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/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
/* */
/* Fichier Include PARI */
/* */
/* commun a toutes les versions */
/* */
/* copyright Babecool */
/* */
/* */
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
typedef long *GEN;
typedef unsigned long ulong;
typedef struct entree {
char *name;
long valence;
void *value;
struct entree *next;
} entree;
typedef unsigned char *byteptr;
/* Variables statiques communes :
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
extern long prec,precdl;
extern GEN bernzone,gpi,geuler;
extern long tglobal;
extern long *ordvar,varchanged;
extern GEN polvar;
extern GEN RAVYZARC;
extern long NUMFUNC;
extern entree fonctions[],*hashtable[];
extern long lontyp[],lontyp2[];
extern jmp_buf environnement;
#ifndef IN_INIT_PARI
extern unsigned long avma,bot,top;
#endif
extern GEN gnil,gun,gdeux,ghalf,gi,gzero;
extern GEN *polun,*polx;
extern byteptr diffptr;
extern GEN *g;
extern entree **varentries; /* noms des inconnues actives */
extern GEN *blocliste; /* tableau des pointeur de blocs */
extern long nvar; /* numero de la prochaine inconnue */
extern long glbfmt[];
extern char *helpmessage[]; /* un message pour chaque fonction predefinei */
extern char *errmessage[]; /* un par numero d'erreur */
#define STACKSIZE 500 /* nombre de gn possibles */
#define MAXVAR 150 /* nombre maximum de variables */
#define TBLSZ 135 /* taille de la table de hashcodes */
#define MAXBLOC 5000 /* nombre de blocs autorises dans le tas */
#define K 9.632959862 /* 32*log(2)/log(10) */
#define K1 0.103810253 /* log(10)/(32*log(2)) */
#define K2 1.1239968 /* 1/(1-(log(2)/(2*pi)))*/
#define K3 0.900643041 /* 1/(1+(log(2)/(2*pi)))*/
#define LOG2 0.693147180559945 /* log(2) */
#define L2SL10 0.301029995663981 /* log(2)/log(10) */
#undef PI
#define PI 3.141592653589 /* pi */
#define rac5 2.23606797749 /* racine de 5 */
#define C1 0.9189385332 /* log(2*pi)/2 */
#define C2 22.18070978 /* 32*log(2) */
#define C3 0.0216950598 /* log((1+sqrt(5))/2)/(32*log(2)) */
#define C4 4294967296.0 /* 2^32 */
#define C31 2147483648.0 /* 2^31 */
#define CN31 -2147483648.0 /* -2^31 */
#define BIGINT 32767 /* 2^15-1 */
#ifndef exp2
#define exp2(x) exp((double)(x)*log(2.))
#define log2(x) log((double)(x))/log(2.)
#endif
#define separe(c) ((c==';')||(c==':')||(c=='\n'))
#define output(x) {brute(x,'g',-1);printf("\n");fflush(stdout);}
#define outbeaut(x) {sor(x,'g',-1,0);printf("\n");fflush(stdout);}
#define addis(x,s) addsi(s,x)
#define addrs(x,s) addsr(s,x)
#define mulis(x,s) mulsi(s,x)
#define mulrs(x,s) mulsr(s,x)
#define gval(x,v) ggval(x,polx[v])
#define lgeti (long)cgeti
#define lgetr (long)cgetr
#define lpile (long)gerepile
#define lstoi (long)stoi
#define lnegi (long)negi
#define lnegr (long)negr
#define lmpneg (long)mpneg
#define labsi (long)absi
#define labsr (long)absr
#define lmpabs (long)mpabs
#define lmptrunc (long)mptrunc
#define lmpent (long)mpent
#define lshifts (long)shifts
#define lshifti (long)shifti
#define lshiftr (long)shiftr
#define lmpshift (long)mpshift
#define laddsi (long)addsi
#define laddsr (long)addsr
#define laddis (long)addis
#define laddrs (long)addrs
