File: [local] / OpenXM_contrib / pari / src / modules / Attic / galois.c (download)
Revision 1.1.1.1 (vendor branch), Sun Jan 9 17:35:33 2000 UTC (24 years, 5 months ago) by maekawa
Branch: PARI_GP
CVS Tags: maekawa-ipv6, VERSION_2_0_17_BETA, RELEASE_20000124, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, RELEASE_1_1_3, RELEASE_1_1_2
Changes since 1.1: +0 -0
lines
Import PARI/GP 2.0.17 beta.
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/**************************************************************/
/* */
/* Galois group for degree between 8 and 11 (included) */
/* */
/**************************************************************/
/* $Id: galois.c,v 1.1.1.1 1999/09/16 13:48:11 karim Exp $ */
#include "pari.h"
#ifndef WINCE
# include <fcntl.h>
#endif
#define NMAX 11 /* maximum degree */
typedef char *OBJ;
typedef OBJ *POBJ;
typedef OBJ PERM;
typedef POBJ GROUP;
typedef POBJ RESOLVANTE;
static long isin_G_H(GEN po, GEN *r, long n1, long n2);
static long N,CAR,PREC,PRMAX,TSCHMAX,coeff[9][10];
static char SID[] = { 0,1,2,3,4,5,6,7,8,9,10,11 };
static char* str_coset = GPDATADIR"/COS";
static char* str_resolv = GPDATADIR"/RES";
static long par_N, *par_vec;
static void
do_par(long k, long n, long m)
{
long i;
if (n<=0)
{
GEN p1 = new_chunk(par_N+1);
for (i=1; i<k ; i++) p1[i] = par_vec[i];
for ( ; i<=par_N; i++) p1[i] = 0;
return;
}
if (n<m) m=n;
for (i=1; i<=m; i++)
{
par_vec[k] = i;
do_par(k+1, n-i, i);
}
}
/* compute the partitions of m. T[0][0] = p(m) */
static long **
partitions(long n)
{
long av,av1,i, j = 1, l = n+1;
GEN T;
par_vec = new_chunk(l); par_N = n;
l = l*sizeof(long);
av = avma; do_par(1,n,n); av1 = avma;
T = new_chunk((av-av1)/l + 1);
for (i=av-l; i>=av1; i-=l) T[j++]=i;
if (DEBUGLEVEL > 7)
{
fprintferr("Partitions of %ld: p(%ld) = %ld\n",n,n,j-1);
for (i=1; i<j; i++)
{
fprintferr("i = %ld: ",i);
for (l=1; l<=n; l++)
fprintferr("%ld ",((long**)T)[i][l]);
fprintferr("\n"); flusherr();
}
}
T[0] = lgeti(1); ((long**)T)[0][0] = j-1;
return (long**)T;
}
/* affect to the permutation x the N arguments that follow */
static void
_aff(char *x,...)
{
va_list args; long i;
va_start(args,x); for (i=1; i<=N; i++) x[i] = va_arg(args,int);
va_end(args);
}
/* return an array of length |len| from the arguments (for galoismodulo) */
static GEN
_gr(long len,...)
{
va_list args;
long i, l = labs(len);
GEN x = new_chunk(l+1);
va_start(args,len); x[0] = len;
for (i=1; i<=l; i++) x[i] = va_arg(args,int);
va_end(args); return x;
}
/* create a permutation with the N arguments of the function */
static PERM
_cr(char a,...)
{
static char x[NMAX+1];
va_list args;
long i;
va_start(args, a); x[0] = N; x[1] = a;
for (i=2; i<=N; i++) x[i] = va_arg(args,int);
va_end(args); return x;
}
static PERM
permmul(PERM s1, PERM s2)
{
long i, n1 = s1[0];
PERM s3 = gpmalloc(n1+1);
for (i=1; i<=n1; i++) s3[i]=s1[(int)s2[i]];
s3[0]=n1; return s3;
}
static void
printperm(PERM perm)
{
long i, n = perm[0];
fprintferr("(");
for (i=1; i<=n; i++) fprintferr(" %d",perm[i]);
fprintferr(" )\n");
}
/* ranger dans l'ordre decroissant (quicksort) */
static void
ranger(long *t, long n)
{
long tpro,l,r,i,j;
l=1+n/2; r=n; tpro=t[1];
for(;;)
{
if (l>1) { l--; tpro=t[l]; }
else
{
tpro=t[r]; t[r]=t[1]; r--;
if (r==1) { t[1]=tpro; return; }
}
i=l;
for (j=i<<1; j<=r; j<<=1)
{
if (j < r && t[j] > t[j+1]) j++;
if (t[j] >= tpro) break;
t[i] = t[j]; i=j;
}
t[i]=tpro;
}
}
/* 0 if t1=t2, -1 if t1<t2, 1 if t1>t2 */
static long
compareupletlong(long *t1,long *t2)
{
long i;
for (i=1; i<=N; i++)
if (t1[i]!=t2[i]) return (t1[i] < t2[i])? -1: 1;
return 0;
}
/* return i if typ = TYP[i], 0 otherwise */
static long
numerotyp(long **TYP, long *galtyp)
{
long i, nb = TYP[0][0];
for (i=1; i<=nb; i++)
if (!compareupletlong(galtyp,TYP[i])) return i;
return 0;
}
static int
raye(long *g, long num)
{
long i, nb = labs(g[0]);
for (i=1; i<=nb; i++)
if (g[i] == num) return 0;
return 1;
}
/* we can never determine the group completely in there */
static long
rayergroup11(long num, long *gr)
{
long r = 0;
if (CAR)
switch(num)
{
case 2: case 5:
if (gr[3]) { gr[3]=0; r++; }
case 3: case 6: case 7:
if (gr[2]) { gr[2]=0; r++; }
case 4:
if (gr[1]) { gr[1]=0; r++; }
}
else
switch(num)
{
case 2: case 3:
if (gr[1]) { gr[1]=0; r++; }
}
return r;
}
static long
rayergroup(long **GR, long num, long *gr)
{
long i,nbgr,r;
if (!GR) return rayergroup11(num,gr);
nbgr = lg(GR); r = 0 ;
if (CAR)
{
for (i=1; i<nbgr; i++)
if (gr[i] && GR[i][0] < 0 && raye(GR[i],num)) { gr[i]=0; r++; }
}
else
{
for (i=1; i<nbgr; i++)
if (gr[i] && GR[i][0] > 0 && raye(GR[i],num)) { gr[i]=0; r++; }
}
return r;
}
static long
galmodp(GEN pol, GEN dpol, long **TYP, long *gr, long **GR)
{
long p = 0, i,k,l,n,nbremain,dtyp[NMAX+1];
byteptr d = diffptr;
GEN p1;
switch(N)
{
case 8: nbremain = CAR? 28: 22; break;
case 9: nbremain = CAR? 18: 16; break;
case 10: nbremain = CAR? 12: 33; break;
case 11: nbremain = CAR? 5: 3; break;
}
k = gr[0]; for (i=1; i<k; i++) gr[i]=1;
for (k=1; k<15; k++, d++)
{
p += *d; if (!*d) err(primer1);
if (smodis(dpol,p)) /* p does not divide dpol */
{
p1 = simplefactmod(pol,stoi(p));
p1 = (GEN)p1[1]; l = lg(p1);
for (i=1; i<l ; i++) dtyp[i] = itos((GEN)(p1[l-i]));
for ( ; i<=N; i++) dtyp[i] = 0;
ranger(dtyp,N); n = numerotyp(TYP,dtyp);
if (!n) return 1; /* only for N=11 */
nbremain -= rayergroup(GR,n,gr);
if (nbremain==1) return 1;
}
}
return 0;
}
static long
_aux(GEN z)
{
return signe(z)? ((expo(z)+165) >> TWOPOTBITS_IN_LONG) - lg(z)
: (expo(z)+101) >> TWOPOTBITS_IN_LONG;
}
static long
suffprec(GEN z)
{
long s,t;
if (typ(z)==t_COMPLEX)
{
s=_aux((GEN)z[1]);
t=_aux((GEN)z[2]); return (t>s)? t: s;
}
return _aux(z);
}
static void
preci(GEN *r, long p)
{
GEN x;
long d,i;
if (p>PRMAX) err(talker,"too large precision in preci()");
for (d=0; d<TSCHMAX; d++) for (i=1; i<=N; i++)
{
x = (GEN) r[d][i];
if (typ(x)==t_COMPLEX) { setlg(x[1],p); setlg(x[2],p); } else setlg(x,p);
}
}
static long
getpreci(GEN *r)
{
GEN x = (GEN)r[0][1];
return (typ(x)==t_COMPLEX)? lg(x[1]): lg(x);
}
static void
new_pol(GEN *r, long *a, long d)
{
long av,i,j;
GEN x, p1;
for (i=1; i<=N; i++)
{
av =avma; p1 = (GEN)r[0][i]; x = gaddsg(a[0], p1);
for (j=1; j<=d; j++) x = gaddsg(a[j], gmul(p1,x));
r[d][i] = (long) gerepileupto(av,x);
}
}
static void
rangeroots(GEN newr, GEN oldr)
{
long av = avma,i,j,k,z[NMAX+1],t[NMAX+1];
GEN diff,diff0;
for (i=1; i<=N; i++) t[i]=1;
for (i=1; i<=N; i++)
{
diff0 = gun;
for (j=1; j<=N; j++)
if (t[j])
{
diff = gabs(gsub((GEN)oldr[i], (GEN)newr[j]), PREC);
if (gcmp(diff,diff0) < 0) { diff0=diff; k=j; }
}
z[i]=newr[k]; t[k]=0;
}
avma=av; for (i=1; i<=N; i++) newr[i]=z[i];
}
/* clean up roots. If root is real replace it by its real part */
GEN
myroots(GEN p, long prec)
{
GEN y,x = roots(p,prec);
long i,lx = lg(x);
for (i=1; i<lx; i++)
{
y = (GEN)x[i];
if (signe(y[2])) break; /* remaining roots are complex */
x[i]=y[1]; /* root is real; take real part */
}
return x;
}
/* increase the roots accuracy */
static void
moreprec(GEN po, GEN *r, long pr)
{
if (DEBUGLEVEL) { fprintferr("$$$$$ New prec = %ld\n",pr); flusherr(); }
if (pr > PRMAX)
{ /* recompute roots */
GEN p1;
long d = PRMAX + 5;
PRMAX = (pr < d)? d: pr;
p1 = myroots(po,PRMAX); rangeroots(p1,*r); *r=p1;
