GEN
nffactormod(GEN nf, GEN x, GEN pr)
{
long j, l, vx = varn(x), vn;
pari_sp av = avma;
GEN F, E, rep, xrd, modpr, T, p;
nf = checknf(nf);
vn = varn(nf[1]);
if (typ(x)!=t_POL) pari_err(typeer,"nffactormod");
if (varncmp(vx,vn) >= 0)
pari_err(talker,"polynomial variable must have highest priority in nffactormod");
modpr = nf_to_ff_init(nf, &pr, &T, &p);
xrd = modprX(x, nf, modpr);
rep = FqX_factor(xrd,T,p);
settyp(rep, t_MAT);
F = gel(rep,1); l = lg(F);
E = gel(rep,2); settyp(E, t_COL);
for (j = 1; j < l; j++) {
gel(F,j) = modprX_lift(gel(F,j), modpr);
gel(E,j) = stoi(E[j]);
}
return gerepilecopy(av, rep);
}
void
install0(char *name, char *code, char *gpname, char *lib)
{
void *f, *handle;
if (! *lib) lib = DL_DFLT_NAME;
if (! *gpname) gpname = name;
if (lib) lib = expand_tilde(lib);
#ifndef RTLD_GLOBAL /* OSF1 has dlopen but not RTLD_GLOBAL*/
# define RTLD_GLOBAL 0
#endif
handle = dlopen(lib, RTLD_LAZY|RTLD_GLOBAL);
if (!handle)
{
const char *s = dlerror(); if (s) fprintferr("%s\n\n",s);
if (lib) pari_err(talker,"couldn't open dynamic library '%s'",lib);
pari_err(talker,"couldn't open dynamic symbol table of process");
}
f = dlsym(handle, name);
if (!f)
{
if (lib) pari_err(talker,"can't find symbol '%s' in library '%s'",name,lib);
pari_err(talker,"can't find symbol '%s' in dynamic symbol table of process",name);
}
if (lib) free(lib);
install(f, gpname, code);
}
void
install0(char *name, char *code, char *gpname, char *lib)
{
FARPROC f;
HMODULE handle;
#ifdef WINCE
short wlib[256], wname[256];
MultiByteToWideChar(CP_ACP, 0, lib, strlen(lib)+1, wlib, 256);
MultiByteToWideChar(CP_ACP, 0, name, strlen(name)+1, wname, 256);
lib = wlib;
name = wname;
#endif
#ifdef DL_DFLT_NAME
if (! *lib) lib = DL_DFLT_NAME;
#endif
if (! *gpname) gpname=name;
if (lib) lib = expand_tilde(lib);
handle = LoadLibrary(lib);
if (!handle)
{
if (lib) pari_err(talker,"couldn't open dynamic library '%s'",lib);
pari_err(talker,"couldn't open dynamic symbol table of process");
}
f = GetProcAddress(handle,name);
if (!f)
{
if (lib) pari_err(talker,"can't find symbol '%s' in library '%s'",name,lib);
pari_err(talker,"can't find symbol '%s' in dynamic symbol table of process",name);
}
if (lib) free(lib);
install((void*)f,gpname,code);
}
/* If flag = 0 (default): check if s existed in 1.39.15 and print verbosely
* the answer.
* If flag > 0: silently return n+1 if function changed, 0 otherwise.
* (where n is the index of s in whatnowlist).
* If flag < 0: -flag-1 is the index in whatnowlist
*/
int
whatnow(char *s, int flag)
{
int n;
char *def;
whatnow_t wp;
entree *ep;
if (flag < 0) { n = -flag; flag = 0; }
else
{
if (flag && strlen(s)==1) return 0; /* special case "i" and "o" */
if (!is_identifier(s) || !is_entry_intern(s,funct_old_hash,NULL))
{
if (flag) return 0;
pari_err(talker,"as far as I can recall, this function never existed");
}
n = 0;
do
def = (oldfonctions[n++]).name;
while (def && strcmp(def,s));
if (!def)
{
int m=0;
do
def = (functions_oldgp[m++]).name;
while (def && strcmp(def,s));
n += m - 1;
}
}
wp=whatnowlist[n-1]; def=wp.name;
if (def == SAME)
{
if (flag) return 0;
pari_err(talker,"this function did not change");
}
if (flag) return n;
if (def == REMOV)
pari_err(talker,"this function was suppressed");
if (!strcmp(def,"x*y"))
{
pariprintf(" %s is now called *.\n\n",s);
pariprintf(" %s%s ===> %s%s\n\n",s,wp.oldarg,wp.name,wp.newarg);
return 1;
}
ep = is_entry(wp.name);
if (!ep) pari_err(bugparier,"whatnow");
pariputs("New syntax: "); term_color(c_ERR);
pariprintf("%s%s ===> %s%s\n\n",s,wp.oldarg,wp.name,wp.newarg);
term_color(c_HELP);
print_text(ep->help); pariputc('\n');
term_color(c_NONE); return 1;
}
static long
check_proto(const char *code)
{
long arity = 0;
const char *s = code, *old;
if (*s == 'l' || *s == 'v' || *s == 'i' || *s == 'm' || *s == 'u') s++;
while (*s && *s != '\n') switch (*s++)
{
case '&':
case 'C':
case 'G':
case 'I':
case 'J':
case 'U':
case 'L':
case 'M':
case 'P':
case 'W':
case 'f':
case 'n':
case 'p':
case 'r':
case 'x':
arity++;
break;
case 'E':
case 's':
if (*s == '*') s++;
arity++;
break;
case 'D':