#define laddii (long)addii
#define laddir (long)addir
#define laddrr (long)addrr
#define lmpadd (long)mpadd
#define lsubsi (long)subsi
#define lsubis (long)subis
#define lsubsr (long)subsr
#define lsubrs (long)subrs
#define lsubii (long)subii
#define lsubir (long)subir
#define lsubri (long)subri
#define lsubrr (long)subrr
#define lmpsub (long)mpsub
#define lmulss (long)mulss
#define lmulsi (long)mulsi
#define lmulsr (long)mulsr
#define lmulis (long)mulis
#define lmulrs (long)mulrs
#define lmulii (long)mulii
#define lmulir (long)mulir
#define lmulrr (long)mulrr
#define lmpmul (long)mpmul
#define ldivsi (long)divsi
#define ldivis (long)divis
#define ldivsr (long)divsr
#define ldivrs (long)divrs
#define ldivii (long)divii
#define ldivir (long)divir
#define ldivri (long)divri
#define ldivrr (long)divrr
#define lmpdiv (long)mpdiv
#define lmodii (long)modii
#define lresii (long)resii
#define ldvmdii (long)dvmdii
#define ldvmdsi (long)dvmdsi
#define ldvmdis (long)dvmdis
#define ltree (long)gettree
#define lgen (long)getgen
#define lcopy (long)gcopy
#define lclone (long)gclone
#define lgetg (long)cgetg
#define lgetp (long)cgetp
#define laddpex (long)gaddpex
#define lgreffe (long)greffe
#define lopsg2 (long)gopsg2
#define lopgs2 (long)gopgs2
#define lco8 (long)co8
#define lneg (long)gneg
#define labs (long)gabs
#define lmax (long)gmax
#define lmin (long)gmin
#define ladd (long)gadd
#define lsub (long)gsub
#define lmul (long)gmul
#define ldiv (long)gdiv
#define linv (long)ginv
#define lmod (long)gmod
#define ldivmod (long)gdivmod
#define lshift (long)gshift
#define lmul2n (long)gmul2n
#define lpuigs (long)gpuigs
#define lpui (long)gpui
#define lsubst (long)gsubst
#define lderiv (long)deriv
#define linteg (long)integ
#define lrecip (long)recip
#define lceil (long)gceil
#define lfloor (long)gfloor
#define lround (long)ground
#define lcvtoi (long)gcvtoi
#define lrndtoi (long)grndtoi
#define lfrac (long)gfrac
#define ltrunc (long)gtrunc
#define lconcat (long)concat
#define lnorm (long)gnorm
#define lnorml2 (long)gnorml2
#define lconj (long)gconj
#define lreal (long)greal
#define limag (long)gimag
#define lmppi (long)mppi
#define lmpeuler (long)mpeuler
#define lmpsqrt (long)mpsqrt
#define lsqrt (long)gsqrt
#define lmpexp1 (long)mpexp1
#define lmpexp (long)mpexp
#define lexp (long)gexp
#define lmplog (long)mplog
#define llog (long)glog
#define lmpsc1 (long)mpsc1
#define lmpcos (long)mpcos
#define lcos (long)gcos
#define lmpsin (long)mpsin
#define lsin (long)gsin
#define lmpaut (long)mpaut
#define lmptan (long)mptan
#define ltan (long)gtan
#define lmpatan (long)mpatan
#define latan (long)gatan
#define lmpasin (long)mpasin
#define lasin (long)gasin
#define lmpacos (long)mpacos
#define lacos (long)gacos
#define lmpch (long)mpch
#define lch (long)gch
#define lmpsh (long)mpsh
#define lsh (long)gsh
#define lmpth (long)mpth
#define lth (long)gth
#define lmpath (long)mpath
#define lath (long)gath
#define lmpash (long)mpash
#define lash (long)gash
#define lmpach (long)mpach
#define lach (long)gach
#define lmpgamma (long)mpgamma
#define lgamma (long)ggamma
#define lgamd (long)ggamd
#define lmppsi (long)mppsi
#define lpsi (long)gpsi
#define lmpgamd (long)mpgamd
