d);
GEN znstar_partial_coset_bits(long n, GEN H, long d, long c);
void znstar_partial_coset_bits_inplace(long n, GEN H, GEN bits, long d, long c);
void znstar_partial_coset_func(long n, GEN H, void (*func) (void *, long), void *data, long d, long c);
GEN znstar_reduce_modulus(GEN H, long n);
/* thue.c */
GEN bnfisintnormabs(GEN bnf, GEN a);
/* trans1.c */
GEN constlog2(long prec);
GEN padic_sqrt(GEN x);
GEN padic_sqrtn(GEN x, GEN n, GEN *zetan);
GEN padic_sqrtn_ram(GEN x, long e);
GEN padic_sqrtn_unram(GEN x, GEN n, GEN *zetan);
void pari_init_floats(void);
GEN rootsof1complex(GEN n, long prec);
GEN rootsof1padic(GEN n, GEN y);
/* trans2.c */
GEN cxpsi(GEN s0, long prec);
double darg(double s, double t);
/* trans3.c */
GEN bernreal_using_zeta(long n, GEN iz, long prec);
GEN czeta(GEN s0, long prec);
GEN inv_szeta_euler(long n, double lba, long prec);
GEN kbesselnew(GEN n, GEN z, long prec);
GEN polylogd0(long m, GEN x, long flag, long prec);
GEN twistpartialzeta(GEN p, GEN q, long f, long c, GEN va, GEN cff);
ENDEXTERN