if (*s == 'G' || *s == '&' || *s == 'n' || *s == 'I' || *s == 'E'
|| *s == 'V' || *s == 'P' || *s == 's' || *s == 'r')
{
if (*s != 'V') arity++;
s++; break;
}
old = s; while (*s && *s != ',') s++;
if (*s != ',') pari_err(e_SYNTAX, "missing comma", old, code);
break;
case 'V':
case '=':
case ',': break;
case '\n': break; /* Before the mnemonic */
case 'm':
case 'l':
case 'i':
case 'v': pari_err(e_SYNTAX, "this code has to come first", s-1, code);
default: pari_err(e_SYNTAX, "unknown parser code", s-1, code);
}
if (arity > 20) pari_err_IMPL("functions with more than 20 parameters");
return arity;
}
/* Kill ep, i.e free all memory it references, and reset to initial value */
void
kill0(const char *e)
{
entree *ep = is_entry(e);
if (!ep || EpSTATIC(ep)) pari_err(e_MISC,"can't kill that");
killep(ep);
}
long
fetch_var_higher(void)
{
if (nvar == max_avail) pari_err(e_MISC,"no more variables available");
varpriority[max_avail] = ++max_priority;
return max_avail--;
}
static void
check_name(const char *name)
{
const char *s = name;
if (isalpha((int)*s))
while (is_keyword_char(*++s)) /* empty */;
if (*s) pari_err(e_SYNTAX,"not a valid identifier", s, name);
}
/* assume x is squarefree */
int
nfissplit(GEN nf, GEN x)
{
pari_sp av = avma;
long l;
if (typ(x) != t_POL) pari_err(typeer, "nfissplit");
l = lg(nfsqff(checknf(nf), x, 2));
avma = av; return l != 1;
}
static void
digit_help(char *s, long flag)
{
long n = atoi(s);
if (n < 0 || n > MAX_SECTION+4)
pari_err(e_SYNTAX,"no such section in help: ?",s,s);
if (n == MAX_SECTION+1)
community();
else if (flag & h_LONG)
external_help(s,3);
else
commands(n);
return;
}
GEN
varhigher(const char *s, long w)
{
long v;
if (w >= 0)
{
hashentry *e = hash_select(h_polvar, (void*)s, (void*)w, _higher);
if (e) return pol_x((long)e->val);
}
/* no luck: need to create */
if (nvar == max_avail) pari_err(e_MISC,"no more variables available");
v = nvar++;
varpriority[v]= ++max_priority;
return var_register(v, s);
}
void
alias0(const char *s, const char *old)
{
entree *ep, *e;
GEN x;
ep = fetch_entry(old);
e = fetch_entry(s);
if (EpVALENCE(e) != EpALIAS && EpVALENCE(e) != EpNEW)
pari_err(e_MISC,"can't replace an existing symbol by an alias");
freeep(e);
x = newblock(2); x[0] = evaltyp(t_STR)|_evallg(2); /* for getheap */
gel(x,1) = (GEN)ep;
e->value=x; e->valence=EpALIAS;
}
/* return the roots of pol in nf */
GEN
nfroots(GEN nf,GEN pol)
{
pari_sp av = avma;
GEN A,g, T;
long d;
if (!nf) return nfrootsQ(pol);
nf = checknf(nf); T = gel(nf,1);
if (typ(pol) != t_POL) pari_err(notpoler,"nfroots");
if (varncmp(varn(pol), varn(T)) >= 0)
pari_err(talker,"polynomial variable must have highest priority in nfroots");
d = degpol(pol);
if (d == 0) return cgetg(1,t_VEC);
if (d == 1)
{
A = gneg_i(gdiv(gel(pol,2),gel(pol,3)));
return gerepilecopy(av, mkvec( basistoalg(nf,A) ));
}
A = fix_relative_pol(nf,pol,0);
A = Q_primpart( lift_intern(A) );
if (DEBUGLEVEL>3) fprintferr("test if polynomial is square-free\n");
g = nfgcd(A, derivpol(A), T, gel(nf,4));
if (degpol(g))
{ /* not squarefree */
g = QXQX_normalize(g, T);
A = RgXQX_div(A,g,T);
}
A = QXQX_normalize(A, T);
A = Q_primpart(A);
A = nfsqff(nf,A,1);
A = RgXQV_to_mod(A, T);
return gerepileupto(av, gen_sort(A, 0, cmp_pol));
}
long
fetch_user_var(const char *s)
{
entree *ep = fetch_entry(s);
long v;
switch (EpVALENCE(ep))
{
case EpVAR: return varn((GEN)initial_value(ep));
case EpNEW: break;
default: pari_err(e_MISC, "%s already exists with incompatible valence", s);
}
v = pari_var_create(ep);
ep->valence = EpVAR;
ep->value = initial_value(ep);
return v;
}
static void
choose_prime(primedata *S, GEN pol, GEN dpol)
{
byteptr di = diffptr + 1;
long i, j, k, r, lcm, oldlcm, pp, N = degpol(pol), minp = N*N / 4;
GEN Z, p, ff, oldff, n, oldn;
pari_sp av;
if (DEBUGLEVEL) (void)timer2();
p = utoipos(2);
while (p[2] <= minp) NEXT_PRIME_VIADIFF(p[2], di);
oldlcm = 0;
oldff = oldn = NULL; pp = 0; /* gcc -Wall */
av = avma;
for(k = 1; k < 11 || !oldlcm; k++,avma = av)
{
do NEXT_PRIME_VIADIFF(p[2], di); while (!smodis(dpol, p[2]));
if (k > 5 * N) pari_err(talker,"sorry, too many block systems in nfsubfields");