for (d=1; d<TSCHMAX; d++) new_pol(r,coeff[d],d);
}
preci(r,pr);
}
#define setcard_obj(x,n) ((x)[0] = (char*)(n))
#define getcard_obj(x) ((long)((x)[0]))
/* allocate a list of m arrays of length n (index 0 is codeword) */
static POBJ
alloc_pobj(long n, long m)
{
long i, sz = (m+1)*sizeof(OBJ) + (n+1)*m;
POBJ g = (POBJ) gpmalloc(sz);
OBJ gpt = (OBJ) (g + (m+1));
for (i=1; i<=m; i++) { g[i] = gpt; gpt += (n+1); }
setcard_obj(g, m); return g;
}
/* swap args ! Return an empty RESOLVANTE */
#define allocresolv(n,m) alloc_pobj(m, n)
static GROUP
allocgroup(long n, long card)
{
GROUP gr = alloc_pobj(n,card);
long i;
for (i=1; i<=card; i++) gr[i][0]=(char)n;
return gr;
}
static char *
name(char *pre, long n, long n1, long n2, long no)
{
static char chn[128];
char ch[6];
sprintf(chn, "%s%ld_%ld_%ld", pre,n,n1,n2);
if (no) { sprintf(ch,"_%ld",no); strcat(chn, ch); }
return chn;
}
static long
galopen(char *s)
{
#ifdef WINCE
HANDLE h;
short ws[256];
MultiByteToWideChar(CP_ACP, 0, s, strlen(s)+1, ws, 256);
h = CreateFile(ws,GENERIC_READ,FILE_SHARE_READ,NULL,OPEN_EXISTING,FILE_ATTRIBUTE_NORMAL,NULL);
if (h == INVALID_HANDLE_VALUE)
err(talker, "galois files not available in this version, sorry");
if (DEBUGLEVEL > 3) msgtimer("opening %s", s);
return (long)h;
#else
long fd = open(s,O_RDONLY);
if (fd == -1)
err(talker,"galois files not available in this version, sorry");
if (DEBUGLEVEL > 3) msgtimer("opening %s",s);
return fd;
#endif
}
static char
bin(char c)
{
if (c>='0' && c<='9') c=c-'0';
else if (c>='A' && c<='Z') c=c-'A'+10;
else if (c>='a' && c<='z') c=c-'a'+36;
else err(talker,"incorrect value in bin()");
return c;
}
#define BUFFS 512
/* fill in g[i][j] (i<=n, j<=m) with (buffered) data from fd */
static void
read_obj(POBJ g, long fd, long n, long m)
{
char ch[BUFFS];
long i,j, k = BUFFS;
i = j = 1;
for(;;)
{
#ifdef WINCE
if (k==BUFFS) { DWORD chRead; ReadFile((HANDLE)fd, ch, BUFFS, &chRead, NULL); k=0; }
#else
if (k==BUFFS) { read(fd,ch,BUFFS); k=0; }
#endif
g[i][j++] = bin(ch[k++]);
if (j>m) { j=1; i++; if (i>n) break; }
}
#ifdef WINCE
CloseHandle((HANDLE)fd); if (DEBUGLEVEL > 3) msgtimer("read_object");
#else
close(fd); if (DEBUGLEVEL > 3) msgtimer("read_object");
#endif
}
#undef BUFFS
/* the first 8 bytes contain size data (possibly padded with \0) */
static GROUP
lirecoset(long n1, long n2, long n)
{
GROUP gr, grptr;
char c, ch[8];
long no,m,cardgr,fd;
#ifdef WINCE
long chRead;
if (n<11 || n1<8)
{
fd = galopen(name(str_coset, n, n1, n2, 0));
ReadFile((HANDLE)fd,&c,1, &chRead, NULL); m=bin(c); ReadFile((HANDLE)fd,&c,1, &chRead, NULL);
ReadFile((HANDLE)fd,ch,6, &chRead, NULL); cardgr=atol(ch); gr=allocgroup(m,cardgr);
read_obj(gr, fd,cardgr,m); return gr;
}
m = 11; cardgr = 45360;
gr = grptr = allocgroup(n, 8 * cardgr);
for (no=1; no<=8; no++)
{
fd = galopen(name(str_coset, n, n1, n2, no)); ReadFile((HANDLE)fd,ch,8, &chRead, NULL);
read_obj(grptr, fd,cardgr,m); grptr += cardgr;
}
return gr;
#else
if (n<11 || n1<8)
{
fd = galopen(name(str_coset, n, n1, n2, 0));
read(fd,&c,1); m=bin(c); read(fd,&c,1);
read(fd,ch,6); cardgr=atol(ch); gr=allocgroup(m,cardgr);
read_obj(gr, fd,cardgr,m); return gr;
}
m = 11; cardgr = 45360;
gr = grptr = allocgroup(n, 8 * cardgr);
for (no=1; no<=8; no++)
{
fd = galopen(name(str_coset, n, n1, n2, no)); read(fd,ch,8);
read_obj(grptr, fd,cardgr,m); grptr += cardgr;
}
return gr;
#endif
}
static RESOLVANTE
lireresolv(long n1, long n2, long n, long *nv, long *nm)
{
RESOLVANTE b;
char ch[5];
long fd;
#ifdef WINCE
long chRead;
fd = galopen(name(str_resolv, n, n1, n2, 0));
ReadFile((HANDLE)fd,ch,5, &chRead, NULL); *nm=atol(ch);
ReadFile((HANDLE)fd,ch,3, &chRead, NULL); *nv=atol(ch);
b = allocresolv(*nm,*nv);
read_obj(b, fd,*nm,*nv); return b;
#else
fd = galopen(name(str_resolv, n, n1, n2, 0));
read(fd,ch,5); *nm=atol(ch);
read(fd,ch,3); *nv=atol(ch);
b = allocresolv(*nm,*nv);
read_obj(b, fd,*nm,*nv); return b;
#endif
}
static GEN
monomial(GEN r, PERM bb, long nbv)
{
long i; GEN p1 = (GEN)r[(int)bb[1]];
for (i=2; i<=nbv; i++) p1 = gmul(p1, (GEN)r[(int)bb[i]]);
return p1;
}
static GEN
gpolynomial(GEN r, RESOLVANTE aa, long nbm, long nbv)
{
long i; GEN p1 = monomial(r,aa[1],nbv);
for (i=2; i<=nbm; i++) p1 = gadd(p1, monomial(r,aa[i],nbv));
return p1;
}
static void
zaux1(GEN *z, GEN *r)
{
GEN p2,p1;
p2=gsub(r[1],gadd(r[2],r[5]));
p2=gmul(p2,gsub(r[2],r[5]));
p1=gmul(p2,r[1]);
p2=gsub(r[3],gadd(r[2],r[4]));
p2=gmul(p2,gsub(r[4],r[2]));
p1=gadd(p1,gmul(p2,r[3]));
p2=gmul(r[5],gsub(r[4],r[5]));
z[1]=gadd(p1,gmul(p2,r[4]));
p2=gsub(r[1],gadd(r[3],r[4]));
p2=gmul(p2,gsub(r[3],r[4]));
p1=gmul(p2,r[1]);
p2=gsub(r[5],gadd(r[3],r[2]));
p2=gmul(p2,gsub(r[2],r[3]));
p1=gadd(p1,gmul(p2,r[5]));
p2=gmul(r[4],gsub(r[2],r[4]));
z[2]=gadd(p1,gmul(p2,r[2]));
}
static void
zaux(GEN *z, GEN *r)
{
zaux1(z, r); zaux1(z+2, r+5);
}
static GEN
gpoly(GEN rr, long n1, long n2)
{
GEN p1,p2,z[6], *r = (GEN*)rr; /* syntaxic kludge */
long i,j;
if (N==8)
{
if (n1==47 && n2==46)
{
p1=gsub(r[3],r[4]);
for (i=1; i<3; i++) for (j=i+1; j<5; j++) p1 = gmul(p1,gsub(r[i],r[j]));
for (i=5; i<8; i++) for (j=i+1; j<9; j++) p1 = gmul(p1,gsub(r[i],r[j]));
p2=r[1];
for (i=2; i<5; i++) p2=gadd(p2,r[i]);
for (i=5; i<9; i++) p2=gsub(p2,r[i]);
}
else /* n1==44 && n2==40 */
{
for (i=1; i<5; i++) z[i] = gadd(r[2*i-1],r[2*i]);
p1 = gsub(r[1],r[2]);
for (i=2; i<5; i++) p1 = gmul(p1,gsub(r[2*i-1],r[2*i]));
p2=gsub(z[3],z[4]);
for (i=1; i<3; i++) for (j=i+1; j<5; j++) p2 = gmul(p2,gsub(z[i],z[j]));
}
return gmul(p1,p2);
}
if (N==9)
{
if (n1==31 && n2==29)
{
p1=gsub(r[2],r[3]);
for (j=2; j<4; j++) p1 = gmul(p1,gsub(r[1],r[j]));
for (i=4; i<6; i++) for (j=i+1; j<7; j++) p1 = gmul(p1,gsub(r[i],r[j]));
p2 = gsub(r[8],r[9]);
for (j=8; j<10; j++) p2 = gmul(p2,gsub(r[7],r[j]));
}
else /* ((n1==34 && n2==31) || (n1=33 && n2==30)) */
{
p1=r[1]; for (i=2; i<4; i++) p1=gadd(p1,r[i]);
p2=r[4]; for (i=5; i<7; i++) p2=gadd(p2,r[i]);
p1=gmul(p1,p2);
p2=r[7]; for (i=8; i<10; i++) p2=gadd(p2,r[i]);
}
return gmul(p1,p2);
}
if (N==10)
{
if ((n1==45 && n2==43) || (n1==44 && n2==42))
{
p1=r[1]; for (i=2; i<6; i++) p1=gadd(p1,r[i]);
p2=r[6]; for (i=7; i<11; i++) p2=gadd(p2,r[i]);
return gmul(p1,p2);
}
else if ((n1==45 && n2==39) || (n1==44 && n2==37))
{
p1 = gadd(r[1],r[2]);
for (i=2; i<6; i++) p1 = gmul(p1,gadd(r[2*i-1],r[2*i]));
return p1;
}
else if ((n1==43 && n2==41) || (n1==33 && n2==27))
{
p1=gsub(r[4],r[5]);
for (i=1; i<4; i++) for (j=i+1; j<6; j++) p1=gmul(p1,gsub(r[i],r[j]));
p2=gsub(r[9],r[10]);
for (i=6; i<9; i++) for (j=i+1; j<11; j++) p2=gmul(p2,gsub(r[i],r[j]));
return gmul(p1,p2);
}
else if ((n1==43 && n2==33) || (n1==42 && n2==28) || (n1==41 && n2==27)
|| (n1==40 && n2==21))
{
p2=gadd(r[2],r[5]);
p2=gsub(p2,gadd(r[3],r[4]));
p1=gmul(p2,r[1]);
p2=gsub(r[3],gadd(r[4],r[5]));
p1=gadd(p1,gmul(p2,r[2]));
p2=gsub(r[4],r[5]);
p1=gadd(p1,gmul(p2,r[3]));
z[1]=gadd(p1,gmul(r[4],r[5]));
p2=gadd(r[7],r[10]);
p2=gsub(p2,gadd(r[8],r[9]));
p1=gmul(p2,r[6]);
p2=gsub(r[8],gadd(r[9],r[10]));
p1=gadd(p1,gmul(p2,r[7]));
p2=gsub(r[9],r[10]);
p1=gadd(p1,gmul(p2,r[8]));
z[2]=gadd(p1,gmul(r[9],r[10]));
return gadd(gsqr(z[1]), gsqr(z[2]));
}
else if (n1==41 && n2==40)
{
p1=gsub(r[4],r[5]);
for (i=1; i<4; i++) for (j=i+1; j<6; j++) p1 = gmul(p1,gsub(r[i],r[j]));
p2=gsub(r[9],r[10]);
