/usr/include/pari/paripriv.h is in libpari-dev 2.5.0-2ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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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
/* hashtables */
hashtable *hashstr_import_static(hashentry *e, ulong size);
void hashstr_dbg(hashtable *h);
/* for qsort */
typedef int (*QSCOMP)(const void *, const void *);
/* for (ulong*) GENs */
typedef ulong *uGEN;
#define ucoeff(a,i,j) (((uGEN*)(a))[j][i])
#define ugel(a,i) ((uGEN*)(a))[i]
/* 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);}
/* unused */
GEN ellheightoo(GEN e, GEN z, long prec);
void ellprint(GEN e);
/* generic */
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_pol(GEN y, int (*cmp)(GEN,GEN));
/* loops */
GEN incloop(GEN a);
GEN resetloop(GEN a, GEN b);
GEN setloop(GEN a);
/* parser */
void forpari(GEN a, GEN b, GEN node);
void untilpari(GEN a, GEN b);
void whilepari(GEN a, GEN b);
GEN ifpari(GEN g, GEN a, GEN b);
GEN andpari(GEN a, GEN b);
GEN orpari(GEN a, GEN b);
void ifpari_void(GEN g, GEN a, GEN b);
GEN geval_gp(GEN x, GEN t);
GEN gadde(GEN *x, GEN y);
GEN gadd1e(GEN *x);
GEN gdive(GEN *x, GEN y);
GEN gdivente(GEN *x, GEN y);
GEN gdivrounde(GEN *x, GEN y);
GEN gmode(GEN *x, GEN y);
GEN gmule(GEN *x, GEN y);
GEN gshiftle(GEN *x, long n);
GEN gshiftre(GEN *x, long n);
GEN gstore(GEN *x, GEN y);
GEN gsube(GEN *x, GEN y);
GEN gsub1e(GEN *x);
GEN gshift_right(GEN x, long n);
GEN derivnum0(GEN a, GEN code, long prec);
GEN derivfun0(GEN code, GEN args, long prec);
GEN direuler0(GEN a, GEN b, GEN code, GEN c);
GEN divsum(GEN num, GEN code);
void fordiv(GEN a, GEN code);
void forell0(long a, long b, GEN code);
void forprime(GEN a, GEN b, GEN code);
void forstep(GEN a, GEN b, GEN s, GEN code);
void forsubgroup0(GEN cyc, GEN bound, GEN code);
void forvec(GEN x, GEN code, long flag);
GEN intcirc0(GEN a, GEN R, GEN code, GEN tab, long prec);
GEN intfourcos0(GEN a, GEN b, GEN x, GEN code, GEN tab, long prec);
GEN intfourexp0(GEN a, GEN b, GEN x, GEN code, GEN tab, long prec);
GEN intfoursin0(GEN a, GEN b, GEN x, GEN code, GEN tab, long prec);
GEN intfuncinit0(GEN a, GEN b, GEN code, long flag, long m, long prec);
GEN intlaplaceinv0(GEN sig, GEN x, GEN code, GEN tab, long prec);
GEN intmellininv0(GEN sig, GEN x, GEN code, GEN tab, long prec);
GEN intnum0(GEN a, GEN b, GEN code, GEN tab, long prec);
GEN intnuminit0(GEN a, GEN b, GEN tab, long prec);
GEN intnuminitgen0(GEN a, GEN b, GEN code, long m, long flag, long prec);
GEN intnumromb0(GEN a, GEN b, GEN code, long flag, long prec);
GEN matrice(GEN nlig, GEN ncol, GEN code);
GEN prodeuler0(GEN a, GEN b, GEN code, long prec);
GEN prodinf0(GEN a, GEN code, long flag, long prec);
GEN produit(GEN a, GEN b, GEN code, GEN x);
GEN somme(GEN a, GEN b, GEN code, GEN x);
GEN sumalt0(GEN a, GEN code,long flag, long prec);
GEN suminf0(GEN a, GEN code, long prec);
GEN sumnum0(GEN a, GEN sig, GEN code, GEN tab, long flag, long prec);
GEN sumnumalt0(GEN a, GEN sig, GEN code, GEN tab, long flag, long prec);
GEN sumnuminit0(GEN a, GEN tab, long sgn, long prec);
GEN sumpos0(GEN a, GEN code, long flag,long prec);
GEN vecteursmall(GEN nmax, GEN code);
GEN vecteur(GEN nmax, GEN n);
GEN vvecteur(GEN nmax, GEN n);
GEN zbrent0(GEN a, GEN b, GEN code, long prec);
/* multiprecision */
GEN addrex01(GEN x);
GEN adduispec_offset(ulong s, GEN x, long offset, long nx);
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);
ulong xxgcduu(ulong d, ulong d1, int f, ulong* u, ulong* u1, ulong* v, ulong* v1, long *s);
GEN divgunu(GEN x, ulong i);
GEN divrunu(GEN x, ulong i);
GEN logagmcx(GEN q, long prec);
GEN muliispec(GEN x, GEN y, long nx, long ny);
GEN red_montgomery(GEN T, GEN N, ulong inv);
GEN sqrispec(GEN x, long nx);