ff = (GEN)FpX_factor(pol, p)[1];
r = lg(ff)-1;
if (r == N || r >= BIL) continue;
n = cgetg(r+1, t_VECSMALL); lcm = n[1] = degpol(ff[1]);
for (j=2; j<=r; j++) { n[j] = degpol(ff[j]); lcm = clcm(lcm, n[j]); }
if (lcm <= oldlcm) continue; /* false when oldlcm = 0 */
if (DEBUGLEVEL) fprintferr("p = %ld,\tlcm = %ld,\torbits: %Z\n",p[2],lcm,n);
pp = p[2];
oldn = n;
oldff = ff;
oldlcm = lcm; if (r == 1) break;
av = avma;
}
if (DEBUGLEVEL) fprintferr("Chosen prime: p = %ld\n", pp);
S->ff = oldff;
S->lcm= oldlcm;
S->p = utoipos(pp);
S->pol = FpX_red(pol, S->p); init_primedata(S);
n = oldn; r = lg(n); Z = cgetg(r,t_VEC);
for (k=0,i=1; i<r; i++)
{
GEN t = cgetg(n[i]+1, t_VECSMALL); gel(Z,i) = t;
for (j=1; j<=n[i]; j++) t[j] = ++k;
}
S->Z = Z;
}
/* return U list of polynomials s.t U[i] = 1 mod fk[i] and 0 mod fk[j] for all
* other j */
static GEN
get_bezout(GEN pol, GEN fk, GEN p)
{
long i, l = lg(fk);
GEN A, B, d, u, v, U = cgetg(l, t_VEC);
for (i=1; i<l; i++)
{
A = gel(fk,i);
B = FpX_div(pol, A, p);
d = FpX_extgcd(A,B,p, &u, &v);
if (degpol(d) > 0) pari_err(talker, "relatively prime polynomials expected");
d = constant_term(d);
if (!gcmp1(d)) v = FpX_Fp_mul(v, Fp_inv(d, p), p);
gel(U,i) = FpX_mul(B,v, p);
}
return U;
}
long
pari_var_create(entree *ep)
{
GEN p = (GEN)initial_value(ep);
long v;
if (*p) return varn(p);
if (nvar == max_avail) pari_err(e_MISC,"no more variables available");
v = nvar++;
/* set p = pol_x(v) */
p[0] = evaltyp(t_POL) | _evallg(4);
p[1] = evalsigne(1) | evalvarn(v);
gel(p,2) = gen_0;
gel(p,3) = gen_1;
varentries_set(v, ep);
varpriority[v]= min_priority--;
return v;
}
void
name_var(long n, const char *s)
{
entree *ep;
char *u;
if (n < pari_var_next())
pari_err(e_MISC, "renaming a GP variable is forbidden");
if (n > (long)MAXVARN)
pari_err_OVERFLOW("variable number");
ep = (entree*)pari_malloc(sizeof(entree) + strlen(s) + 1);
u = (char *)initial_value(ep);
ep->valence = EpVAR;
ep->name = u; strcpy(u,s);
ep->value = gen_0; /* in case geval is called */
varentries_reset(n, ep);
}
entree *
install(void *f, const char *name, const char *code)
{
long arity = check_proto(code);
entree *ep;
check_name(name);
ep = fetch_entry(name);
if (ep->valence != EpNEW)
{
if (ep->valence != EpINSTALL)
pari_err(e_MISC,"[install] identifier '%s' already in use", name);
pari_warn(warner, "[install] updating '%s' prototype; module not reloaded", name);
if (ep->code) pari_free((void*)ep->code);
}
else
{
ep->value = f;
ep->valence = EpINSTALL;
}
ep->code = pari_strdup(code);
ep->arity = arity; return ep;
}
/* return the characteristic polynomial of alpha over nf, where alpha
is an element of the algebra nf[X]/(T) given as a polynomial in X */
GEN
rnfcharpoly(GEN nf, GEN T, GEN alpha, long v)
{
long vnf, vT, lT;
pari_sp av = avma;
GEN p1;
nf=checknf(nf); vnf = varn(nf[1]);
if (v<0) v = 0;
T = fix_relative_pol(nf,T,1);
if (typ(alpha) == t_POLMOD) alpha = lift_to_pol(alpha);
lT = lg(T);
if (typ(alpha) != t_POL || varn(alpha) == vnf)
return gerepileupto(av, gpowgs(gsub(pol_x[v], alpha), lT - 3));
vT = varn(T);
if (varn(alpha) != vT || varncmp(v, vnf)>=0)
pari_err(talker,"incorrect variables in rnfcharpoly");
if (lg(alpha) >= lT) alpha = RgX_rem(alpha, T);
if (lT <= 4)
return gerepileupto(av, gsub(pol_x[v], alpha));
p1 = caract2(T, unifpol(nf,alpha, t_POLMOD), v);
return gerepileupto(av, unifpol(nf, p1, t_POLMOD));
}
/* query external help program for s. num < 0 [keyword] or chapter number */
static void
external_help(const char *s, int num)
{
long nbli = term_height()-3, li = 0;
char buf[256], *str;
const char *opt = "", *ar = "", *cdir = "";
char *t, *help = GP_DATA->help;
pariFILE *z;
FILE *f;
if (!has_ext_help()) pari_err(e_MISC,"no external help program");
t = filter_quotes(s);
if (num < 0)
opt = "-k";
else if (t[strlen(t)-1] != '@')
ar = stack_sprintf("@%d",num);
#ifdef _WIN32
if (*help=='@')
{
const char *basedir = win32_basedir();
help++;
cdir = stack_sprintf("%c:& cd %s & ", *basedir, basedir);
}
#endif
str=stack_sprintf("%s%s -fromgp %s %c%s%s%c",cdir,help,opt,
SHELL_Q,t,ar,SHELL_Q);
z = try_pipe(str,0); f = z->file;
pari_free(t);