for (i=6; i<9; i++) for (j=i+1; j<11; j++) p2 = gmul(p2,gsub(r[i],r[j]));
return gadd(p1,p2);
}
else if ((n1==41 && n2==22) || (n1==40 && n2==11) || (n1==17 && n2==5)
|| (n1==10 && n2==4) || (n1==9 && n2==3) || (n1==6 && n2==1))
{
p1=gadd(r[1],r[6]);
for (i=2; i<6; i++) p1=gmul(p1,gadd(r[i],r[i+5]));
return p1;
}
else if ((n1==39 && n2==38) || (n1==29 && n2==25))
{
for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
p1=gsub(r[1],r[2]);
for (i=2; i<6; i++) p1=gmul(p1,gsub(r[2*i-1],r[2*i]));
p2=gsub(z[4],z[5]);
for (i=1; i<4; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
return gmul(p1,p2);
}
else if ((n1==39 && n2==36) || (n1==37 && n2==34) || (n1==29 && n2==23)
|| (n1==24 && n2==15))
{
for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
p1=gsub(z[4],z[5]); p2=gmul(gsub(z[3],z[4]),gsub(z[3],z[5]));
for (i=1; i<3; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
return gmul(p1,p2);
}
else if ((n1==39 && n2==29) || (n1==38 && n2==25) || (n1==37 && n2==24)
|| (n1==36 && n2==23) || (n1==34 && n2==15))
{
for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
p2=gadd(z[2],z[5]); p2=gsub(p2,gadd(z[3],z[4]));
p1=gmul(p2,z[1]);
p2=gsub(z[3],gadd(z[4],z[5]));
p1=gadd(p1,gmul(p2,z[2]));
p2=gsub(z[4],z[5]);
p1=gadd(p1,gmul(p2,z[3]));
p1=gadd(p1,gmul(z[4],z[5])); return gsqr(p1);
}
else if ((n1==39 && n2==22) || (n1==38 && n2==12) || (n1==36 && n2==11)
|| (n1==29 && n2== 5) || (n1==25 && n2== 4) || (n1==23 && n2== 3)
|| (n1==16 && n2== 2) || (n1==14 && n2== 1))
{
p1=r[1]; for (i=2; i<6; i++) p1=gadd(p1,r[2*i-1]);
p2=r[2]; for (i=2; i<6; i++) p2=gadd(p2,r[2*i]);
return gmul(p1,p2);
}
else if (n1==28 && n2==18)
{
zaux(z, r);
p1=gmul(z[1],gsub(z[3],z[4]));
p2=gmul(z[2],gadd(z[3],z[4])); return gadd(p1,p2);
}
else if (n1==27 && n2==20)
{
zaux(z, r); p1=gmul(z[1],z[3]); p2=gmul(z[2],z[4]);
p1 = gsub(p1,p2); p2=r[1];
for (i=2; i<6 ; i++) p2=gadd(p2,r[i]);
for ( ; i<11; i++) p2=gsub(p2,r[i]);
return gmul(p1,p2);
}
else if (n1==27 && n2==19)
{
zaux(z, r); p1=gmul(z[1],z[3]); p2=gmul(z[2],z[4]);
return gsub(p1,p2);
}
else if ((n1==27 && n2==17) || (n1==21 && n2==9))
{
zaux(z, r); p1=gmul(z[1],z[3]); p2=gmul(z[2],z[4]);
return gadd(p1,p2);
}
else if (n1==23 && n2==16)
{
for (i=1; i<6; i++) z[i]=gadd(r[2*i-1],r[2*i]);
p1=gsub(z[1],gadd(z[2],z[5])); p1=gmul(p1,gsub(z[2],z[5]));
p2=gmul(p1,z[1]); p1=gsub(z[3],gadd(z[2],z[4]));
p1=gmul( p1,gsub(z[4],z[2])); p2=gadd(p2,gmul(p1,z[3]));
p1=gmul(z[5],gsub(z[4],z[5])); p2=gadd(p2,gmul(p1,z[4]));
p1=gsub(r[1],r[2]);
for (i=2; i<6; i++) p1=gmul(p1,gsub(r[2*i-1],r[2*i]));
return gmul(p1,p2);
}
else if (n1==22 && n2==12)
{
for (i=1; i<6; i++) z[i]=gadd(r[i],r[i+5]);
p1=gsub(r[1],r[6]);
for (i=2; i<6; i++) p1=gmul(p1,gsub(r[i],r[i+5]));
p2=gsub(z[4],z[5]);
for (i=1; i<4; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
return gmul(p1,p2);
}
else if ((n1==22 && n2==11) || (n1==5 && n2==3))
{
for (i=1; i<6; i++) z[i]=gadd(r[i],r[i+5]);
p1=gsub(z[4],z[5]); p2=gmul(gsub(z[3],z[4]),gsub(z[3],z[5]));
for (i=1; i<3; i++) for (j=i+1; j<6; j++) p2=gmul(p2,gsub(z[i],z[j]));
return gmul(p1,p2);
}
else if ((n1==22 && n2==5) || (n1==12 && n2==4) || (n1==11 && n2==3))
{
for (i=1; i<6; i++) z[i]=gadd(r[i],r[i+5]);
p2=gadd(z[2],z[5]); p2=gsub(p2,gadd(z[3],z[4])); p1=gmul(p2,z[1]);
p2=gsub(z[3],gadd(z[4],z[5])); p1=gadd(p1,gmul(p2,z[2]));
p2=gsub(z[4],z[5]);
p1=gadd(p1,gmul(p2,z[3])); p1=gadd(p1,gmul(z[4],z[5]));
return gsqr(p1);
}
else if (n1==21 && n2==10)
{
zaux(z, r); p1=gmul(z[1],z[4]); p2=gmul(z[2],z[3]);
return gsub(p1,p2);
}
}
err(talker,"indefinite invariant polynomial in gpoly()");
return NULL; /* not reached */
}
static void
tschirn(GEN po, GEN *r, long pr)
{
long av0 = avma, a[NMAX],v,i,d;
GEN h,u;
d = TSCHMAX+1;
if (d>=N)
err(talker,"too large degree for Tschirnhaus transformation in tschirn");
if (DEBUGLEVEL)
{
fprintferr("\n$$$$$ Tschirnhaus transformation of degree %ld: $$$$$\n",d);
flusherr();
}
v=varn(po); h=polun[v];
do
{
avma = av0;
for (i=0; i<d; i++)
{
a[i] = ((mymyrand()>>4) & 7) + 1;
h = gaddsg(a[i],gmul(polx[v],h));
}
u=caract(gmodulcp(h,po),v);
}
while (lgef(srgcd(u,deriv(u,v))) > 3);
if (DEBUGLEVEL>2) { bruterr(u,'g',-1); fprintferr("\n"); flusherr(); }
avma = av0; d = TSCHMAX;
for (i=0; i<=d; i++) coeff[d][i] = a[i];
preci(r,PRMAX); r[d]=cgetg(N+1,t_VEC);
new_pol(r,a,d); preci(r,pr); TSCHMAX++;
}
static GEN
get_pol_perm(PERM S1, PERM S2, GEN rr, RESOLVANTE a,
long nbm, long nbv)
{
static long r[NMAX+1];
long i;
for (i=1; i<=N; i++) r[i] = rr[(int)S1[(int)S2[i]]];
return a? gpolynomial(r,a,nbm,nbv): gpoly(r,nbm,nbv);
}
static void
dbg_rac(long nri,long nbracint,long numi[],GEN racint[],long multi[])
{
long k;
if (nbracint>nri+1)
fprintferr(" there are %ld rational integer roots:\n",nbracint-nri);
else if (nbracint==nri+1)
fprintferr(" there is 1 rational integer root:\n");
else
fprintferr(" there is no rational integer root.\n");
for (k=nri+1; k<=nbracint; k++)
{
fprintferr(" number%2ld: ",numi[k]);
bruterr(racint[k],'g',-1); fprintferr(", order %ld.\n",multi[k]);
}
flusherr();
}
static GEN
is_int(GEN g)
{
GEN gint,p1;
long av;
if (typ(g) == t_COMPLEX)
{
p1 = (GEN)g[2];
if (signe(p1) && expo(p1) >= - (bit_accuracy(lg(p1))>>1)) return NULL;
g = (GEN)g[1];
}
gint = ground(g); av=avma; p1 = subri(g,gint);
if (signe(p1) && expo(p1) >= - (bit_accuracy(lg(p1))>>1)) return NULL;
avma=av; return gint;
}
static PERM
isin_end(PERM S, PERM uu, PERM s0, GEN gpol, long av1)
{
PERM vv = permmul(S,uu), ww = permmul(vv,s0);
if (DEBUGLEVEL)
{
fprintferr(" testing roots reordering: ");
bruterr(gpol,'g',-1); flusherr();
}
free(vv); avma = av1; return ww;
}
#define M 2521
/* return NULL if not included, the permutation of the roots otherwise */
static PERM
check_isin(GEN po,GEN *r,long nbm,long nbv, POBJ a, POBJ tau, POBJ ss, PERM s0)
{
long pr = PREC, av1 = avma, av2,nogr,nocos,init,i,j,k,l,d,nrm,nri,sp;
long nbgr,nbcos,nbracint,nbrac,lastnbri,lastnbrm;
static long numi[M],numj[M],lastnum[M],multi[M],norac[M],lastnor[M];
GEN rr,ro,roint,racint[M];
PERM uu;
nbcos = getcard_obj(ss);
nbgr = getcard_obj(tau);
lastnbri = lastnbrm = -1; /* for lint */
for (nogr=1; nogr<=nbgr; nogr++)
{
if (DEBUGLEVEL)
{ fprintferr(" ----> Group # %ld/%ld:\n",nogr,nbgr); flusherr(); }
init = 0;
for (d=1; ; d++)
{
if (d > 1)
{
if (DEBUGLEVEL)
{
fprintferr(" all integer roots are double roots\n");
fprintferr(" Working with polynomial #%ld:\n", d); flusherr();
}
if (d > TSCHMAX) { tschirn(po,r,pr); av1 = avma; }
}
if (!init)
{
init = 1;
for(;;)
{
av2=avma; rr = r[d-1]; nbrac = nbracint = 0;
for (nocos=1; nocos<=nbcos; nocos++)
{
ro = get_pol_perm(tau[nogr], ss[nocos], rr,a,nbm,nbv);
sp = suffprec(ro); if (sp > 0) break;
roint = is_int(ro);
if (roint)
{
nbrac++;
if (nbrac >= M)
{
err(warner, "more than %ld rational integer roots\n", M);
avma = av1; init = 0; break;
}
for (j=1; j<=nbracint; j++)
if (gegal(roint,racint[j])) { multi[j]++; break; }
if (j > nbracint)
{
nbracint = j; multi[j]=1; numi[j]=nocos;
racint[j] = gerepileupto(av2,roint); av2=avma;
}
numj[nbrac]=nocos; norac[nbrac]=j;
}
avma=av2;
}
if (sp <= 0) break;
avma = av1; pr+=sp; moreprec(po,r,pr); av1 = avma;
}
if (!init) continue;
if (DEBUGLEVEL) dbg_rac(0,nbracint,numi,racint,multi);
for (i=1; i<=nbracint; i++)