#define larg (long)garg
#define lsqr (long)gsqr
#define ltrans (long)gtrans
#define lscalmat (long)gscalmat
#define lscalsmat (long)gscalsmat
#define laddmat (long)gaddmat
#define laddsmat (long)gaddsmat
#define lgauss (long)gauss
#define linvmat (long)invmat
#define linvmulmat (long)invmulmat
#define ldet (long)det
#define ldet2 (long)det2
#define lcaract (long)caract
#define lcaradj (long)caradj
#define ladj (long)adj
#define ltrace (long)trace
#define lassmat (long)assmat
#define lscal (long)gscal
#define linvmod (long)ginvmod
#define lred (long)gred
#define ldeuc (long)gdeuc
#define lres (long)gres
#define ldivres (long)poldivres
#define lpoleval (long)poleval
#define lroots (long)roots
#define lgcd (long)ggcd
#define lpolgcd (long)polgcd
#define lcontent (long)content
#define lprimpart (long)primpart
#define lpsres (long)psres
#define lsubres (long)subres
#define ldiscsr (long)discsr
#define lquadpoly (long)quadpoly
#define lquadgen (long)quadgen
#define llegendre (long)legendre
#define ltchebi (long)tchebi
#define lhilb (long)hilb
#define lpasc (long)pasc
#define lprec (long)gprec
#define lbinome (long)binome
#define lracine (long)racine
#define lmppgcd (long)mppgcd
#define lmpfact (long)mpfact
#define lsfcont (long)sfcont
#define lbezout (long)bezout
#define lmpinvmod (long)mpinvmod
#define lpuissmodulo (long)puissmodulo
#define lfibo (long)fibo
#define lchangevar (long)changevar
#define zero (long)gzero
#define un (long)gun
#define deux (long)gdeux
#define lhalf (long)ghalf
#define lpolx (long)polx
#define lpolun (long)polun
#define laddsg(s,y) (lopsg2(gadd,s,y))
#define laddgs(y,s) (lopsg2(gadd,s,y))
#define lsubsg(s,y) (lopsg2(gsub,s,y))
#define lsubgs(y,s) (lopgs2(gsub,y,s))
#define lmulsg(s,y) ((long)gmulsg(s,y))
#define lmulgs(y,s) ((long)gmulsg(s,y))
#define ldivsg(s,y) (lopsg2(gdiv,s,y))
#define ldivgs(x,s) ((long)gdivgs(x,s))
#define lmodsg(s,y) (lopsg2(gmod,s,y))
#define lmodgs(y,s) (lopgs2(gmod,y,s))
#define ldiventsg(s,y) (lopsg2(gdivent,s,y))
#define ldiventgs(y,s) (lopgs2(gdivent,y,s))
#define lminsg(s,y) (lopsg2(gmin,s,y))
#define lmings(y,s) (lopgs2(gmin,y,s))
#define lmaxsg(s,y) (lopsg2(gmax,s,y))
#define lmaxgs(y,s) (lopgs2(gmax,y,s))
#define mppiz(x) (gop0z(mppi,x))
#define mpeulerz(x) (gop0z(mpeuler,x))
#define mpsqrtz(x,y) (gop1z(mpsqrt,x,y))
#define mpexpz(x,y) (gop1z(mpexp,x,y))
#define mpexp1z(x,y) (gop1z(mpexp1,x,y))
#define mplogz(x,y) (gop1z(mplog,x,y))
#define mpcosz(x,y) (gop1z(mpcos,x,y))
#define mpsinz(x,y) (gop1z(mpsin,x,y))
#define autz(x,y) (gop1z(mpaut,x,y))
#define mptanz(x,y) (gop1z(mptan,x,y))
#define mpatanz(x,y) (gop1z(mpatan,x,y))
#define mpasinz(x,y) (gop1z(mpasin,x,y))
#define mpacosz(x,y) (gop1z(mpacos,x,y))
#define mpchz(x,y) (gop1z(mpch,x,y))
#define mpshz(x,y) (gop1z(mpsh,x,y))
#define mpthz(x,y) (gop1z(mpth,x,y))
#define mpathz(x,y) (gop1z(mpath,x,y))
#define mpashz(x,y) (gop1z(mpash,x,y))
#define mpachz(x,y) (gop1z(mpach,x,y))
#define mpgammaz(x,y) (gop1z(mpgamma,x,y))
#define mpargz(x,y,z) (gop2z(mparg,x,y,z))
#define mpfactz(s,y) (gops1z(mpfact,s,y))
#define gredz(x,y) (gop1z(gred,x,y))
#define gnegz(x,y) (gop1z(gneg,x,y))
#define gabsz(x,y) (gop1z(gabs,x,y))