while (fgets(buf, numberof(buf), f))
{
if (!strncmp("ugly_kludge_done",buf,16)) break;
pari_puts(buf);
if (nl_read(buf) && ++li > nbli) { pari_hit_return(); li = 0; }
}
pari_fclose(z);
}
/* return the factorization of x in nf */
GEN
nffactor(GEN nf,GEN pol)
{
GEN A,g,y,p1,T, rep = cgetg(3, t_MAT);
long l, j, dA;
pari_sp av = avma;
pari_timer ti;
if (DEBUGLEVEL>2) { TIMERstart(&ti); fprintferr("\nEntering nffactor:\n"); }
nf = checknf(nf); T = gel(nf,1);
if (typ(pol) != t_POL) pari_err(notpoler,"nffactor");
if (varncmp(varn(pol), varn(T)) >= 0)
pari_err(talker,"polynomial variable must have highest priority in nffactor");
A = fix_relative_pol(nf,pol,0);
dA = degpol(A);
if (dA <= 0) {
avma = (pari_sp)(rep + 3);
return dA == 0? trivfact(): zerofact(varn(pol));
}
A = Q_primpart( QXQX_normalize(A, T) );
if (dA == 1) {
GEN c;
A = gerepilecopy(av, A); c = gel(A,2);
if (typ(c) == t_POL && degpol(c) > 0) gel(A,2) = mkpolmod(c, gcopy(T));
gel(rep,1) = mkcol(A);
gel(rep,2) = mkcol(gen_1); return rep;
}
if (degpol(T) == 1)
return gerepileupto(av, factpol(Q_primpart(simplify(pol)), 0));
A = Q_primpart( lift_intern(A) );
g = nfgcd(A, derivpol(A), T, gel(nf,4));
A = QXQX_normalize(A, T);
A = Q_primpart(A);
if (DEBUGLEVEL>2) msgTIMER(&ti, "squarefree test");
if (degpol(g))
{ /* not squarefree */
pari_sp av1;
GEN ex;
g = QXQX_normalize(g, T);
A = RgXQX_div(A,g, T);
y = nfsqff(nf,A,0); av1 = avma;
l = lg(y);
ex=(GEN)gpmalloc(l * sizeof(long));
for (j=l-1; j>=1; j--)
{
GEN fact = lift(gel(y,j)), quo = g, q;
long e = 0;
for(e = 1;; e++)
{
q = RgXQX_divrem(quo,fact,T, ONLY_DIVIDES);
if (!q) break;
quo = q;
}
ex[j] = e;
}
avma = av1; y = gerepileupto(av, RgXQXV_to_mod(y,T));
p1 = cgetg(l, t_COL); for (j=l-1; j>=1; j--) gel(p1,j) = utoipos(ex[j]);
free(ex);
}
else
{
y = gerepileupto(av, RgXQXV_to_mod(nfsqff(nf,A,0), T));
l = lg(y);
p1 = cgetg(l, t_COL); for (j=l-1; j>=1; j--) gel(p1,j) = gen_1;
}
if (DEBUGLEVEL>3)
fprintferr("number of factor(s) found: %ld\n", lg(y)-1);
gel(rep,1) = y;
gel(rep,2) = p1; return sort_factor(rep, cmp_pol);
}
/* nf = K[y] / (P) [P irreducible / K]. Is nf Galois over K ? */
int
nfisgalois(GEN nf, GEN P)
{
if (typ(P) != t_POL) pari_err(typeer, "nfissplit");
return degpol(P) <= 2 || nfissplit(nf, P);
}
/* LOCATE GPRC */
static void
err_gprc(const char *s, char *t, char *u)
{
err_printf("\n");
pari_err(e_SYNTAX,s,t,u);
}
/* return the factorization of the square-free polynomial x.
The coeffs of x are in Z_nf and its leading term is a rational integer.
deg(x) > 1, deg(nfpol) > 1
If fl = 1, return only the roots of x in nf
If fl = 2, as fl=1 if pol splits, [] otherwise */
static GEN
nfsqff(GEN nf, GEN pol, long fl)
{
long n, nbf, dpol = degpol(pol);
GEN pr, C0, polbase, init_fa = NULL;
GEN N2, rep, polmod, polred, lt, nfpol = gel(nf,1);
nfcmbf_t T;
nflift_t L;
pari_timer ti, ti_tot;
if (DEBUGLEVEL>2) { TIMERstart(&ti); TIMERstart(&ti_tot); }
n = degpol(nfpol);
polbase = unifpol(nf, pol, t_COL);
if (typ(polbase) != t_POL) pari_err(typeer, "nfsqff");
polmod = lift_intern( unifpol(nf, pol, t_POLMOD) );
if (dpol == 1) return mkvec(QXQX_normalize(polmod, nfpol));
/* heuristic */
if (dpol*3 < n)
{
GEN z, t;
long i;
if (DEBUGLEVEL>2) fprintferr("Using Trager's method\n");
z = (GEN)polfnf(polmod, nfpol)[1];
if (fl) {
long l = lg(z);
for (i = 1; i < l; i++)
{
t = gel(z,i); if (degpol(t) > 1) break;
gel(z,i) = gneg(gdiv(gel(t,2), gel(t,3)));
}
setlg(z, i);
if (fl == 2 && i != l) return cgetg(1,t_VEC);
}
return z;
}
nbf = nf_pick_prime(5, nf, polbase, fl, <, &init_fa, &pr, &L.Tp);
if (fl == 2 && nbf < dpol) return cgetg(1,t_VEC);
if (nbf <= 1)
{
if (!fl) return mkvec(QXQX_normalize(polmod, nfpol)); /* irreducible */
if (!nbf) return cgetg(1,t_VEC); /* no root */
}
if (DEBUGLEVEL>2) {
msgTIMER(&ti, "choice of a prime ideal");
fprintferr("Prime ideal chosen: %Z\n", pr);
}
pol = simplify_i(lift(polmod));
L.tozk = gel(nf,8);
L.topow= Q_remove_denom(gel(nf,7), &L.topowden);
T.ZC = L2_bound(nf, L.tozk, &(T.dn));
T.Br = nf_root_bounds(pol, nf); if (lt) T.Br = gmul(T.Br, lt);
if (fl) C0 = normlp(T.Br, 2, n);