if (multi[i]==1)
{
uu = ss[numi[i]];
ro = DEBUGLEVEL? get_pol_perm(SID,uu,rr,a,nbm,nbv): (GEN)NULL;
return isin_end(tau[nogr], uu, s0, ro, av1);
}
}
else
{
nrm = nri = 0;
for (l=1; l<=lastnbri; l++)
{
for(;;)
{
av2=avma; rr = r[d-1]; nbrac=nrm; nbracint=nri;
for (k=1; k<=lastnbrm; k++)
if (lastnor[k]==l)
{
nocos = lastnum[k];
ro = get_pol_perm(tau[nogr], ss[nocos], rr,a,nbm,nbv);
sp = suffprec(ro); if (sp > 0) break;
roint = is_int(ro);
if (roint)
{
nbrac++;
for (j=nri+1; j<=nbracint; j++)
if (gegal(roint,racint[j])) { multi[j]++; break; }
if (j > nbracint)
{
nbracint = j; multi[j]=1; numi[j]=nocos;
racint[j] = gerepileupto(av2,roint); av2=avma;
}
numj[nbrac]=nocos; norac[nbrac]=j;
}
avma=av2;
}
if (sp <= 0) break;
avma = av1; pr+=sp; moreprec(po,r,pr); av1 = avma;
}
if (DEBUGLEVEL) dbg_rac(nri,nbracint,numi,racint,multi);
for (i=nri+1; i<=nbracint; i++)
if (multi[i]==1)
{
uu = ss[numi[i]];
ro = DEBUGLEVEL? get_pol_perm(SID,uu,rr,a,nbm,nbv): (GEN)NULL;
return isin_end(tau[nogr], uu, s0, ro, av1);
}
avma = av1; nri=nbracint; nrm=nbrac;
}
}
avma = av1; if (!nbracint) break;
lastnbri=nbracint; lastnbrm=nbrac;
for (j=1; j<=nbrac; j++)
{ lastnum[j]=numj[j]; lastnor[j]=norac[j]; }
}
}
return NULL;
}
#undef M
/* BIBLIOTHEQUE POUR LE DEGRE 8 */
static long
galoisprim8(GEN po, GEN *r)
{
long rep;
/* PRIM_8_1: */
rep=isin_G_H(po,r,50,43);
if (rep) return CAR? 37: 43;
/* PRIM_8_2: */
if (!CAR) return 50;
/* PRIM_8_3: */
rep=isin_G_H(po,r,49,48);
if (!rep) return 49;
/* PRIM_8_4: */
rep=isin_G_H(po,r,48,36);
if (!rep) return 48;
/* PRIM_8_5: */
rep=isin_G_H(po,r,36,25);
return rep? 25: 36;
}
static long
galoisimpodd8(GEN po, GEN *r, long nh)
{
long rep;
/* IMPODD_8_1: */
if (nh!=47) goto IMPODD_8_6;
/* IMPODD_8_2: */
rep=isin_G_H(po,r,47,46);
if (!rep) goto IMPODD_8_5;
/* IMPODD_8_4: */
rep=isin_G_H(po,r,46,28);
if (rep) goto IMPODD_8_7; else return 46;
IMPODD_8_5:
rep=isin_G_H(po,r,47,35);
if (rep) goto IMPODD_8_9; else return 47;
IMPODD_8_6:
rep=isin_G_H(po,r,44,40);
if (rep) goto IMPODD_8_10; else goto IMPODD_8_11;
IMPODD_8_7:
rep=isin_G_H(po,r,28,21);
if (rep) return 21; else goto IMPODD_8_33;
IMPODD_8_9:
rep=isin_G_H(po,r,35,31);
if (rep) goto IMPODD_8_13; else goto IMPODD_8_14;
IMPODD_8_10:
rep=isin_G_H(po,r,40,26);
if (rep) goto IMPODD_8_15; else goto IMPODD_8_16;
IMPODD_8_11:
rep=isin_G_H(po,r,44,38);
if (rep) goto IMPODD_8_17; else goto IMPODD_8_18;
IMPODD_8_12:
rep=isin_G_H(po,r,16,7);
if (rep) goto IMPODD_8_19; else return 16;
IMPODD_8_13:
rep=isin_G_H(po,r,31,21);
return rep? 21: 31;
IMPODD_8_14:
rep=isin_G_H(po,r,35,30);
if (rep) goto IMPODD_8_34; else goto IMPODD_8_20;
IMPODD_8_15:
rep=isin_G_H(po,r,26,16);
if (rep) goto IMPODD_8_12; else goto IMPODD_8_21;
IMPODD_8_16:
rep=isin_G_H(po,r,40,23);
if (rep) goto IMPODD_8_22; else return 40;
IMPODD_8_17:
rep=isin_G_H(po,r,38,31);
if (rep) goto IMPODD_8_13; else return 38;
IMPODD_8_18:
rep=isin_G_H(po,r,44,35);
if (rep) goto IMPODD_8_9; else return 44;
IMPODD_8_19:
rep=isin_G_H(po,r,7,1);
return rep? 1: 7;
IMPODD_8_20:
rep=isin_G_H(po,r,35,28);
if (rep) goto IMPODD_8_7; else goto IMPODD_8_23;
IMPODD_8_21:
rep=isin_G_H(po,r,26,17);
if (rep) goto IMPODD_8_24; else goto IMPODD_8_25;
IMPODD_8_22:
rep=isin_G_H(po,r,23,8);
if (rep) goto IMPODD_8_26; else return 23;
IMPODD_8_23:
rep=isin_G_H(po,r,35,27);
if (rep) goto IMPODD_8_27; else goto IMPODD_8_28;
IMPODD_8_24:
rep=isin_G_H(po,r,17,7);
if (rep) goto IMPODD_8_19; else return 17;
IMPODD_8_25:
rep=isin_G_H(po,r,26,15);
if (rep) goto IMPODD_8_29; else return 26;
IMPODD_8_26:
rep=isin_G_H(po,r,8,1);
return rep? 1: 8;
IMPODD_8_27:
rep=isin_G_H(po,r,27,16);
if (rep) goto IMPODD_8_12; else return 27;
IMPODD_8_28:
rep=isin_G_H(po,r,35,26);
if (rep) goto IMPODD_8_15; else return 35;
IMPODD_8_29:
rep=isin_G_H(po,r,15,7);
if (rep) goto IMPODD_8_19;
/* IMPODD_8_30: */
rep=isin_G_H(po,r,15,6);
if (!rep) goto IMPODD_8_32;
/* IMPODD_8_31: */
rep=isin_G_H(po,r,6,1);
return rep? 1: 6;
IMPODD_8_32:
rep=isin_G_H(po,r,15,8);
if (rep) goto IMPODD_8_26; else return 15;
IMPODD_8_33:
rep=isin_G_H(po,r,28,16);
if (rep) goto IMPODD_8_12; else return 28;
IMPODD_8_34:
rep=isin_G_H(po,r,30,21);
return rep? 21: 30;
}
static long
galoisimpeven8(GEN po, GEN *r, long nh)
{
long rep;
/* IMPEVEN_8_1: */
if (nh!=45) goto IMPEVEN_8_6;
/* IMPEVEN_8_2: */
rep=isin_G_H(po,r,45,42);
if (!rep) goto IMPEVEN_8_5;
/* IMPEVEN_8_4: */
rep=isin_G_H(po,r,42,34);
if (rep) goto IMPEVEN_8_7; else goto IMPEVEN_8_8;
IMPEVEN_8_5:
rep=isin_G_H(po,r,45,41);
if (rep) goto IMPEVEN_8_9; else return 45;
IMPEVEN_8_6:
rep=isin_G_H(po,r,39,32);
if (rep) goto IMPEVEN_8_10; else goto IMPEVEN_8_11;
IMPEVEN_8_7:
rep=isin_G_H(po,r,34,18);
if (rep) goto IMPEVEN_8_21; else goto IMPEVEN_8_45;
IMPEVEN_8_8:
rep=isin_G_H(po,r,42,33);
if (rep) goto IMPEVEN_8_14; else return 42;
IMPEVEN_8_9:
rep=isin_G_H(po,r,41,34);
if (rep) goto IMPEVEN_8_7; else goto IMPEVEN_8_15;
IMPEVEN_8_10:
rep=isin_G_H(po,r,32,22);
if (rep) goto IMPEVEN_8_16; else goto IMPEVEN_8_17;
IMPEVEN_8_11:
rep=isin_G_H(po,r,39,29);
if (rep) goto IMPEVEN_8_18; else goto IMPEVEN_8_19;
IMPEVEN_8_12:
rep=isin_G_H(po,r,14,4);
return rep? 4: 14;
IMPEVEN_8_14:
rep=isin_G_H(po,r,33,18);
if (rep) goto IMPEVEN_8_21; else goto IMPEVEN_8_22;
IMPEVEN_8_15:
rep=isin_G_H(po,r,41,33);
if (rep) goto IMPEVEN_8_14; else goto IMPEVEN_8_23;
IMPEVEN_8_16:
rep=isin_G_H(po,r,22,11);
if (rep) goto IMPEVEN_8_24; else goto IMPEVEN_8_25;
IMPEVEN_8_17:
rep=isin_G_H(po,r,32,13);
if (rep) goto IMPEVEN_8_26; else goto IMPEVEN_8_27;
IMPEVEN_8_18:
rep=isin_G_H(po,r,29,22);
if (rep) goto IMPEVEN_8_16; else goto IMPEVEN_8_28;
IMPEVEN_8_19:
rep=isin_G_H(po,r,39,24);
if (rep) goto IMPEVEN_8_29; else return 39;
IMPEVEN_8_20:
rep=isin_G_H(po,r,9,4);
if (rep) return 4; else goto IMPEVEN_8_30;
IMPEVEN_8_21:
rep=isin_G_H(po,r,18,10);
if (rep) goto IMPEVEN_8_31; else goto IMPEVEN_8_32;
IMPEVEN_8_22:
rep=isin_G_H(po,r,33,13);
if (rep) goto IMPEVEN_8_26; else return 33;
IMPEVEN_8_23:
rep=isin_G_H(po,r,41,29);
if (rep) goto IMPEVEN_8_18; else goto IMPEVEN_8_33;
IMPEVEN_8_24:
rep=isin_G_H(po,r,11,5);
if (rep) return 5; else goto IMPEVEN_8_34;
IMPEVEN_8_25:
rep=isin_G_H(po,r,22,9);
if (rep) goto IMPEVEN_8_20; else return 22;
IMPEVEN_8_26:
rep=isin_G_H(po,r,13,3);
return rep? 3: 13;
IMPEVEN_8_27:
rep=isin_G_H(po,r,32,12);
if (rep) goto IMPEVEN_8_35; else return 32;
IMPEVEN_8_28:
rep=isin_G_H(po,r,29,20);
if (rep) goto IMPEVEN_8_36; else goto IMPEVEN_8_37;
IMPEVEN_8_29:
rep=isin_G_H(po,r,24,14);
if (rep) goto IMPEVEN_8_12; else goto IMPEVEN_8_38;
IMPEVEN_8_30:
rep=isin_G_H(po,r,9,3);
if (rep) return 3; else goto IMPEVEN_8_39;
IMPEVEN_8_31:
rep=isin_G_H(po,r,10,2);
return rep? 2: 10;
IMPEVEN_8_32:
rep=isin_G_H(po,r,18,9);
if (rep) goto IMPEVEN_8_20; else return 18;
IMPEVEN_8_33:
rep=isin_G_H(po,r,41,24);
if (rep) goto IMPEVEN_8_29; else return 41;
IMPEVEN_8_34:
rep=isin_G_H(po,r,11,4);
if (rep) return 4; else goto IMPEVEN_8_44;
IMPEVEN_8_35:
rep=isin_G_H(po,r,12,5);
return rep? 5: 12;
IMPEVEN_8_36:
rep=isin_G_H(po,r,20,10);
if (rep) goto IMPEVEN_8_31; else return 20;
IMPEVEN_8_37:
rep=isin_G_H(po,r,29,19);
if (rep) goto IMPEVEN_8_40; else goto IMPEVEN_8_41;
IMPEVEN_8_38:
rep=isin_G_H(po,r,24,13);
if (rep) goto IMPEVEN_8_26; else goto IMPEVEN_8_42;