GEN subrex01(GEN x);
GEN modr_safe(GEN x, GEN y);
ulong *convi(GEN x, long *l);
int approx_0(GEN x, GEN y);
GEN bernfrac_using_zeta(long n);
int OK_bern(long nb, long prec);
/* powers */
GEN rpowuu(ulong a, ulong n, long prec);
ulong u_pow10(int n);
/* floats */
double dabs(double s, double t);
void dcxlog(double s, double t, double *a, double *b);
double dnorm(double s, double t);
double dbllog2(GEN z);
ulong usqrtsafe(ulong a);
/* hnf */
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 hnfspec_i(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
GEN hnfspec(GEN m,GEN p,GEN* ptdep,GEN* ptA,GEN* ptC,long k0);
GEN mathnfspec(GEN x, GEN *ptperm, GEN *ptdep, GEN *ptB, GEN *ptC);
GEN LLL_check_progress(GEN Bnorm, long n0, GEN m, int final, long *ti_LLL);
GEN extendedgcd(GEN A);
/* miscellaneous linear algebra */
GEN imagecomplspec(GEN x, long *nlze);
INLINE void rowselect_p(GEN A, GEN B, GEN p, long init);
GEN dim1proj(GEN prh);
GEN detcyc(GEN cyc, long *L);
GEN merge_factor_i(GEN f, GEN g);
/* integer factorization / discrete log */
GEN coprime_part(GEN x, GEN f);
ulong ucoprime_part(ulong x, ulong f);
ulong is_kth_power(GEN x, ulong p, GEN *pt, byteptr d);
GEN mpqs(GEN N);
ulong gcduodd(ulong x, ulong y);
long Z_lvalrem_stop(GEN n, ulong p, int *stop);
long u_lvalrem_stop(ulong *n, ulong p, int *stop);
/* 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);
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 RgX_recipspec_shallow(GEN x, long l, long n);
/* b) Modular */
GEN bezout_lift_fact(GEN T, GEN Tmod, GEN p, long e);
GEN Kronecker_to_FpXQX(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 polsym_gen(GEN P, GEN y0, long n, GEN T, GEN N);
GEN ZXQ_charpoly_sqf(GEN A, GEN B, long *lambda, long v);
GEN ZX_disc_all(GEN,ulong);
GEN ZX_resultant_all(GEN A, GEN B, GEN dB, ulong bound);
GEN ZX_ZXY_resultant_all(GEN A, GEN B, long *lambda, GEN *LPRS);
GEN RgXQ_minpoly_naive(GEN y, GEN P);
GEN lift_intern0(GEN x,long v);
#define lift_intern(x) (lift_intern0((x),-1))
/* c) factorization */
double cauchy_bound(GEN p);
GEN chk_factors_get(GEN lt, GEN famod, GEN c, GEN T, GEN N);
long cmbf_maxK(long nb);
GEN ZX_DDF(GEN x);
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 special_pivot(GEN x);
GEN vandermondeinversemod(GEN L, GEN T, GEN den, GEN mod);
GEN ZX_monic_factorpadic(GEN f, GEN p, long prec);
/* Finite field */
enum { t_FF_FpXQ = 0, t_FF_Flxq = 1, t_FF_F2xq = 2 };
/* for Buchall_param */
enum { fupb_NONE, fupb_RELAT, fupb_LARGE, fupb_PRECI };
/* Allocation / gerepile */
void debug_stack(void);
void fill_stack(void);
void init_dalloc(void);
double *dalloc(size_t n);
INLINE 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_block(entree *ep, long loc);
int pop_val_if_newer(entree *ep, long loc);
/* general printing */
void print_errcontext(PariOUT *out, const char *msg, const char *s, const char *entry);
void print_prefixed_text(PariOUT *out, const char *s, const char *prefix, const char *str);
INLINE void
print_text(const char *s) { print_prefixed_text(pariOut, s,NULL,NULL); }
INLINE void
out_print_text(PariOUT *out, const char *s) { print_prefixed_text(out, s,NULL,NULL); }
INLINE long
is_keyword_char(char c) { return (isalnum((int)c) || c=='_'); }
/* Interfaces (GP, etc.) */
entree* is_entry_intern(const char *s, entree **table, long *hash);
entree* do_alias(entree *ep);
char* get_sep(const char *t);
long get_int(const char *s, long dflt);
ulong get_uint(const char *s);
int gp_init_functions(void);
GEN pari_compile_str(char *lex, int strict);
void pari_sigint(const char *s);
pariFILE *pari_last_tmp_file();
void* get_stack(double fraction, long min);
void init_graph(void);
void free_graph(void);
void initout(int initerr);
void init80col(void);
int pari_kernel_init(void);
