long
group_ident(GEN G, GEN S)
{
pari_sp av = avma;
long idx = group_ident_i(G, S);
if (idx < 0) pari_err_TYPE("group_ident [not a group]", G);
if (!idx) pari_err_IMPL("galoisidentify for groups of order > 127");
avma = av; return idx;
}
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;
}
long
group_ident_trans(GEN G, GEN S)
{
const long tab[]={
4, 1, 2, -1,
6, 2, 1, -1,
8, 1, 2, 4, 5, 3, -1,
9, 1, 2, -1,
10, 2, 1, -1,
12, 5, 1, 4, 3, 2, -1,
14, 2, 1, -1,
15, 1, -1,
16, 1, 4, 10, 8, 5, 6, 13, 12, 14, 2, 9, 7, 11, 3, -1,
18, 5, 1, 3, 4, 2, -1,
20, 2, 1, 5, 4, 3, -1,
21, 2, 1, -1,
22, 2, 1, -1,
24, 8, 1, 7, 5, 12, 13, 6, 14, 2, 15, 4, 10, 9, 11, 3, -1,
25, 1, 2, -1,
26, 2, 1, -1,
27, 1, 2, 3, 5, 4, -1,
28, 3, 1, 4, 2, -1,
30, 2, 4, 3, 1, -1,
-1};
long n = group_order(G), s;
const long *t;
if (n == 1) return 1;
/* N.B. known up to 32 (Cannon-Holt) */
if (n > 30) pari_err_IMPL("group_ident_trans [n > 30]");
if (uisprime(n)) return 1;
s = group_ident(G,S);
for(t=tab;*t>=0;t++)
{
if (t[0]==n) return t[s];
while (*t>=0) t++;
}
return 0; /*NOT REACHED*/
}
/* [L:K] = ell^k; return 1 if L/K is locally cyclotomic at ell, 0 otherwise */
long
rnfislocalcyclo(GEN rnf)
{
pari_sp av = avma;
GEN K, L, S, SK, TK, SLs, SL2, TL, ell;
ulong ll;
long i, j, k, lk, lSK;
checkrnf(rnf);
lk = rnf_get_degree(rnf);
if (lk == 1) return 1;
k = uisprimepower(lk, &ll);
if (!k) pari_err_IMPL("rnfislocalcyclo for non-l-extensions");
ell = utoi(ll);
K = rnf_get_nf(rnf);
L = rnf_build_nfabs(rnf, nf_get_prec(K));
S = rnfidealprimedec(rnf, ell);
SK = gel(S,1);
SLs = gel(S,2);
SL2 = shallowconcat1(SLs);
TK = padicfact(K, SK, 100); lSK = lg(SK);
TL = padicfact(L, SL2, 100);
for (i = 1; i < lSK; i++)
{
long eK = etilde(K, gel(SK,i), gel(TK,i));
GEN SL = gel(SLs,i);
long lSL = lg(SL);
for (j = 1; j < lSL; j++)
{
long iS = gen_search(SL2, gel(SL,j), 0, (void*)&cmp_prime_over_p,
&cmp_nodata);
long eL = etilde(L, gel(SL,j), gel(TL,iS));
if (dvdui(eL/eK, ell)) { avma = av; return 0; }
}
};
avma = av; return 1;
}