IMPEVEN_8_39:
rep=isin_G_H(po,r,9,2);
return rep? 2: 9;
IMPEVEN_8_40:
rep=isin_G_H(po,r,19,10);
if (rep) goto IMPEVEN_8_31; else goto IMPEVEN_8_43;
IMPEVEN_8_41:
rep=isin_G_H(po,r,29,18);
if (rep) goto IMPEVEN_8_21; else return 29;
IMPEVEN_8_42:
rep=isin_G_H(po,r,24,9);
if (rep) goto IMPEVEN_8_20; else return 24;
IMPEVEN_8_43:
rep=isin_G_H(po,r,19,9);
if (rep) goto IMPEVEN_8_20; else return 19;
IMPEVEN_8_44:
rep=isin_G_H(po,r,11,2);
return rep? 2: 11;
IMPEVEN_8_45:
rep=isin_G_H(po,r,34,14);
if (rep) goto IMPEVEN_8_12; else return 34;
}
static long
closure8(GEN po)
{
long nbrac,rep;
GEN r[NMAX];
r[0]=myroots(po,PRMAX); nbrac=lg(r[0])-1;
if (nbrac!=N) err(talker,"incompatible number of roots in closure8()");
preci(r,PREC);
if (!CAR)
{
/* CLOS_8_1: */
rep=isin_G_H(po,r,50,47);
if (rep) return galoisimpodd8(po,r,47);
/* CLOS_8_2: */
rep=isin_G_H(po,r,50,44);
if (rep) return galoisimpodd8(po,r,44);
}
else
{
/* CLOS_8_3: */
rep=isin_G_H(po,r,49,45);
if (rep) return galoisimpeven8(po,r,45);
/* CLOS_8_4: */
rep=isin_G_H(po,r,49,39);
if (rep) return galoisimpeven8(po,r,39);
}
return galoisprim8(po,r);
}
static GROUP
initgroup(long n, long nbgr)
{
GROUP t = allocgroup(n,nbgr);
t[1] = SID; return t;
}
static PERM
data8(long n1, long n2, GROUP *t)
{
switch(n1)
{
case 7: if (n2!=1) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 6, 5, 8, 7);
return SID;
case 9: if (n2!=4) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 4, 3, 5, 6, 8, 7);
return SID;
case 10: if (n2!=2) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 6, 5, 8, 7);
return SID;
case 11:
switch(n2)
{
case 2:
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 5, 6, 3, 4, 8, 7);
return _cr(1, 3, 5, 8, 2, 4, 6, 7);
case 4:
*t=initgroup(N,1);
return _cr(1, 3, 7, 5, 2, 4, 8, 6);
}break;
case 14: if (n2!=4) break;
*t=initgroup(N,1);
return _cr(1, 2, 4, 3, 5, 6, 8, 7);
case 15: if (n2!=6 && n2!=8) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 6, 5, 8, 7);
return SID;
case 16: if (n2!=7) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 18:
switch(n2)
{
case 9: *t=initgroup(N,3);
_aff((*t)[2], 1, 5, 3, 7, 2, 6, 4, 8);
_aff((*t)[3], 1, 2, 3, 4, 6, 5, 8, 7);
return SID;
case 10: *t=initgroup(N,3);
_aff((*t)[2], 1, 6, 3, 8, 2, 5, 4, 7);
_aff((*t)[3], 1, 5, 3, 7, 2, 6, 4, 8);
return SID;
}break;
case 19: if (n2!=9) break;
*t=initgroup(N,1);
return _cr(1, 5, 3, 8, 2, 6, 4, 7);
case 20: if (n2!=10) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 22:
switch(n2)
{
case 9: *t=initgroup(N,6);
_aff((*t)[2], 1, 2, 7, 8, 3, 4, 6, 5);
_aff((*t)[3], 1, 2, 7, 8, 3, 4, 5, 6);
_aff((*t)[4], 1, 2, 5, 6, 3, 4, 8, 7);
_aff((*t)[5], 1, 2, 5, 6, 3, 4, 7, 8);
_aff((*t)[6], 1, 2, 3, 4, 5, 6, 8, 7);
return _cr(1, 3, 5, 7, 2, 4, 6, 8);
case 11: *t=initgroup(N,6);
_aff((*t)[2], 1, 2, 5, 6, 7, 8, 4, 3);
_aff((*t)[3], 1, 2, 5, 6, 7, 8, 3, 4);
_aff((*t)[4], 1, 2, 3, 4, 7, 8, 6, 5);
_aff((*t)[5], 1, 2, 3, 4, 7, 8, 5, 6);
_aff((*t)[6], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
}break;
case 23: if (n2!=8) break;
*t=initgroup(N,1);
return _cr(1, 2, 3, 4, 6, 5, 8, 7);
case 26: if (n2!=15 && n2!=17) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 28: if (n2!=21) break;
*t=initgroup(N,1);
return _cr(1, 2, 3, 4, 7, 8, 5, 6);
case 29: if (n2!=18 && n2!=19) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 30: if (n2!=21) break;
*t=initgroup(N,1);
return _cr(1, 2, 3, 4, 7, 8, 5, 6);
case 31: if (n2!=21) break;
*t=initgroup(N,3);
_aff((*t)[2], 1, 2, 3, 4, 7, 8, 5, 6);
_aff((*t)[3], 1, 2, 5, 6, 7, 8, 3, 4);
return SID;
case 32: if (n2!=12 && n2!=13) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 33:
switch(n2)
{
case 13: *t=initgroup(N,1);
return _cr(1, 5, 2, 6, 3, 7, 4, 8);
case 18: *t=initgroup(N,1);
return _cr(1, 2, 5, 6, 3, 4, 7, 8);
}break;
case 34:
switch(n2)
{
case 14: *t=initgroup(N,3);
_aff((*t)[2], 1, 2, 3, 4, 5, 8, 6, 7);
_aff((*t)[3], 1, 2, 3, 4, 5, 7, 8, 6);
return _cr(1, 5, 2, 6, 3, 7, 4, 8);
case 18: *t=initgroup(N,1);
return _cr(1, 2, 5, 6, 3, 4, 8, 7);
}break;
case 39: if (n2!=24) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 40: if (n2!=23) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 41:
switch(n2)
{
case 24: *t=initgroup(N,1);
return _cr(1, 5, 2, 6, 3, 7, 4, 8);
case 29: *t=initgroup(N,1);
return _cr(1, 2, 5, 6, 3, 4, 7, 8);
}break;
case 42: if (n2!=34) break;
*t=initgroup(N,1);
return _cr(1, 2, 3, 4, 5, 6, 8, 7);
case 45: if (n2!=41 && n2!=42) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
case 46: if (n2!=28) break;
*t=initgroup(N,1);
return _cr(1, 2, 5, 6, 3, 4, 7, 8);
case 47: if (n2!=35) break;
*t=initgroup(N,1);
return _cr(1, 2, 5, 6, 3, 4, 7, 8);
case 49: if (n2!=48) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 7);
return SID;
}
*t=initgroup(N,1); return SID;
}
static long
galoismodulo8(GEN pol, GEN dpol)
{
long av = avma, res, gr[51];
long **TYP = partitions(8), **GR = (long**)cgeti(49);
/* List of possible types in group j: GR[j][0] = #GR[j] if
* the group is odd, - #GR[j] if even */
GR[ 1]= _gr( 4, 1,5,15,22);
GR[ 2]= _gr( -3, 1,5,15);
GR[ 3]= _gr( -2, 1,5);
GR[ 4]= _gr( -3, 1,5,15);
GR[ 5]= _gr( -3, 1,5,15);
GR[ 6]= _gr( 5, 1,4,5,15,22);
GR[ 7]= _gr( 5, 1,3,5,15,22);
GR[ 8]= _gr( 5, 1,4,5,15,22);
GR[ 9]= _gr( -4, 1,3,5,15);
GR[10]= _gr( -4, 1,3,5,15);
GR[11]= _gr( -4, 1,3,5,15);
GR[12]= _gr( -5, 1,5,9,15,20);
GR[13]= _gr( -4, 1,5,9,20);
GR[14]= _gr( -4, 1,5,9,15);
GR[15]= _gr( 6, 1,3,4,5,15,22);
GR[16]= _gr( 5, 1,3,5,15,22);
GR[17]= _gr( 7, 1,3,5,11,13,15,22);
GR[18]= _gr( -4, 1,3,5,15);
GR[19]= _gr( -5, 1,3,5,12,15);
GR[20]= _gr( -4, 1,3,5,15);
GR[21]= _gr( 5, 1,3,5,13,15);
GR[22]= _gr( -4, 1,3,5,15);
GR[23]= _gr( 7, 1,4,5,9,15,20,22);
GR[24]= _gr( -6, 1,3,5,9,15,20);
GR[25]= _gr( -3, 1,5,21);
GR[26]= _gr( 8, 1,3,4,5,11,13,15,22);
GR[27]= _gr( 8, 1,2,3,4,5,13,15,22);
GR[28]= _gr( 7, 1,3,5,12,13,15,22);
GR[29]= _gr( -5, 1,3,5,12,15);
GR[30]= _gr( 7, 1,3,4,5,11,13,15);
GR[31]= _gr( 7, 1,2,3,4,5,13,15);
GR[32]= _gr( -6, 1,3,5,9,15,20);
GR[33]= _gr( -6, 1,3,5,9,15,20);
GR[34]= _gr( -5, 1,3,5,9,15);
GR[35]= _gr( 10, 1,2,3,4,5,11,12,13,15,22);
GR[36]= _gr( -5, 1,5,9,20,21);
GR[37]= _gr( -5, 1,5,9,15,21);
GR[38]= _gr( 11, 1,2,3,4,5,9,10,13,15,19,20);
GR[39]= _gr( -7, 1,3,5,9,12,15,20);
GR[40]= _gr( 10, 1,3,4,5,9,11,13,15,20,22);
GR[41]= _gr( -7, 1,3,5,9,12,15,20);
GR[42]= _gr( -8, 1,3,5,6,8,9,15,20);
GR[43]= _gr( 8, 1,4,5,9,15,19,21,22);
GR[44]= _gr( 14, 1,2,3,4,5,9,10,11,12,13,15,19,20,22);
GR[45]= _gr( -9, 1,3,5,6,8,9,12,15,20);
GR[46]= _gr( 10, 1,3,5,6,8,9,12,13,15,22);
GR[47]= _gr( 16, 1,2,3,4,5,6,7,8,9,11,12,13,14,15,20,22);
GR[48]= _gr( -8, 1,3,5,9,12,15,20,21);
gr[0]=51; res = galmodp(pol,dpol,TYP,gr,GR);
avma=av; if (!res) return 0;
return CAR? 49: 50;
}
/* BIBLIOTHEQUE POUR LE DEGRE 9 */
static long
galoisprim9(GEN po, GEN *r)
{
long rep;
if (!CAR)
{
/* PRIM_9_1: */
rep=isin_G_H(po,r,34,26);
if (!rep) return 34;
/* PRIM_9_2: */
rep=isin_G_H(po,r,26,19);
if (!rep) return 26;
/* PRIM_9_3: */
rep=isin_G_H(po,r,19,16);
if (rep) return 16;
/* PRIM_9_4: */
rep=isin_G_H(po,r,19,15);
return rep? 15: 19;
}
/* PRIM_9_5: */
rep=isin_G_H(po,r,33,32);
if (!rep) goto PRIM_9_7;
/* PRIM_9_6: */
rep=isin_G_H(po,r,32,27);
return rep? 27: 32;
PRIM_9_7:
rep=isin_G_H(po,r,33,23);
if (!rep) return 33;
