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/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
/* */
/* Fichier Include PARI */
/* */
/* commun a toutes les versions */
/* */
/* copyright Babecool */
/* */
/* */
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
typedef plong *GEN;
typedef unsigned plong ulong;
typedef struct entree {
char *name;
plong valence;
void *value;
struct entree *next;
} entree;
typedef unsigned char *byteptr;
/* Variables statiques communes :
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
extern plong prec,precdl;
extern GEN bernzone,gpi,geuler;
extern plong tglobal;
extern plong *ordvar,varchanged;
extern GEN polvar;
extern GEN RAVYZARC;
extern plong NUMFUNC;
extern entree fonctions[],*hashtable[];
extern plong lontyp[],lontyp2[];
extern jmp_buf environnement;
#ifndef IN_INIT_PARI
extern unsigned plong avma,bot,top;
#endif
extern GEN gzero,gnil,gun,gdeux,ghalf,gi;
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 plong nvar; /* numero de la prochaine inconnue */
extern plong 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 (plong)cgeti
#define lgetr (plong)cgetr
#define lpile (plong)gerepile
#define lstoi (plong)stoi
#define lnegi (plong)negi
#define lnegr (plong)negr
#define lmpneg (plong)mpneg
#define labsi (plong)absi
#define labsr (plong)absr
#define lmpabs (plong)mpabs
#define lmptrunc (plong)mptrunc
#define lmpent (plong)mpent
#define lshifts (plong)shifts
#define lshifti (plong)shifti
#define lshiftr (plong)shiftr
#define lmpshift (plong)mpshift
#define laddsi (plong)addsi
#define laddsr (plong)addsr
#define laddis (plong)addis
#define laddrs (plong)addrs
#define laddii (plong)addii
#define laddir (plong)addir
#define laddrr (plong)addrr
#define lmpadd (plong)mpadd
#define lsubsi (plong)subsi
#define lsubis (plong)subis
#define lsubsr (plong)subsr
#define lsubrs (plong)subrs
#define lsubii (plong)subii
#define lsubir (plong)subir
#define lsubri (plong)subri
#define lsubrr (plong)subrr
#define lmpsub (plong)mpsub
#define lmulss (plong)mulss
#define lmulsi (plong)mulsi
#define lmulsr (plong)mulsr
#define lmulis (plong)mulis
#define lmulrs (plong)mulrs
#define lmulii (plong)mulii
#define lmulir (plong)mulir
#define lmulrr (plong)mulrr
#define lmpmul (plong)mpmul
#define ldivsi (plong)divsi
#define ldivis (plong)divis
#define ldivsr (plong)divsr
#define ldivrs (plong)divrs
#define ldivii (plong)divii
#define ldivir (plong)divir
#define ldivri (plong)divri
#define ldivrr (plong)divrr
#define lmpdiv (plong)mpdiv
#define lmodii (plong)modii
#define lresii (plong)resii
#define ldvmdii (plong)dvmdii
#define ldvmdsi (plong)dvmdsi
#define ldvmdis (plong)dvmdis
#define ltree (plong)gettree
#define lgen (plong)getgen
#define lcopy (plong)gcopy
#define lclone (plong)gclone
#define lgetg (plong)cgetg
#define lgetp (plong)cgetp
#define laddpex (plong)gaddpex
#define lgreffe (plong)greffe
#define lopsg2 (plong)gopsg2
#define lopgs2 (plong)gopgs2
#define lco8 (plong)co8
#define lneg (plong)gneg
#define labs (plong)gabs
#define lmax (plong)gmax
#define lmin (plong)gmin
#define ladd (plong)gadd
#define lsub (plong)gsub
#define lmul (plong)gmul
#define ldiv (plong)gdiv
#define linv (plong)ginv
#define lmod (plong)gmod
#define ldivmod (plong)gdivmod
#define lshift (plong)gshift
#define lmul2n (plong)gmul2n
#define lpuigs (plong)gpuigs
#define lpui (plong)gpui
#define lsubst (plong)gsubst
#define lderiv (plong)deriv
#define linteg (plong)integ
#define lrecip (plong)recip
#define lceil (plong)gceil
#define lfloor (plong)gfloor
#define lround (plong)ground
#define lcvtoi (plong)gcvtoi
#define lrndtoi (plong)grndtoi
#define lfrac (plong)gfrac
#define ltrunc (plong)gtrunc
#define lconcat (plong)concat
#define lnorm (plong)gnorm
#define lnorml2 (plong)gnorml2