else C0 = nf_factor_bound(nf, polbase); /* bound for T_2(Q_i), Q | P */
T.bound = mulrr(T.ZC, C0); /* bound for |Q_i|^2 in Z^n on chosen Z-basis */
N2 = mulsr(dpol*dpol, normlp(T.Br, 4, n)); /* bound for T_2(lt * S_2) */
T.BS_2 = mulrr(T.ZC, N2); /* bound for |S_2|^2 on chosen Z-basis */
if (DEBUGLEVEL>2) {
msgTIMER(&ti, "bound computation");
fprintferr(" 1) T_2 bound for %s: %Z\n", fl?"root":"factor", C0);
fprintferr(" 2) Conversion from T_2 --> | |^2 bound : %Z\n", T.ZC);
fprintferr(" 3) Final bound: %Z\n", T.bound);
}
L.p = gel(pr,1);
if (L.Tp && degpol(L.Tp) == 1) L.Tp = NULL;
bestlift_init(0, nf, pr, T.bound, &L);
if (DEBUGLEVEL>2) TIMERstart(&ti);
polred = ZqX_normalize(polbase, lt, &L); /* monic */
if (fl) {
GEN z = nf_DDF_roots(pol, polred, nfpol, lt, init_fa, nbf, fl, &L);
if (lg(z) == 1) return cgetg(1, t_VEC);
return z;
}
{
pari_sp av = avma;
if (L.Tp)
rep = FqX_split_all(init_fa, L.Tp, L.p);
else
{
long d;
rep = cgetg(dpol + 1, t_VEC); gel(rep,1) = FpX_red(polred,L.p);
d = FpX_split_Berlekamp((GEN*)(rep + 1), L.p);
setlg(rep, d + 1);
}
T.fact = gerepilecopy(av, sort_vecpol(rep, &cmp_pol));
}
if (DEBUGLEVEL>2) msgTIMER(&ti, "splitting mod %Z", pr);
T.pr = pr;
T.L = &L;
T.polbase = polbase;
T.pol = pol;
T.nf = nf;
T.hint = 1; /* useless */
rep = nf_combine_factors(&T, polred, L.p, L.k, dpol-1);
if (DEBUGLEVEL>2)
fprintferr("Total Time: %ld\n===========\n", TIMER(&ti_tot));
return rep;
}
void
install0(char *name, char *code, char *gpname, char *lib) { pari_err(archer); }
long
eval_mnemonic(GEN str, const char *tmplate)
{
pari_sp av=avma;
ulong retval = 0;
const char *etmplate = NULL;
const char *arg;
if (typ(str)==t_INT) return itos(str);
if (typ(str)!=t_STR) pari_err_TYPE("eval_mnemonic",str);
arg=GSTR(str);
etmplate = strchr(tmplate, '\n');
if (!etmplate)
etmplate = tmplate + strlen(tmplate);
while (1)
{
long numarg;
const char *e, *id;
const char *negated; /* action found with 'no'-ID */
int negate; /* Arg has 'no' prefix removed */
ulong l, action = 0, first = 1, singleton = 0;
char *buf, *inibuf;
static char b[80];
while (isspace((int)*arg)) arg++;
if (!*arg)
break;
e = arg;
while (IS_ID(*e)) e++;
/* Now the ID is whatever is between arg and e. */
l = e - arg;
if (l >= sizeof(b))
pari_err(e_MISC,"id too long in a stringified flag");
if (!l) /* Garbage after whitespace? */
pari_err(e_MISC,"a stringified flag does not start with an id");
strncpy(b, arg, l);
b[l] = 0;
arg = e;
e = inibuf = buf = b;
while (('0' <= *e) && (*e <= '9'))
e++;
if (*e == 0)
pari_err(e_MISC,"numeric id in a stringified flag");
negate = 0;
negated = NULL;
find:
id = tmplate;
while ((id = strstr(id, buf)) && id < etmplate)
{
if (IS_ID(id[l])) { /* We do not allow abbreviations yet */
id += l; /* False positive */
continue;
}
if ((id >= tmplate + 2) && (IS_ID(id[-1])))
{
const char *s = id;
if ( !negate && s >= tmplate+3
&& ((id[-1] == '_') || (id[-1] == '-')) )
s--;
/* Check whether we are preceeded by "no" */
if ( negate /* buf initially started with "no" */
|| (s < tmplate+2) || (s[-1] != 'o') || (s[-2] != 'n')
|| (s >= tmplate+3 && IS_ID(s[-3]))) {
id += l; /* False positive */
continue;
}
/* Found noID in the template! */
id += l;
negated = id;
continue; /* Try to find without 'no'. */
}
/* Found as is */
id += l;
break;
}
if ( !id && !negated && !negate
&& (l > 2) && buf[0] == 'n' && buf[1] == 'o' ) {
/* Try to find the flag without the prefix "no". */
buf += 2; l -= 2;
if ((buf[0] == '_') || (buf[0] == '-')) { buf++; l--; }
negate = 1;
if (buf[0])
goto find;
}
if (!id && negated) /* Negated and AS_IS forms, prefer AS_IS */
{
id = negated; /* Otherwise, use negated form */
negate = 1;
}
if (!id)
pari_err(e_MISC,"Unrecognized id '%s' in a stringified flag", inibuf);
if (singleton && !first)
pari_err(e_MISC,"Singleton id non-single in a stringified flag");
if (id[0] == '=') {
if (negate)
pari_err(e_MISC,"Cannot negate id=value in a stringified flag");
if (!first)
pari_err(e_MISC,"Assign action should be first in a stringified flag");
action = A_ACTION_ASSIGN;
id++;
if (id[0] == '=') {
singleton = 1;
id++;
}
} else if (id[0] == '^') {
if (id[1] != '~')