/* PRIM_9_8: */
rep=isin_G_H(po,r,23,14);
if (!rep) return 23;
/* PRIM_9_9: */
rep=isin_G_H(po,r,14,9);
return rep? 9: 14;
}
static long
galoisimpodd9(GEN po, GEN *r)
{
long rep;
/* IMPODD_9_1: */
rep=isin_G_H(po,r,31,29);
if (!rep) goto IMPODD_9_5;
/* IMPODD_9_2: */
rep=isin_G_H(po,r,29,20);
if (!rep) return 29;
IMPODD_9_3:
rep=isin_G_H(po,r,20,12);
if (!rep) return 20;
IMPODD_9_4:
rep=isin_G_H(po,r,12,4);
return rep? 4: 12;
IMPODD_9_5:
rep=isin_G_H(po,r,31,28);
if (!rep) goto IMPODD_9_9;
/* IMPODD_9_6: */
rep=isin_G_H(po,r,28,22);
if (!rep) return 28;
IMPODD_9_7:
rep=isin_G_H(po,r,22,13);
if (!rep) return 22;
IMPODD_9_8:
rep=isin_G_H(po,r,13,4);
return rep? 4: 13;
IMPODD_9_9:
rep=isin_G_H(po,r,31,24);
if (!rep) return 31;
/* IMPODD_9_10: */
rep=isin_G_H(po,r,24,22);
if (rep) goto IMPODD_9_7;
/* IMPODD_9_11: */
rep=isin_G_H(po,r,24,20);
if (rep) goto IMPODD_9_3;
/* IMPODD_9_12: */
rep=isin_G_H(po,r,24,18);
if (!rep) return 24;
/* IMPODD_9_13: */
rep=isin_G_H(po,r,18,13);
if (rep) goto IMPODD_9_8;
/* IMPODD_9_14: */
rep=isin_G_H(po,r,18,12);
if (rep) goto IMPODD_9_4;
/* IMPODD_9_15: */
rep=isin_G_H(po,r,18,8);
if (!rep) return 18;
/* IMPODD_9_16: */
rep=isin_G_H(po,r,8,4);
return rep? 4: 8;
}
static long
galoisimpeven9(GEN po, GEN *r)
{
long rep;
/* IMPEVEN_9_1: */
rep=isin_G_H(po,r,30,25);
if (!rep) goto IMPEVEN_9_7;
/* IMPEVEN_9_2: */
rep=isin_G_H(po,r,25,17);
if (!rep) return 25;
IMPEVEN_9_3:
rep=isin_G_H(po,r,17,7);
if (!rep) goto IMPEVEN_9_5;
IMPEVEN_9_4:
rep=isin_G_H(po,r,7,2);
return rep? 2: 7;
IMPEVEN_9_5:
rep=isin_G_H(po,r,17,6);
if (!rep) return 17;
IMPEVEN_9_6:
rep=isin_G_H(po,r,6,1);
return rep? 1: 6;
IMPEVEN_9_7:
rep=isin_G_H(po,r,30,21);
if (!rep) return 30;
/* IMPEVEN_9_8: */
rep=isin_G_H(po,r,21,17);
if (rep) goto IMPEVEN_9_3;
/* IMPEVEN_9_9: */
rep=isin_G_H(po,r,21,11);
if (!rep) goto IMPEVEN_9_13;
/* IMPEVEN_9_10: */
rep=isin_G_H(po,r,11,7);
if (rep) goto IMPEVEN_9_4;
/* IMPEVEN_9_11: */
rep=isin_G_H(po,r,11,5);
if (!rep) return 11;
/* IMPEVEN_9_12: */
rep=isin_G_H(po,r,5,2);
return rep? 2: 5;
IMPEVEN_9_13:
rep=isin_G_H(po,r,21,10);
if (!rep) return 21;
/* IMPEVEN_9_14: */
rep=isin_G_H(po,r,10,6);
if (rep) goto IMPEVEN_9_6;
/* IMPEVEN_9_15: */
rep=isin_G_H(po,r,10,3);
if (!rep) return 10;
/* IMPEVEN_9_16: */
rep=isin_G_H(po,r,3,1);
return rep? 1: 3;
}
static long
closure9(GEN po)
{
long nbrac,rep;
GEN r[NMAX];
r[0]=myroots(po,PRMAX); nbrac=lg(r[0])-1;
if (nbrac!=N) err(talker,"incompatible number of roots in closure9()");
preci(r,PREC);
if (!CAR)
{
/* CLOS_9_1: */
rep=isin_G_H(po,r,34,31);
if (rep) return galoisimpodd9(po,r);
}
else
{
/* CLOS_9_2: */
rep=isin_G_H(po,r,33,30);
if (rep) return galoisimpeven9(po,r);
}
return galoisprim9(po,r);
}
static PERM
data9(long n1, long n2, GROUP *t)
{
switch(n1)
{
case 6: if (n2!=1) break;
*t=initgroup(N,3);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 9, 7);
_aff((*t)[3], 1, 2, 3, 4, 5, 6, 9, 7, 8);
return SID;
case 7: if (n2!=2) break;
*t=initgroup(N,3);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 9, 7);
_aff((*t)[3], 1, 2, 3, 4, 5, 6, 9, 7, 8);
return SID;
case 8: if (n2!=4) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 4, 7, 2, 5, 8, 3, 6, 9);
return SID;
case 12: if (n2!=4) break;
*t=initgroup(N,3);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 9, 7);
_aff((*t)[3], 1, 2, 3, 4, 5, 6, 9, 7, 8);
return SID;
case 13: if (n2!=4) break;
*t=initgroup(N,1);
return _cr(1, 4, 7, 2, 5, 8, 3, 6, 9);
case 14: if (n2!=9) break;
*t=initgroup(N,3);
_aff((*t)[2], 1, 2, 3, 5, 6, 4, 9, 7, 8);
_aff((*t)[3], 1, 2, 3, 6, 4, 5, 8, 9, 7);
return SID;
case 17: if (n2!=6) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 7, 8, 9, 4, 5, 6);
return SID;
case 21: if (n2!=10) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 7, 8, 9, 4, 5, 6);
return SID;
case 33: if (n2!=32) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 7, 9, 8);
return SID;
}
*t=initgroup(N,1); return SID;
}
static long
galoismodulo9(GEN pol, GEN dpol)
{
long av = avma, res, gr[35];
long **TYP = partitions(9), **GR = (long**) cgeti(33);
/* 42 TYPES ORDONNES CROISSANT (T[1],...,T[30])*/
GR[ 1]= _gr( -3, 1,12,30);
GR[ 2]= _gr( -2, 1,12);
GR[ 3]= _gr( -4, 1,5,12,30);
GR[ 4]= _gr( 4, 1,4,12,26);
GR[ 5]= _gr( -3, 1,5,12);
GR[ 6]= _gr( -4, 1,10,12,30);
GR[ 7]= _gr( -3, 1,10,12);
GR[ 8]= _gr( 5, 1,4,5,12,26);
GR[ 9]= _gr( -4, 1,5,12,18);
GR[10]= _gr( -6, 1,5,10,12,25,30);
GR[11]= _gr( -5, 1,5,10,12,25);
GR[12]= _gr( 5, 1,4,10,12,26);
GR[13]= _gr( 5, 1,4,10,12,26);
GR[14]= _gr( -4, 1,5,12,18);
GR[15]= _gr( 5, 1,5,12,18,29);
GR[16]= _gr( 6, 1,4,5,12,18,26);
GR[17]= _gr( -5, 1,6,10,12,30);
GR[18]= _gr( 7, 1,4,5,10,12,25,26);
GR[19]= _gr( 7, 1,4,5,12,18,26,29);
GR[20]= _gr( 9, 1,4,6,9,10,12,24,26,30);
GR[21]= _gr( -7, 1,5,6,10,12,25,30);
GR[22]= _gr( 7, 1,4,6,10,12,26,30);
GR[23]= _gr( -6, 1,5,10,12,18,25);
GR[24]= _gr( 11, 1,4,5,6,9,10,12,24,25,26,30);
GR[25]= _gr( -7, 1,3,6,8,10,12,30);
GR[26]= _gr( 9, 1,4,5,10,12,18,25,26,29);
GR[27]= _gr( -5, 1,5,12,27,30);
GR[28]= _gr( 12, 1,2,3,4,6,7,8,10,11,12,26,30);
GR[29]= _gr( 12, 1,3,4,6,8,9,10,12,15,24,26,30);
GR[30]= _gr(-11, 1,3,5,6,8,10,12,14,17,25,30);
GR[31]= _gr( 19, 1,2,3,4,5,6,7,8,9,10,11,12,14,15,17,24,25,26,30);
GR[32]= _gr( -7, 1,5,10,12,25,27,30);
gr[0]=35; res = galmodp(pol,dpol,TYP,gr,GR);
avma=av; if (!res) return 0;
return CAR? 33: 34;
}
/* BIBLIOTHEQUE POUR LE DEGRE 10 */
static long
galoisprim10(GEN po, GEN *r)
{
long rep;
if (CAR)
{
/* PRIM_10_1: */
rep=isin_G_H(po,r,44,31);
if (!rep) return 44;
/* PRIM_10_2: */
rep=isin_G_H(po,r,31,26);
if (!rep) return 31;
/* PRIM_10_3: */
rep=isin_G_H(po,r,26,7);
return rep? 7: 26;
}
else
{
/* PRIM_10_4: */
rep=isin_G_H(po,r,45,35);
if (!rep) return 45;
/* PRIM_10_5: */
rep=isin_G_H(po,r,35,32);
if (!rep) goto PRIM_10_7;
/* PRIM_10_6: */
rep=isin_G_H(po,r,32,13);
return rep? 13: 32;
PRIM_10_7:
rep=isin_G_H(po,r,35,30);
return rep? 30: 35;
}
}
static long
galoisimpeven10(GEN po, GEN *r, long nogr)
{
long rep;
if (nogr==42)
{
/* IMPEVEN_10_1: */
rep=isin_G_H(po,r,42,28);
if (!rep) return 42;
/* IMPEVEN_10_2: */
rep=isin_G_H(po,r,28,18);
return rep? 18: 28;
}
else
{
/* IMPEVEN_10_3: */
rep=isin_G_H(po,r,37,34);
if (!rep) goto IMPEVEN_10_5;
/* IMPEVEN_10_4: */
rep=isin_G_H(po,r,34,15);
if (rep) goto IMPEVEN_10_7; else return 34;
IMPEVEN_10_5:
rep=isin_G_H(po,r,37,24);
if (!rep) return 37;
/* IMPEVEN_10_6: */
rep=isin_G_H(po,r,24,15);
if (!rep) return 24;
IMPEVEN_10_7:
rep=isin_G_H(po,r,15,8);
return rep? 8: 15;
}
}
static long
galoisimpodd10(GEN po, GEN *r, long nogr)
{
long rep;
if (nogr==43)
{
/* IMPODD_10_1: */
rep=isin_G_H(po,r,43,41);
if (!rep) goto IMPODD_10_3;
/* IMPODD_10_2: */
rep=isin_G_H(po,r,41,40);
if (rep) goto IMPODD_10_4; else goto IMPODD_10_5;
IMPODD_10_3:
rep=isin_G_H(po,r,43,33);
if (rep) goto IMPODD_10_6; else return 43;
IMPODD_10_4:
rep=isin_G_H(po,r,40,21);
if (rep) goto IMPODD_10_7; else goto IMPODD_10_8;
IMPODD_10_5:
rep=isin_G_H(po,r,41,27);
if (rep) goto IMPODD_10_9; else goto IMPODD_10_10;
IMPODD_10_6:
rep=isin_G_H(po,r,33,27);
if (rep) goto IMPODD_10_9; else return 33;
IMPODD_10_7:
rep=isin_G_H(po,r,21,10);
if (rep) goto IMPODD_10_12; else goto IMPODD_10_13;
IMPODD_10_8:
rep=isin_G_H(po,r,40,12);