#define lconj (plong)gconj
#define lreal (plong)greal
#define limag (plong)gimag
#define lmppi (plong)mppi
#define lmpeuler (plong)mpeuler
#define lmpsqrt (plong)mpsqrt
#define lsqrt (plong)gsqrt
#define lmpexp1 (plong)mpexp1
#define lmpexp (plong)mpexp
#define lexp (plong)gexp
#define lmplog (plong)mplog
#define llog (plong)glog
#define lmpsc1 (plong)mpsc1
#define lmpcos (plong)mpcos
#define lcos (plong)gcos
#define lmpsin (plong)mpsin
#define lsin (plong)gsin
#define lmpaut (plong)mpaut
#define lmptan (plong)mptan
#define ltan (plong)gtan
#define lmpatan (plong)mpatan
#define latan (plong)gatan
#define lmpasin (plong)mpasin
#define lasin (plong)gasin
#define lmpacos (plong)mpacos
#define lacos (plong)gacos
#define lmpch (plong)mpch
#define lch (plong)gch
#define lmpsh (plong)mpsh
#define lsh (plong)gsh
#define lmpth (plong)mpth
#define lth (plong)gth
#define lmpath (plong)mpath
#define lath (plong)gath
#define lmpash (plong)mpash
#define lash (plong)gash
#define lmpach (plong)mpach
#define lach (plong)gach
#define lmpgamma (plong)mpgamma
#define lgamma (plong)ggamma
#define lgamd (plong)ggamd
#define lmppsi (plong)mppsi
#define lpsi (plong)gpsi
#define lmpgamd (plong)mpgamd
#define larg (plong)garg
#define lsqr (plong)gsqr
#define ltrans (plong)gtrans
#define lscalmat (plong)gscalmat
#define lscalsmat (plong)gscalsmat
#define laddmat (plong)gaddmat
#define laddsmat (plong)gaddsmat
#define lgauss (plong)gauss
#define linvmat (plong)invmat
#define linvmulmat (plong)invmulmat
#define ldet (plong)det
#define ldet2 (plong)det2
#define lcaract (plong)caract
#define lcaradj (plong)caradj
#define ladj (plong)adj
#define ltrace (plong)trace
#define lassmat (plong)assmat
#define lscal (plong)gscal
#define linvmod (plong)ginvmod
#define lred (plong)gred
#define ldeuc (plong)gdeuc
#define lres (plong)gres
#define ldivres (plong)poldivres
#define lpoleval (plong)poleval
#define lroots (plong)roots
#define lgcd (plong)ggcd
#define lpolgcd (plong)polgcd
#define lcontent (plong)content
#define lprimpart (plong)primpart
#define lpsres (plong)psres
#define lsubres (plong)subres
#define ldiscsr (plong)discsr
#define lquadpoly (plong)quadpoly
#define lquadgen (plong)quadgen
#define llegendre (plong)legendre
#define ltchebi (plong)tchebi
#define lhilb (plong)hilb
#define lpasc (plong)pasc
#define lprec (plong)gprec
#define lbinome (plong)binome
#define lracine (plong)racine
#define lmppgcd (plong)mppgcd
#define lmpfact (plong)mpfact
#define lsfcont (plong)sfcont
#define lbezout (plong)bezout
#define lmpinvmod (plong)mpinvmod
#define lpuissmodulo (plong)puissmodulo
#define lfibo (plong)fibo
#define lchangevar (plong)changevar
#define zero (plong)gzero
#define un (plong)gun
#define deux (plong)gdeux
#define lhalf (plong)ghalf
#define lpolx (plong)polx
#define lpolun (plong)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) ((plong)gmulsg(s,y))
#define lmulgs(y,s) ((plong)gmulsg(s,y))
#define ldivsg(s,y) (lopsg2(gdiv,s,y))
#define ldivgs(x,s) ((plong)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) (*((plong*)(*(a+(j)))+(i)))
#define coef1(a,i,j) (*((plong*)(*(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):(plong)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();
plong 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();
plong kronecker(),krosg(),krogs(),kross(),kro8();
plong mu(),omega(),bigomega(),hil(),carreparfait();
plong 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();
plong taille(),gexpo(),gsigne(),gcmp(),gtolong(),gegal();
plong polegal(),tdeg(),ismonome(),iscomplex(),gvar(),ggval();
double rtodbl(),gtodouble();
/* init.c */
GEN newbloc(),geni();
plong 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();
plong 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.