pari_err(e_MISC, "Unrecognized action in a template");
id += 2;
if (negate)
action = A_ACTION_SET;
else
action = A_ACTION_UNSET;
} else if (id[0] == '|') {
id++;
if (negate)
action = A_ACTION_UNSET;
else
action = A_ACTION_SET;
}
e = id;
while ((*e >= '0' && *e <= '9')) e++;
while (isspace((int)*e))
e++;
if (*e && (*e != ';') && (*e != ','))
pari_err(e_MISC, "Non-numeric argument of an action in a template");
numarg = atol(id); /* Now it is safe to get it... */
switch (action) {
case A_ACTION_SET:
retval |= numarg;
break;
case A_ACTION_UNSET:
retval &= ~numarg;
break;
case A_ACTION_ASSIGN:
retval = numarg;
break;
default:
pari_err(e_MISC,"error in parse_option_string");
}
first = 0;
while (isspace((int)*arg))
arg++;
if (*arg && !(ispunct((int)*arg) && *arg != '-'))
pari_err(e_MISC,"Junk after an id in a stringified flag");
/* Skip punctuation */
if (*arg)
arg++;
}
avma=av;
return retval;
}
int
invmod(GEN a, GEN b, GEN *res)
#endif
{
GEN v,v1,d,d1,q,r;
pari_sp av, av1, lim;
long s;
ulong g;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
if (typ(a) != t_INT || typ(b) != t_INT) pari_err(arither1);
if (!signe(b)) { *res=absi(a); return 0; }
av = avma;
if (lgefint(b) == 3) /* single-word affair */
{
ulong d1 = umodiu(a, (ulong)(b[2]));
if (d1 == 0)
{
if (b[2] == 1L)
{ *res = gen_0; return 1; }
else
{ *res = absi(b); return 0; }
}
g = xgcduu((ulong)(b[2]), d1, 1, &xv, &xv1, &s);
#ifdef DEBUG_LEHMER
fprintferr(" <- %lu,%lu\n", (ulong)(b[2]), (ulong)(d1[2]));
fprintferr(" -> %lu,%ld,%lu; %lx\n", g,s,xv1,avma);
#endif
avma = av;
if (g != 1UL) { *res = utoipos(g); return 0; }
xv = xv1 % (ulong)(b[2]); if (s < 0) xv = ((ulong)(b[2])) - xv;
*res = utoipos(xv); return 1;
}
(void)new_chunk(lgefint(b));
d = absi(b); d1 = modii(a,d);
v=gen_0; v1=gen_1; /* general case */
#ifdef DEBUG_LEHMER
fprintferr("INVERT: -------------------------\n");
output(d1);
#endif
av1 = avma; lim = stack_lim(av,1);
while (lgefint(d) > 3 && signe(d1))
{
#ifdef DEBUG_LEHMER
fprintferr("Calling Lehmer:\n");
#endif
lhmres = lgcdii((ulong*)d, (ulong*)d1, &xu, &xu1, &xv, &xv1, MAXULONG);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
#ifdef DEBUG_LEHMER
fprintferr("Lehmer returned %d [%lu,%lu;%lu,%lu].\n",
lhmres, xu, xu1, xv, xv1);
#endif
if ((lhmres == 1) || (lhmres == -1))
{
if (xv1 == 1)
{
r = subii(d,d1); d=d1; d1=r;
a = subii(v,v1); v=v1; v1=a;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
a = subii(v, mului(xv1,v1)); v=v1; v1=a;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
a = subii(muliu(v,xu), muliu(v1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
v1 = subii(muliu(v,xu1), muliu(v1,xv1)); v = a;
if (lhmres&1)
{
setsigne(d,-signe(d));
setsigne(v,-signe(v));
}
else
{
if (signe(d1)) { setsigne(d1,-signe(d1)); }
setsigne(v1,-signe(v1));
}
}
}
#ifdef DEBUG_LEHMER
else
fprintferr("Lehmer returned 0.\n");
output(d); output(d1); output(v); output(v1);
sleep(1);
#endif
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
#ifdef DEBUG_LEHMER
fprintferr("Full division:\n");
printf(" q = "); output(q); sleep (1);
#endif
a = subii(v,mulii(q,v1));
v=v1; v1=a;
d=d1; d1=r;
}
if (low_stack(lim, stack_lim(av,1)))
{
GEN *gptr[4]; gptr[0]=&d; gptr[1]=&d1; gptr[2]=&v; gptr[3]=&v1;
if(DEBUGMEM>1) pari_warn(warnmem,"invmod");
gerepilemany(av1,gptr,4);
}
} /* end while */
/* Postprocessing - final sprint */
if (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3, and
* gcd(d,d1) is nonzero and fits into one word
*/
g = xxgcduu((ulong)d[2], (ulong)d1[2], 1, &xu, &xu1, &xv, &xv1, &s);
#ifdef DEBUG_LEHMER
output(d);output(d1);output(v);output(v1);
fprintferr(" <- %lu,%lu\n", (ulong)d[2], (ulong)d1[2]);
fprintferr(" -> %lu,%ld,%lu; %lx\n", g,s,xv1,avma);
#endif
if (g != 1UL) { avma = av; *res = utoipos(g); return 0; }
/* (From the xgcduu() blurb:)
* For finishing the multiword modinv, we now have to multiply the
* returned matrix (with properly adjusted signs) onto the values
* v' and v1' previously obtained from the multiword division steps.
* Actually, it is sufficient to take the scalar product of [v',v1']
* with [u1,-v1], and change the sign if s==1.