if (rep) goto IMPODD_10_14; else goto IMPODD_10_15;
IMPODD_10_9:
rep=isin_G_H(po,r,27,21);
if (rep) goto IMPODD_10_7; else goto IMPODD_10_16;
IMPODD_10_10:
rep=isin_G_H(po,r,41,22);
if (!rep) return 41;
/* IMPODD_10_11: */
rep=isin_G_H(po,r,22,12);
if (rep) goto IMPODD_10_14; else goto IMPODD_10_18;
IMPODD_10_12:
rep=isin_G_H(po,r,10,4);
return rep? 4: 10;
IMPODD_10_13:
rep=isin_G_H(po,r,21,9);
if (rep) goto IMPODD_10_19; else return 21;
IMPODD_10_14:
rep=isin_G_H(po,r,12,4);
return rep? 4: 12;
IMPODD_10_15:
rep=isin_G_H(po,r,40,11);
if (rep) goto IMPODD_10_20; else return 40;
IMPODD_10_16:
rep=isin_G_H(po,r,27,20);
if (!rep) goto IMPODD_10_21;
/* IMPODD_10_17: */
rep=isin_G_H(po,r,20,10);
if (rep) goto IMPODD_10_12; return 20;
IMPODD_10_18:
rep=isin_G_H(po,r,22,11);
if (rep) goto IMPODD_10_20; else goto IMPODD_10_23;
IMPODD_10_19:
rep=isin_G_H(po,r,9,6);
if (rep) goto IMPODD_10_24; else goto IMPODD_10_25;
IMPODD_10_20:
rep=isin_G_H(po,r,11,3);
if (rep) goto IMPODD_10_26; else return 11;
IMPODD_10_21:
rep=isin_G_H(po,r,27,19);
if (rep) goto IMPODD_10_27;
/* IMPODD_10_22: */
rep=isin_G_H(po,r,27,17);
if (rep) goto IMPODD_10_28; else return 27;
IMPODD_10_23:
rep=isin_G_H(po,r,22,5);
if (rep) goto IMPODD_10_29; else return 22;
IMPODD_10_24:
rep=isin_G_H(po,r,6,2);
if (rep) return 2; else goto IMPODD_10_30;
IMPODD_10_25:
rep=isin_G_H(po,r,9,3);
if (!rep) return 9;
IMPODD_10_26:
rep=isin_G_H(po,r,3,2);
if (rep) return 2; else goto IMPODD_10_31;
IMPODD_10_27:
rep=isin_G_H(po,r,19,9);
if (rep) goto IMPODD_10_19; else return 19;
IMPODD_10_28:
rep=isin_G_H(po,r,17,10);
if (rep) goto IMPODD_10_12; else goto IMPODD_10_32;
IMPODD_10_29:
rep=isin_G_H(po,r,5,4);
if (rep) return 4; else goto IMPODD_10_33;
IMPODD_10_30:
rep=isin_G_H(po,r,6,1);
return rep? 1: 6;
IMPODD_10_31:
rep=isin_G_H(po,r,3,1);
return rep? 1: 3;
IMPODD_10_32:
rep=isin_G_H(po,r,17,9);
if (rep) goto IMPODD_10_19; else goto IMPODD_10_60;
IMPODD_10_33:
rep=isin_G_H(po,r,5,3);
if (rep) goto IMPODD_10_26; else return 5;
IMPODD_10_60:
rep=isin_G_H(po,r,17,5);
if (rep) goto IMPODD_10_29; else return 17;
}
else
{
/* IMPODD_10_34: */
rep=isin_G_H(po,r,39,38);
if (!rep) goto IMPODD_10_36;
/* IMPODD_10_35: */
rep=isin_G_H(po,r,38,25);
if (rep) goto IMPODD_10_37; else goto IMPODD_10_38;
IMPODD_10_36:
rep=isin_G_H(po,r,39,36);
if (rep) goto IMPODD_10_39; else goto IMPODD_10_40;
IMPODD_10_37:
rep=isin_G_H(po,r,25,4);
return rep? 4: 25;
IMPODD_10_38:
rep=isin_G_H(po,r,38,12);
if (rep) goto IMPODD_10_41; else return 38;
IMPODD_10_39:
rep=isin_G_H(po,r,36,23);
if (rep) goto IMPODD_10_42; else goto IMPODD_10_43;
IMPODD_10_40:
rep=isin_G_H(po,r,39,29);
if (rep) goto IMPODD_10_44; else goto IMPODD_10_45;
IMPODD_10_41:
rep=isin_G_H(po,r,12,4);
return rep? 4: 12;
IMPODD_10_42:
rep=isin_G_H(po,r,23,16);
if (rep) goto IMPODD_10_46; else goto IMPODD_10_47;
IMPODD_10_43:
rep=isin_G_H(po,r,36,11);
if (rep) goto IMPODD_10_48; else return 36;
IMPODD_10_44:
rep=isin_G_H(po,r,29,25);
if (rep) goto IMPODD_10_37; else goto IMPODD_10_49;
IMPODD_10_45:
rep=isin_G_H(po,r,39,22);
if (rep) goto IMPODD_10_50; else return 39;
IMPODD_10_46:
rep=isin_G_H(po,r,16,2);
return rep? 2: 16;
IMPODD_10_47:
rep=isin_G_H(po,r,23,14);
if (rep) goto IMPODD_10_51; else goto IMPODD_10_52;
IMPODD_10_48:
rep=isin_G_H(po,r,11,3);
if (rep) goto IMPODD_10_53; else return 11;
IMPODD_10_49:
rep=isin_G_H(po,r,29,23);
if (rep) goto IMPODD_10_42; else goto IMPODD_10_54;
IMPODD_10_50:
rep=isin_G_H(po,r,22,12);
if (rep) goto IMPODD_10_41; else goto IMPODD_10_55;
IMPODD_10_51:
rep=isin_G_H(po,r,14,1);
return rep? 1: 14;
IMPODD_10_52:
rep=isin_G_H(po,r,23,3);
if (!rep) return 23;
IMPODD_10_53:
rep=isin_G_H(po,r,3,2);
if (rep) return 2; else goto IMPODD_10_57;
IMPODD_10_54:
rep=isin_G_H(po,r,29,5);
if (rep) goto IMPODD_10_58; else return 29;
IMPODD_10_55:
rep=isin_G_H(po,r,22,11);
if (rep) goto IMPODD_10_48;
/* IMPODD_10_56: */
rep=isin_G_H(po,r,22,5);
if (rep) goto IMPODD_10_58; else return 22;
IMPODD_10_57:
rep=isin_G_H(po,r,3,1);
return rep? 1: 3;
IMPODD_10_58:
rep=isin_G_H(po,r,5,4);
if (rep) return 4;
/* IMPODD_10_59: */
rep=isin_G_H(po,r,5,3);
if (rep) goto IMPODD_10_53; else return 5;
}
}
static long
closure10(GEN po)
{
long nbrac,rep;
GEN r[NMAX];
r[0]=myroots(po,PRMAX); nbrac=lg(r[0])-1;
if (nbrac!=N) err(talker,"incompatible number of roots in closure10()");
preci(r,PREC);
if (CAR)
{
/* CLOS_10_1: */
rep=isin_G_H(po,r,44,42);
if (rep) return galoisimpeven10(po,r,42);
/* CLOS_10_2: */
rep=isin_G_H(po,r,44,37);
if (rep) return galoisimpeven10(po,r,37);
}
else
{
/* CLOS_10_3: */
rep=isin_G_H(po,r,45,43);
if (rep) return galoisimpodd10(po,r,43);
/* CLOS_10_4: */
rep=isin_G_H(po,r,45,39);
if (rep) return galoisimpodd10(po,r,39);
}
return galoisprim10(po,r);
}
static PERM
data10(long n1,long n2,GROUP *t)
{
switch(n1)
{
case 6: if (n2!=2) break;
*t=initgroup(N,1);
return _cr(1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
case 9: if (n2!=3 && n2!=6) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
return SID;
case 10: *t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
return SID;
case 14: case 16:*t=initgroup(N,1);
return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
case 17: if (n2!=5) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 10, 9, 8, 7);
return SID;
case 19: case 20: *t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
return SID;
case 21: if (n2!=10) break;
*t=initgroup(N,1);
return _cr(1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
case 23: if (n2!=3) break;
*t=initgroup(N,1);
return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
case 25: *t=initgroup(N,1);
return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
case 26: *t=initgroup(N,2);
_aff((*t)[2], 1, 2, 4, 9, 6, 8, 10, 3, 7, 5);
return _cr(1, 2, 3, 10, 6, 5, 7, 4, 8, 9);
case 27: if (n2!=17 && n2!=21) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
return SID;
case 28: *t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 8, 10, 7, 9);
return SID;
case 29: if (n2!=5) break;
*t=initgroup(N,1);
return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
case 32: *t=initgroup(N,2);
_aff((*t)[2], 1, 2, 4, 9, 6, 8, 10, 3, 7, 5);
return _cr(1, 2, 3, 10, 6, 5, 7, 4, 8, 9);
case 36: if (n2!=11) break;
*t=initgroup(N,1);
return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
case 38: if (n2!=12) break;
*t=initgroup(N,1);
return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
case 39: if (n2!=22) break;
*t=initgroup(N,1);
return _cr(1, 3, 5, 7, 9, 2, 4, 6, 8, 10);
case 40: if (n2!=12) break;
*t=initgroup(N,1);
return _cr(1, 2, 3, 4, 5, 6, 7, 8, 10, 9);
case 41: if (n2!=22 && n2!=40) break;
*t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 7, 8, 10, 9);
return SID;
}
*t=initgroup(N,1); return SID;
}
static long
galoismodulo10(GEN pol, GEN dpol)
{
long av = avma, res, gr[46];
long **TYP = partitions(10), **GR = (long**) cgeti(45);
GR[ 1]= _gr( 4, 1,6,30,42);
GR[ 2]= _gr( 3, 1,6,30);
GR[ 3]= _gr( 5, 1,5,6,30,42);
GR[ 4]= _gr( 4, 1,5,23,30);
GR[ 5]= _gr( 7, 1,5,6,22,23,30,42);
GR[ 6]= _gr( 5, 1,6,24,30,42);
GR[ 7]= _gr( -4, 1,5,14,30);
GR[ 8]= _gr( -4, 1,3,5,30);
GR[ 9]= _gr( 6, 1,5,6,24,30,42);
GR[10]= _gr( 5, 1,5,23,24,30);
GR[11]= _gr( 7, 1,5,6,11,30,33,42);
GR[12]= _gr( 7, 1,5,6,11,23,30,33);