#define gmaxz(x,y,z) (gop2z(gmax,x,y,z))
#define gminz(x,y,z) (gop2z(gmin,x,y,z))
#define gaddz(x,y,z) (gop2z(gadd,x,y,z))
#define gsubz(x,y,z) (gop2z(gsub,x,y,z))
#define gmulz(x,y,z) (gop2z(gmul,x,y,z))
#define gdivz(x,y,z) (gop2z(gdiv,x,y,z))
#define gdeucz(x,y,z) (gop2z(gdeuc,x,y,z))
#define gmodz(x,y,z) (gop2z(gmod,x,y,z))
#define gshiftz(x,s,z) (gops2gsz(gshift,x,s,z))
#define gmul2nz(x,s,z) (gops2gsz(gmul2n,x,s,z))
#define gaddsg(s,y) (gopsg2(gadd,s,y))
#define gaddgs(y,s) (gopsg2(gadd,s,y))
#define gsubsg(s,y) (gopsg2(gsub,s,y))
#define gsubgs(y,s) (gopgs2(gsub,y,s))
#define gcmpsg(s,y) (-opgs2(gcmp,y,s))
#define gcmpgs(y,s) (opgs2(gcmp,y,s))
#define gegalsg(s,y) (opgs2(gegal,y,s))
#define gegalgs(y,s) (opgs2(gegal,y,s))
#define gmulgs(y,s) (gmulsg(s,y))
#define gdivsg(s,y) (gopsg2(gdiv,s,y))
#define gdiventsg(s,y) (gopsg2(gdivent,s,y))
#define gdiventgs(y,s) (gopgs2(gdivent,y,s))
#define gmodsg(s,y) (gopsg2(gmod,s,y))
#define gmodgs(y,s) (gopgs2(gmod,y,s))
#define gminsg(s,y) (gopsg2(gmin,s,y))
#define gmings(y,s) (gopgs2(gmin,y,s))
#define gmaxsg(s,y) (gopsg2(gmax,s,y))
#define gmaxgs(y,s) (gopgs2(gmax,y,s))
#define gaddsgz(s,y,z) (gopsg2z(gadd,s,y,z))
#define gaddgsz(y,s,z) (gopsg2z(gadd,s,y,z))
#define gsubsgz(s,y,z) (gopsg2z(gsub,s,y,z))
#define gsubgsz(y,s,z) (gopgs2z(gsub,y,s,z))
#define gmulsgz(s,y,z) (gops2sgz(gmulsg,s,y,z))
#define gmulgsz(y,s,z) (gops2sgz(gmulsg,s,y,z))
#define gdivsgz(s,y,z) (gopsg2z(gdiv,s,y,z))
#define gdivgsz(y,s,z) (gops2gsz(gdivgs,y,s,z))
#define gdiventsgz(s,y,z) (gopsg2z(gdivent,s,y,z))
#define gdiventgsz(y,s,z) (gopgs2z(gdivent,y,s,z))
#define gmodsgz(s,y,z) (gopsg2z(gmod,s,y,z))
#define gmodgsz(y,s,z) (gopgs2z(gmod,y,s,z))
#define gminsgz(s,y,z) (gopsg2z(gmin,s,y,z))
#define gmingsz(y,s,z) (gopgs2z(gmin,y,s,z))
#define gmaxsgz(s,y,z) (gopsg2z(gmax,s,y,z))
#define gmaxgsz(y,s,z) (gopgs2z(gmax,y,s,z))
#define coeff(a,i,j) (*((long*)(*(a+(j)))+(i)))
#define coef1(a,i,j) (*((long*)(*(a+(j)+1))+(i)+1))
#define bern(i) (bernzone + (i)*(*(bernzone + 2)) + 3)
#define isonstack(x) (RAVYZARC=(GEN)(x),((RAVYZARC>=(GEN)bot)&&(RAVYZARC<(GEN)top)))
#define copyifstack(x) (RAVYZARC=(GEN)(x),((RAVYZARC>=(GEN)bot)&&(RAVYZARC<(GEN)top))?lcopy(RAVYZARC):(long)RAVYZARC)
#define odd(x) (x & 1)
#define mpodd(x) (signe(x) && odd(mant(x,lgef(x) - 2)))
/* alglin.c */
GEN gtrans(),gscalmat(),gscalsmat(),gaddmat(),gaddsmat();
GEN ker(),keri(),kerreel(),eigen(),hess(),carhess();
GEN gauss(),invmat(),det(),detreel(),det2(),caract(),caradj(),adj(),trace();
GEN assmat(),gnorm(),gnorml2(),gconj(),concat(),idmat();
GEN extract(),matextract(),gtomat(),invmulmat(),invmulmatreel(),invmatreel();
GEN sqred(),sqred1(),signat(),jacobi();
long rank();
/* anal.c */
GEN lisexpr(),readexpr(),lisseq(),readseq();
/* arith.c */
GEN racine(),mppgcd(),mpfact(),sfcont(),fc(),bezout(),chinois();
GEN mpinvmod(),puissmodulo(),fibo(),bigprem(),prime(),primes();
GEN phi(),decomp(),auxdecomp(),smallfact(),boundfact(),sumdiv(),sumdivk(),numbdiv();
GEN ellfacteur(),classno(),classno2(),classno3(),fundunit(),regula();
GEN compose(),sqcomp(),qf(),compose2(),sqcomp2(),qfred1(),primeform();
GEN binaire(),order(),gener(),divisors();