*/
v = subii(muliu(v,xu1),muliu(v1,xv1));
if (s > 0) setsigne(v,-signe(v));
avma = av; *res = modii(v,b);
#ifdef DEBUG_LEHMER
output(*res); fprintfderr("============================Done.\n");
sleep(1);
#endif
return 1;
}
/* get here when the final sprint was skipped (d1 was zero already) */
avma = av;
if (!equalii(d,gen_1)) { *res = icopy(d); return 0; }
*res = modii(v,b);
#ifdef DEBUG_LEHMER
output(*res); fprintferr("============================Done.\n");
sleep(1);
#endif
return 1;
}
int
ratlift(GEN x, GEN m, GEN *a, GEN *b, GEN amax, GEN bmax)
{
GEN d,d1,v,v1,q,r;
pari_sp av = avma, av1, lim;
long lb,lr,lbb,lbr,s,s0;
ulong vmax;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
if ((typ(x) | typ(m) | typ(amax) | typ(bmax)) != t_INT) pari_err(arither1);
if (signe(bmax) <= 0)
pari_err(talker, "ratlift: bmax must be > 0, found\n\tbmax=%Z\n", bmax);
if (signe(amax) < 0)
pari_err(talker, "ratilft: amax must be >= 0, found\n\tamax=%Z\n", amax);
/* check 2*amax*bmax < m */
if (cmpii(shifti(mulii(amax, bmax), 1), m) >= 0)
pari_err(talker, "ratlift: must have 2*amax*bmax < m, found\n\tamax=%Z\n\tbmax=%Z\n\tm=%Z\n", amax,bmax,m);
/* we _could_ silently replace x with modii(x,m) instead of the following,
* but let's leave this up to the caller
*/
avma = av; s = signe(x);
if (s < 0 || cmpii(x,m) >= 0)
pari_err(talker, "ratlift: must have 0 <= x < m, found\n\tx=%Z\n\tm=%Z\n", x,m);
/* special cases x=0 and/or amax=0 */
if (s == 0)
{
if (a != NULL) *a = gen_0;
if (b != NULL) *b = gen_1;
return 1;
}
else if (signe(amax)==0)
return 0;
/* assert: m > x > 0, amax > 0 */
/* check here whether a=x, b=1 is a solution */
if (cmpii(x,amax) <= 0)
{
if (a != NULL) *a = icopy(x);
if (b != NULL) *b = gen_1;
return 1;
}
/* There is no special case for single-word numbers since this is
* mainly meant to be used with large moduli.
*/
(void)new_chunk(lgefint(bmax) + lgefint(amax)); /* room for a,b */
d = m; d1 = x;
v = gen_0; v1 = gen_1;
/* assert d1 > amax, v1 <= bmax here */
lb = lgefint(bmax);
lbb = bfffo(*int_MSW(bmax));
s = 1;
av1 = avma; lim = stack_lim(av, 1);
/* general case: Euclidean division chain starting with m div x, and
* with bounds on the sequence of convergents' denoms v_j.
* Just to be different from what invmod and bezout are doing, we work
* here with the all-nonnegative matrices [u,u1;v,v1]=prod_j([0,1;1,q_j]).
* Loop invariants:
* (a) (sign)*[-v,v1]*x = [d,d1] (mod m) (componentwise)
* (sign initially +1, changes with each Euclidean step)
* so [a,b] will be obtained in the form [-+d,v] or [+-d1,v1];
* this congruence is a consequence of
* (b) [x,m]~ = [u,u1;v,v1]*[d1,d]~,
* where u,u1 is the usual numerator sequence starting with 1,0
* instead of 0,1 (just multiply the eqn on the left by the inverse
* matrix, which is det*[v1,-u1;-v,u], where "det" is the same as the
* "(sign)" in (a)). From m = v*d1 + v1*d and
* (c) d > d1 >= 0, 0 <= v < v1,
* we have d >= m/(2*v1), so while v1 remains smaller than m/(2*amax),
* the pair [-(sign)*d,v] satisfies (1) but violates (2) (d > amax).
* Conversely, v1 > bmax indicates that no further solutions will be
* forthcoming; [-(sign)*d,v] will be the last, and first, candidate.
* Thus there's at most one point in the chain division where a solution
* can live: v < bmax, v1 >= m/(2*amax) > bmax, and this is acceptable
* iff in fact d <= amax (e.g. m=221, x=34 or 35, amax=bmax=10 fail on
* this count while x=32,33,36,37 succeed). However, a division may leave
* a zero residue before we ever reach this point (consider m=210, x=35,
* amax=bmax=10), and our caller may find that gcd(d,v) > 1 (numerous
* examples -- keep m=210 and consider any of x=29,31,32,33,34,36,37,38,
* 39,40,41).
* Furthermore, at the start of the loop body we have in fact
* (c') 0 <= v < v1 <= bmax, d > d1 > amax >= 0,
* (and are never done already).
*
* Main loop is similar to those of invmod() and bezout(), except for
* having to determine appropriate vmax bounds, and checking termination
* conditions. The signe(d1) condition is only for paranoia
*/
while (lgefint(d) > 3 && signe(d1))
{
/* determine vmax for lgcdii so as to ensure v won't overshoot.