GR[13]= _gr( 7, 1,4,5,14,23,30,34);
GR[14]= _gr( 8, 1,2,3,4,5,6,30,42);
GR[15]= _gr( -6, 1,3,5,18,22,30);
GR[16]= _gr( 7, 1,3,5,6,17,23,30);
GR[17]= _gr( 8, 1,5,6,22,23,24,30,42);
GR[18]= _gr( -6, 1,5,22,24,30,40);
GR[19]= _gr( 7, 1,5,6,22,24,30,42);
GR[20]= _gr( 6, 1,5,22,23,24,30);
GR[21]= _gr( 9, 1,3,5,6,23,24,26,30,42);
GR[22]= _gr( 11, 1,3,5,6,11,13,22,23,30,33,42);
GR[23]= _gr( 12, 1,2,3,4,5,6,17,18,22,23,30,42);
GR[24]= _gr( -7, 1,3,5,18,22,30,40);
GR[25]= _gr( 8, 1,3,5,18,22,23,30,39);
GR[26]= _gr( -5, 1,5,14,22,30);
GR[27]= _gr( 10, 1,3,5,6,22,23,24,26,30,42);
GR[28]= _gr( -8, 1,3,5,22,24,26,30,40);
GR[29]= _gr( 14, 1,2,3,4,5,6,17,18,22,23,30,39,40,42);
GR[30]= _gr( 8, 1,5,6,14,22,30,39,42);
GR[31]= _gr( -6, 1,5,14,22,30,40);
GR[32]= _gr( 8, 1,4,5,14,22,23,30,34);
GR[33]= _gr( 14, 1,3,5,6,15,17,22,23,24,26,29,30,40,42);
GR[34]= _gr( -9, 1,3,5,11,13,18,22,30,32);
GR[35]= _gr( 12, 1,4,5,6,14,22,23,30,34,39,40,42);
GR[36]= _gr( 18, 1,2,3,4,5,6,11,12,13,17,18,22,23,30,31,32,33,42);
GR[37]= _gr(-12, 1,3,5,11,13,16,18,22,30,32,35,40);
GR[38]= _gr( 18, 1,3,4,5,6,11,13,15,17,18,21,22,23,30,32,33,35,39);
GR[39]= _gr( 24, 1,2,3,4,5,6,11,12,13,15,16,17,18,21,22,23,30,31,32,33,35,39,40,42);
GR[40]= _gr( 14, 1,3,5,6,7,9,11,23,24,26,27,30,33,42);
GR[41]= _gr( 18, 1,3,5,6,7,9,11,13,16,20,22,23,24,26,27,30,33,42);
GR[42]= _gr(-17, 1,3,5,7,9,11,13,16,18,20,22,24,26,27,30,35,40);
GR[43]= _gr( 32, 1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,33,35,40,42);
GR[44]= _gr(-22, 1,3,5,7,9,11,13,14,16,18,20,22,24,26,27,30,32,35,36,38,40,41);
gr[0]=46; res = galmodp(pol,dpol,TYP,gr,GR);
avma=av; if (!res) return 0;
return CAR? 44: 45;
}
/* BIBLIOTHEQUE POUR LE DEGRE 11 */
static long
closure11(GEN po)
{
long nbrac,rep;
GEN r[NMAX];
r[0]=myroots(po,PRMAX); nbrac=lg(r[0])-1;
if (nbrac!=N) err(talker,"incompatible number of roots in closure11()");
preci(r,PREC);
if (CAR)
{
/* EVEN_11_1: */
rep=isin_G_H(po,r,7,6);
if (!rep) return 7;
/* EVEN_11_2: */
rep=isin_G_H(po,r,6,5);
if (!rep) return 6;
/* EVEN_11_3: */
rep=isin_G_H(po,r,5,3);
if (!rep) return 5;
/* EVEN_11_4: */
rep=isin_G_H(po,r,3,1);
return rep? 1: 3;
}
else
{
/* ODD_11_1: */
rep=isin_G_H(po,r,8,4);
if (!rep) return 8;
/* ODD_11_2: */
rep=isin_G_H(po,r,4,2);
return rep? 2: 4;
}
}
static PERM
data11(long n1, GROUP *t)
{
switch(n1)
{
case 5: *t=initgroup(N,1);
return _cr(1, 2, 3, 7, 8, 6, 11, 5, 9, 4, 10);
case 6: *t=initgroup(N,1);
return _cr(1, 2, 3, 4, 6, 10, 11, 9, 7, 5, 8);
case 7: *t=initgroup(N,2);
_aff((*t)[2], 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10);
return SID;
}
*t=initgroup(N,1); return SID;
}
static long
galoismodulo11(GEN pol, GEN dpol)
{
long av = avma, res, gr[6] = {0, 1,1,1,1,1};
long **TYP = (long**) cgeti(9);
TYP[0] = new_chunk(1);
TYP[1] = _gr(11, 11,0,0,0,0,0,0,0,0,0,0);
if (CAR)
{
TYP[2] = _gr(11, 8,2,1,0,0,0,0,0,0,0,0);
TYP[3] = _gr(11, 6,3,2,0,0,0,0,0,0,0,0);
TYP[4] = _gr(11, 5,5,1,0,0,0,0,0,0,0,0);
TYP[5] = _gr(11, 4,4,1,1,1,0,0,0,0,0,0);
TYP[6] = _gr(11, 3,3,3,1,1,0,0,0,0,0,0);
TYP[7] = _gr(11, 2,2,2,2,1,1,1,0,0,0,0);
TYP[8] = _gr(11, 1,1,1,1,1,1,1,1,1,1,1);
TYP[0][0] = 8;
}
else
{
TYP[2] = _gr(11,10,1,0,0,0,0,0,0,0,0,0);
TYP[3] = _gr(11, 5,5,1,0,0,0,0,0,0,0,0);
TYP[4] = _gr(11, 2,2,2,2,2,1,0,0,0,0,0);
TYP[5] = _gr(11, 1,1,1,1,1,1,1,1,1,1,1);
TYP[0][0] = 5;
}
res = galmodp(pol,dpol,TYP,gr,NULL);
avma=av; if (!res) return 0;
return CAR? 7: 8;
}
/* return 1 iff we need to read a resolvent */
static long
init_isin(long n1, long n2, GROUP *tau, GROUP *ss, PERM *s0)
{
long fl = 1;
if (DEBUGLEVEL) {
fprintferr("\n*** Entering isin_%ld_G_H_(%ld,%ld)\n",N,n1,n2); flusherr();
}
switch(N)
{
case 8:
if ((n1==47 && n2==46) || (n1==44 && n2==40)) fl=0;
*s0=data8(n1,n2,tau); break;
case 9:
if ((n1==31 && n2==29) || (n1==34 && n2==31) || (n1==33 && n2==30)) fl=0;
*s0=data9(n1,n2,tau); break;
case 10:
if ((n1==45 && (n2==43||n2==39))
|| (n1==44 && (n2==42||n2==37))
|| (n1==43 && (n2==41||n2==33))
|| (n1==42 && n2==28)
|| (n1==41 && (n2==40||n2==27||n2==22))
|| (n1==40 && (n2==21||n2==11))
|| (n1==39 && (n2==38||n2==36||n2==29||n2==22))
|| (n1==38 && (n2==25||n2==12))
|| (n1==37 && (n2==34||n2==24))
|| (n1==36 && (n2==23||n2==11))
|| (n1==34 && n2==15)
|| (n1==33 && n2==27)
|| (n1==29 && (n2==25||n2==23||n2==5))
|| (n1==28 && n2==18)
|| (n1==27 && (n2==20||n2==19||n2==17))
|| (n1==25 && n2==4)
|| (n1==24 && n2==15)
|| (n1==23 && (n2==16||n2==3))
|| (n1==22 && (n2==12||n2==11||n2==5))
|| (n1==21 && (n2==10||n2==9))
|| (n1==17 && n2==5)
|| (n1==16 && n2==2)
|| (n1==14 && n2==1)
|| (n1==12 && n2==4)
|| (n1==11 && n2==3)
|| (n1==10 && n2==4)
|| (n1== 9 && n2==3)
|| (n1== 6 && n2==1)
|| (n1== 5 && n2==3)) fl = 0;
*s0=data10(n1,n2,tau); break;
case 11:
*s0=data11(n1,tau); break;
}
*ss = lirecoset(n1,n2,N); return fl;
}
static long
isin_G_H(GEN po, GEN *r, long n1, long n2)
{
long nbv,nbm,i,j;
PERM s0, ww;
RESOLVANTE a;
GROUP ss,tau;
if (init_isin(n1,n2, &tau, &ss, &s0))
a = lireresolv(n1,n2,N,&nbv,&nbm);
else
{ a = NULL; nbm=n1; nbv=n2; }
ww = check_isin(po,r,nbm,nbv,a,tau,ss,s0);
if (getpreci(r) != PREC) preci(r,PREC);
free(ss); free(tau); if (a) free(a);
if (ww)
{
long z[NMAX+1];
if (DEBUGLEVEL)
{
fprintferr("\n Output of isin_%ld_G_H(%ld,%ld): %ld",N,n1,n2,n2);
fprintferr("\n Reordering of the roots: "); printperm(ww);
flusherr();
}
for (i=0; i<TSCHMAX; i++)
{
GEN p1 = r[i];
for (j=1; j<=N; j++) z[j]=p1[(int)ww[j]];
for (j=1; j<=N; j++) p1[j]=z[j];
}
free(ww); return n2;
}
if (DEBUGLEVEL)
{
fprintferr(" Output of isin_%ld_G_H(%ld,%ld): not included.\n",N,n1,n2);
flusherr();
}
return 0;
}
GEN
galoisbig(GEN pol, long prec)
{
GEN dpol, res = cgetg(4,t_VEC);
long *tab,t, av = avma;
long tab8[]={0,
8,8,8,8,8,16,16,16,16,16, 16,24,24,24,32,32,32,32,32,32,
32,32,48,48,56,64,64,64,64,64, 64,96,96,96,128,168,168,192,192,192,
192,288,336,384,576,576,1152,1344,20160,40320};
long tab9[]={0,
9,9,18,18,18,27,27,36,36,54, 54,54,54,72,72,72,81,108,144,162,
162,162,216,324,324,432,504,648,648,648, 1296,1512,181440,362880};
long tab10[]={0,
10,10,20,20,40,50,60,80,100,100, 120,120,120,160,160,160,200,200,200,200,
200,240,320,320,320,360,400,400,640,720, 720,720,800,960,1440,
1920,1920,1920,3840,7200,14400,14400,28800,1814400,3628800};
long tab11[]={0, 11,22,55,110,660,7920,19958400,39916800};
N = lgef(pol)-3; dpol = discsr(pol); CAR = carreparfait(dpol);
prec += 2 * (MEDDEFAULTPREC-2);
PREC = prec;
if (DEBUGLEVEL)
{
fprintferr("Entering galoisbig (prec = %ld)\n",prec);
fprintferr("Working with reduced polynomial #1 = "); bruterr(pol,'g',-1);
fprintferr("\ndiscriminant = "); bruterr(dpol,'g',-1);
fprintferr(CAR? "\nEVEN group\n": "\nODD group\n"); flusherr();
}
PRMAX = prec+5; TSCHMAX = 1; SID[0] = N;
switch(N)
{
case 8: t = galoismodulo8(pol,dpol);
if (!t) t = closure8(pol);
tab=tab8; break;
case 9: t = galoismodulo9(pol,dpol);
if (!t) t = closure9(pol);
tab=tab9; break;
case 10: t = galoismodulo10(pol,dpol);
if (!t) t = closure10(pol);
tab=tab10; break;
case 11: t = galoismodulo11(pol,dpol);
if (!t) t = closure11(pol);
tab=tab11; break;
default: err(impl,"galois in degree > 11");
}
avma = av;
res[1]=lstoi(tab[t]);
res[2]=lstoi(CAR? 1 : -1);
res[3]=lstoi(t); return res;
}
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