void print_functions_hash(const char *s);
void print_all_user_fun(int member);
GEN readbin(const char *name, FILE *f, int *vector);
int term_height(void);
int term_width(void);
void whatnow_new_syntax(const char *f, long n);
/* gp_colors */
void decode_color(long n, long *c);
extern GEN pari_colormap, pari_graphcolors;
/* defaults */
extern ulong precreal;
/* 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 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;
void lim_lines_output(char *s, long n, long max);
void gen_output(GEN x, pariout_t *T);
void parsestate_reset(void);
void parsestate_save(struct pari_parsestate *state);
void parsestate_restore(struct pari_parsestate *state);
void compilestate_reset(void);
void compilestate_save(struct pari_compilestate *comp);
void compilestate_restore(struct pari_compilestate *comp);
void evalstate_clone(void);
void evalstate_reset(void);
void evalstate_restore(struct pari_evalstate *state);
void evalstate_save(struct pari_evalstate *state);
void debug_context(void);
/* GP_DATA */
typedef struct {
gp_hist *hist;
gp_pp *pp;
gp_path *path;
pariout_t *fmt;
ulong lim_lines, flags;
int echo, breakloop, recover, use_readline; /* GP-specific */
int secure, simplify, strictmatch, chrono; /* libpari ? */
pari_timer *T;
long last_time; /* duration of last interactive gp command */
} gp_data;
extern gp_data *GP_DATA;
/* GP_DATA->flags */
enum { gpd_QUIET=1, gpd_TEST=2, gpd_EMACS=256, gpd_TEXMACS=512};
/* GP output && output format */
void gpwritebin(const char *s, GEN x);
extern char *current_logfile;
/* colors */
extern long gp_colors[];
extern int disable_color;
/* backward compatibility */
extern ulong compatible;
enum { NONE, WARN, OLDFUN, OLDALL };
#define new_fun_set (compatible == NONE || compatible == WARN)
/* entrees */
#define EpVALENCE(ep) ((ep)->valence & 0xFF)
#define EpSTATIC(ep) ((ep)->valence & 0x100)
#define EpSETSTATIC(ep) ((ep)->valence |= 0x100)
enum { EpNEW = 100, EpALIAS, EpVAR, EpINSTALL };
#define initial_value(ep) ((ep)+1)
/* functions lists */
extern const long functions_tblsz; /* hashcodes table size */
extern entree **functions_hash; /* functions hashtable */
extern entree **defaults_hash; /* defaults hashtable */
extern entree oldfonctions[];
/* buffers */
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 {
const char *s; /* source */
char *t, *end; /* 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(const 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);
void delete_dirs(gp_path *p);
void gp_expand_path(gp_path *p);
const char *pari_default_path(void);
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 */
const 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);
char *file_getline(Buffer *b, char **s0, input_method *IM);
/* 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 zxX_to_Kronecker(GEN P, GEN Q);
GEN zxX_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 Kronecker_to_FlxqX(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 redimagsl2(GEN q, GEN *U);
GEN redrealsl2(GEN V);
GEN redrealsl2step(GEN A);
GEN redtausl2(GEN t, GEN *U);
/* alglin1.c */
typedef long (*pivot_fun)(GEN,GEN,long,GEN);
GEN RgM_pivots(GEN x0, GEN data, long *rr, pivot_fun pivot);
INLINE void vecselect_p(GEN A, GEN B, GEN p, long init, long lB);
/* arith1.c */
GEN bestappr_mod(GEN x, GEN A, GEN B);
int is_gener_Fp(GEN x, GEN p, GEN p_1, GEN L);
int is_gener_Fl(ulong x, ulong p, ulong p_1, GEN L);
/* arith2.c */
byteptr initprimes0(ulong maxnum, long *lenp, ulong *lastp);
long set_optimize(long what, GEN g);
/* base1.c */
GEN nffromhnfbasis(GEN nf, GEN x);
GEN nftohnfbasis(GEN nf, GEN x);
/* base2.c */
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);
/* base3.c */
void check_nfelt(GEN x, GEN *den);