* If v+v1 > bmax, the next step would take v1 beyond the limit, so
* since [+-d1,v1] is not a solution, we give up. Otherwise if v+v1
* is way shorter than bmax, use vmax=MAXULUNG. Otherwise, set vmax
* to a crude lower approximation of bmax/(v+v1), or to 1, which will
* allow the inner loop to do one step
*/
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG;
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1);
/* the latter is pessimistic but faster than a division */
}
/* do a Lehmer-Jebelean round */
lhmres = lgcdii((ulong *)d, (ulong *)d1, &xu, &xu1, &xv, &xv1, vmax);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
if ((lhmres == 1) || (lhmres == -1))
{
s = -s;
if (xv1 == 1)
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (lhmres&1)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1))
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done. Assert v <= bmax here. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise
* proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* lhmres != 0 */
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
#ifdef DEBUG_LEHMER
fprintferr("Full division:\n");
printf(" q = "); output(q); sleep (1);
#endif
d=d1; d1=r;
r = addii(v,mulii(q,v1));
v=v1; v1=r;
s = -s;
/* check whether we are done now. Since we weren't before the div, it
* suffices to examine v1 and d1 -- the new d (former d1) cannot cut it
*/
if (cmpii(v1,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (cmpii(d1,amax) <= 0) /* done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
}
if (low_stack(lim, stack_lim(av,1)))
{
GEN *gptr[4]; gptr[0]=&d; gptr[1]=&d1; gptr[2]=&v; gptr[3]=&v1;
if(DEBUGMEM>1) pari_warn(warnmem,"ratlift");
gerepilemany(av1,gptr,4);
}
} /* end while */
/* Postprocessing - final sprint. Since we usually underestimate vmax,
* this function needs a loop here instead of a simple conditional.
* Note we can only get here when amax fits into one word (which will
* typically not be the case!). The condition is bogus -- d1 is never
* zero at the start of the loop. There will be at most a few iterations,
* so we don't bother collecting garbage
*/
while (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3.
* Moreover, we aren't done already, or we would have returned by now.
* Recompute vmax...
*/
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: d,d1=%Z,%Z\n", d, d1);
fprintferr("rl-fs: v,v1=%Z,%Z\n", v, v1);
#endif
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG; /* (cannot in fact happen) */
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1); /* as above */
}
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: vmax=%lu\n", vmax);
#endif
/* single-word "Lehmer", discarding the gcd or whatever it returns */
(void)rgcduu((ulong)*int_MSW(d), (ulong)*int_MSW(d1), vmax, &xu, &xu1, &xv, &xv1, &s0);
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: [%lu,%lu; %lu,%lu] %s\n",
xu, xu1, xv, xv1,
s0 < 0 ? "-" : "+");
#endif
if (xv1 == 1) /* avoid multiplications */
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
s = -s;
}
else if (xu == 0) /* and xv==1, xu1==1, xv1 > 1 */
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
s = -s;
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (s0 < 0)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1)) /* sic: might vanish now */
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done, as above. Assert v <= bmax. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* while */
/* get here when we have run into d1 == 0 before returning... in fact,
* this cannot happen.
*/
pari_err(talker, "ratlift failed to catch d1 == 0\n");
/* NOTREACHED */
return 0;
}
/* Computation of potential block systems of given size d associated to a
* rational prime p: give a row vector of row vectors containing the
* potential block systems of imprimitivity; a potential block system is a
* vector of row vectors (enumeration of the roots). */
static GEN
calc_block(blockdata *B, GEN Z, GEN Y, GEN SB)
{
long r = lg(Z), lK, i, j, t, tp, T, u, nn, lnon, lY;
GEN K, n, non, pn, pnon, e, Yp, Zp, Zpp;
pari_sp av0 = avma;
if (DEBUGLEVEL>3)
{
fprintferr("lg(Z) = %ld, lg(Y) = %ld\n", r,lg(Y));
if (DEBUGLEVEL > 5)
{
fprintferr("Z = %Z\n",Z);
fprintferr("Y = %Z\n",Y);
}
}
lnon = min(BIL, r);
e = new_chunk(BIL);
n = new_chunk(r);
non = new_chunk(lnon);
pnon = new_chunk(lnon);
pn = new_chunk(lnon);
Zp = cgetg(lnon,t_VEC);
Zpp = cgetg(lnon,t_VEC); nn = 0;
for (i=1; i<r; i++) { n[i] = lg(Z[i])-1; nn += n[i]; }
lY = lg(Y); Yp = cgetg(lY+1,t_VEC);
for (j=1; j<lY; j++) Yp[j] = Y[j];
{
pari_sp av = avma;
long k = nn / B->size;
for (j = 1; j < r; j++)
if (n[j] % k) break;
if (j == r)
{
gel(Yp,lY) = Z;
SB = print_block_system(B, Yp, SB);
avma = av;
}
}
gel(Yp,lY) = Zp;
K = divisors(utoipos(n[1])); lK = lg(K);
for (i=1; i<lK; i++)
{
long ngcd = n[1], k = itos(gel(K,i)), dk = B->size*k, lpn = 0;
for (j=2; j<r; j++)
if (n[j]%k == 0)
{
if (++lpn >= BIL) pari_err(talker,"overflow in calc_block");
pn[lpn] = n[j]; pnon[lpn] = j;
ngcd = cgcd(ngcd, n[j]);
}
if (dk % ngcd) continue;
T = 1<<lpn;
if (lpn == r-2)
{
T--; /* done already above --> print_block_system */
if (!T) continue;
}
if (dk == n[1])
{ /* empty subset, t = 0. Split out for clarity */
Zp[1] = Z[1]; setlg(Zp, 2);
for (u=1,j=2; j<r; j++) Zpp[u++] = Z[j];
setlg(Zpp, u);
SB = calc_block(B, Zpp, Yp, SB);
}
for (t = 1; t < T; t++)
{ /* loop through all non-empty subsets of [1..lpn] */
for (nn=n[1],tp=t, u=1; u<=lpn; u++,tp>>=1)
{
if (tp&1) { nn += pn[u]; e[u] = 1; } else e[u] = 0;
}
if (dk != nn) continue;
for (j=1; j<r; j++) non[j]=0;
Zp[1] = Z[1];
for (u=2,j=1; j<=lpn; j++)
if (e[j]) { Zp[u] = Z[pnon[j]]; non[pnon[j]] = 1; u++; }
setlg(Zp, u);
for (u=1,j=2; j<r; j++)
if (!non[j]) Zpp[u++] = Z[j];
setlg(Zpp, u);
SB = calc_block(B, Zpp, Yp, SB);
}
}
avma = av0; return SB;
}