long kronecker(),krosg(),krogs(),kross(),kro8();
long mu(),omega(),bigomega(),hil(),carreparfait();
long isprime(),ispsp(),issquarefree(),isfundamental();
byteptr initprimes();
/* base.c */
GEN base(),discf(),hnf(),smith();
/* bibli1.c */
GEN tayl(),legendre(),tchebi(),hilb(),pasc(),laplace();
GEN gprec(),convol(),ggrando(),gconvsp(),gaminc();
GEN lll(),lllrat(),lllgram(),binome(),gscal();
GEN lindep(),lindep2(),algdep(),changevar(),ordred();
GEN polrecip(),reorder(),sort(),indexsort(),polred(),polsym();
/* bibli2.c */
GEN somme(),produit(),suminf(),prodinf(),prodinf1(),prodeuler();
GEN vecteur(),vvecteur(),matrice(),divsomme();
GEN qromb(),qromo(),qromi(),rombint();
GEN polint(),plot(),ploth(),ploth2(),zbrent(),sumalt(),sumpos();
GEN forpari(),forstep(),fordiv(),forprime(),ghell(),ghell2(),ghell3();
GEN initell(),zell(),coordch(),pointch();
GEN addell(),subell(),powell(),matell(),ordell(),apell(),apell1(),apell2();
int oncurve();
void eulsum();
/* es.c */
void sor(),brute(),texe();
/* gen1.c */
GEN gadd(),gsub(),gmul(),gdiv();
/* gen2.c gen3.c */
GEN gcopy(),gclone(),cgetg(),cgetp(),gaddpex();
GEN greffe(),gopsg2(),gopgs2(),co8(),cvtop(),compo(),gsqr();
GEN gneg(),gabs(),gmax(),gmin(),ginv(),denom(),numer(),lift();
GEN gmulsg(),gdivgs(),gmodulo(),gmodulcp();
GEN gmod(),gshift(),gmul2n(),gpuigs(),gpui();
GEN gsubst(),deriv(),integ(),recip(),ground(),gcvtoi(),grndtoi();
GEN gceil(),gfloor(),gfrac(),gtrunc(),gdivent(),gdiventres();
GEN gdivmod(),geval(),glt(),gle(),ggt(),gge(),geq(),gne();
GEN gand(),gor(),glength(),truecoeff();
GEN gtopoly(),gtoser(),gtovec(),dbltor();
void gop0z(),gop1z(),gop2z(),gops2gsz(),gops2sgz(),gops2ssz();
void gop3z(),gops1z(),gopsg2z(),gopgs2z();
long taille(),gexpo(),gsigne(),gcmp(),gtolong(),gegal();
long polegal(),tdeg(),ismonome(),iscomplex(),gvar(),ggval();
double rtodbl(),gtodouble();
/* init.c */
GEN newbloc(),geni();
long marklist();
void init(),killbloc(),newvalue(),killvalue();
void err(),recover(),changevalue();
/* polarit.c */
GEN ginvmod(),gred(),gdeuc(),gres(),poldivres();
GEN poleval(),roots(),ggcd(),gbezout(),vecbezout(),glcm();
GEN polgcd(),srgcd(),polgcdnun(),content(),primpart(),psres();
GEN factmod(),rootmod(),decpol(),factor(),factpol(),factpol2();
GEN subres(),discsr(),quadpoly(),quadgen(),bezoutpol(),polinvmod();
long sturm();
void gredsp();
/* trans.c */
GEN greal(),gimag(),teich(),agm(),palog();
GEN mpsqrt(),gsqrt(),mpexp1(),mpexp(),gexp(),logagm(),glogagm();
GEN mplog(),glog(),mpsc1(),mpcos(),gcos(),mpsin(),gsin();
GEN mpaut(),mptan(),gtan(),mpatan(),gatan(),mpasin(),gasin();
GEN mpacos(),gacos(),mparg(),mpch(),gch(),mpsh(),gsh();
GEN mpth(),gth(),mpath(),gath(),mpash(),gash();
GEN garg(),sarg(),mppsi(),gpsi(),transc(),kbessel(),hyperu();
GEN cxpsi(),jbesselh(),gzeta();
GEN kbessel2(),eint1(),gerfc(),eta(),jell(),wf2(),wf();
GEN incgam(),incgam1(),incgam2(),incgam3(),bernreal(),bernvec();
GEN mpach(),gach(),mpgamma(),cxgamma(),ggamma(),mpgamd(),ggamd(),mppi();
GEN mpeuler(),polylog(),dilog(),polylogd(),polylogp();
GEN theta(),thetanullk();
void constpi(),consteuler(),gsincos();
/* version.c */
GEN gerepilc();
void printversion();
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.