GEN zk_ei_mul(GEN nf, GEN x, long i);
/* base4.c */
void check_listpr(GEN x);
GEN extideal_HNF_mul(GEN nf, GEN x, GEN y);
GEN factor_norm(GEN x);
GEN factorbackprime(GEN nf, GEN L, GEN e);
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);
/* bibli1.c */
GEN plindep(GEN x);
GEN pslq(GEN x);
GEN pslqL2(GEN x);
/* buch1.c */
GEN form_to_ideal(GEN x);
GEN qfbforms(GEN D);
/* buch2.c */
typedef struct GRHcheck_t { double cD, cN; long checkok; } GRHcheck_t;
void init_GRHcheck(GRHcheck_t *S, long N, long R1, double LOGD);
int GRHok(GRHcheck_t *S, double L, double SA, double SB);
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);
/* buch3.c */
GEN minkowski_bound(GEN D, long N, long r2, long prec);
int subgroup_conductor_ok(GEN H, GEN L);
GEN subgrouplist_cond_sub(GEN bnr, GEN C, GEN bound);
/* elliptic.c */
GEN weipell0(GEN e, long prec, long PREC);
/* ellsea.c */
void pari_close_seadata(void);
void pari_init_seadata(void);
/* es.c */
const char * eng_ord(long i);
char * env_ok(const char *s);
void filestate_restore(pariFILE *F);
void killallfiles(void);
pariFILE* newfile(FILE *f, const char *name, int type);
void pari_init_files(void);
void pari_close_files(void);
int popinfile(void);
GEN readobj(FILE *f, int *ptc);
pariFILE* try_pipe(const char *cmd, int flag);
void writeGEN(GEN x, FILE *f);
void writenamedGEN(GEN x, const char *s, FILE *f);
/* galconj.c */
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 vandermondeinverseprep(GEN L);
/* galois.c */
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);
GEN sqr_ser_part(GEN x, long l1, long l2);
/* gen3.c */
GEN gsubst_expr(GEN pol, GEN from, GEN to);
GEN poltoser(GEN x, long v, long prec);
GEN rfractoser(GEN x, long v, long prec);
/* ifactor1.c */
GEN ellfacteur(GEN n, int insist);
GEN pollardbrent(GEN n);
ulong snextpr(ulong p, byteptr *d, long *rcn, long *q, long k);
GEN squfof(GEN n);
/* prime.c */
long BPSW_psp_nosmalldiv(GEN N);
int Fl_MR_Jaeschke(ulong n, long k);
int MR_Jaeschke(GEN n, long k);
int uisprime_nosmalldiv(ulong n);
/* init.c */
void err_recover(long numerr);
void pari_init_defaults(void);
void pari_init_stack(size_t size, size_t old);
/* nffactor.c */
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_generate(GEN S, GEN H, long o);
long perm_relorder(GEN p, GEN S);
GEN perm_to_GAP(GEN p);
/* polarit1.c */
GEN F2x_Berlekamp_ker(GEN u);
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 trivfact(void);
/* polarit2.c */
GEN sylvestermatrix_i(GEN x, GEN y);
/* QX_factor */
GEN DDF_roots(GEN pol, GEN polp, GEN p);
void factor_quad(GEN x, GEN res, long *ptcnt);
long logint(GEN B, GEN y, GEN *ptq);
/* FpX.c */
GEN FpX_gcd_check(GEN x, GEN y, GEN p);
/* polarit3.c */
GEN Flm_Frobenius_pow(GEN M, long d, GEN T, ulong p);
GEN FpM_Frobenius_pow(GEN M, long d, GEN T, GEN p);
GEN FpX_compositum(GEN A, GEN B, GEN p);
GEN FpX_direct_compositum(GEN A, GEN B, GEN p);
ulong ZX_ZXY_ResBound(GEN A, GEN B, GEN dB);
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);
/* random.c */
void pari_init_rand(void);
/* 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 znstar_bits(long n, GEN H);
long znstar_conductor(long n, GEN H);
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_elts(GEN Z, GEN H);
GEN znstar_hnf_generators(GEN Z, GEN M);
GEN znstar_reduce_modulus(GEN H, long n);
GEN znstar_small(GEN zn);
/* trans1.c */
void pari_init_floats(void);
void pari_close_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 double_eta_quotient(GEN a, GEN w, GEN D, long p, long q, GEN pq, GEN sqrtD);
GEN inv_szeta_euler(long n, double lba, long prec);
GEN polylogd0(long m, GEN x, long flag, long prec);
GEN twistpartialzeta(GEN q, long f, long c, GEN va, GEN cff);
ENDEXTERN
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