OpenXM_contrib/pari-2.2/src/modules/subfield.c - diff

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Diff for /OpenXM_contrib/pari-2.2/src/modules/Attic/subfield.c between version 1.1 and 1.2

version 1.1, 2001/10/02 11:17:12

version 1.2, 2002/09/11 07:27:06

Line 24 extern GEN matrixpow(long n, long m, GEN y, GEN P,GEN

extern GEN Fp_factor_irred(GEN P,GEN l, GEN Q);

extern GEN FpX_rand(long d1, long v, GEN p);

extern GEN hensel_lift_fact(GEN pol, GEN Q, GEN T, GEN p, GEN pe, long e);

extern GEN ZX_disc_all(GEN x, ulong bound);

extern GEN indexpartial(GEN P, GEN DP);

extern GEN initgaloisborne(GEN T, GEN dn, long prec, GEN *ptL, GEN *ptprep, GEN *ptdis);

extern long ZX_get_prec(GEN x);

static GEN print_block_system(long N,GEN Y,long d,GEN vbs,long maxl);

Line 83 calc_block(long N,GEN Z,long d,GEN Y,GEN vbs,ulong max

Line 87 calc_block(long N,GEN Z,long d,GEN Y,GEN vbs,ulong max

}

if (dk == nn)

{

long av=avma;

gpmem_t av=avma;

int Z_equal_Zp = 1;

for (j=1; j<lnon; j++) non[j]=0;

Line 108 calc_block(long N,GEN Z,long d,GEN Y,GEN vbs,ulong max

Line 112 calc_block(long N,GEN Z,long d,GEN Y,GEN vbs,ulong max

setlg(Zpp, u);

vbs = calc_block(N,Zpp,d,Yp,vbs,maxl);

}

if (vbs && lg(vbs) > maxl) return vbs;

if (vbs && (ulong)lg(vbs) > maxl) return vbs;

avma=av;

}

Line 119 calc_block(long N,GEN Z,long d,GEN Y,GEN vbs,ulong max

Line 123 calc_block(long N,GEN Z,long d,GEN Y,GEN vbs,ulong max

static GEN

potential_block_systems(long N, long d, GEN n, ulong maxl)

{

long av=avma,r,i,j,k;

long r, i, j, k;

gpmem_t av=avma;

GEN p1,vbs,Z;

r=lg(n); Z=cgetg(r,t_VEC);

Line 134 potential_block_systems(long N, long d, GEN n, ulong m

Line 139 potential_block_systems(long N, long d, GEN n, ulong m

/* product of permutations. Put the result in perm1. */

static void

perm_mul(GEN perm1,GEN perm2)

perm_mul_i(GEN perm1,GEN perm2)

{

long av = avma,i, N = lg(perm1);

long i, N = lg(perm1);

gpmem_t av = avma;

GEN perm=new_chunk(N);

for (i=1; i<N; i++) perm[i]=perm1[perm2[i]];

for (i=1; i<N; i++) perm1[i]=perm[i];

Line 153 cycle_power_to_perm(GEN perm,GEN cy,long l)

Line 159 cycle_power_to_perm(GEN perm,GEN cy,long l)

for (i=1; i<N; i++) perm[i] = i;

if (lp)

{

long av = avma;

gpmem_t av = avma;

GEN p1 = new_chunk(N);

b = cy[1];

for (i=1; i<lcy; i++) b = (perm[b] = cy[i+1]);

perm[b] = cy[1];

for (i=1; i<N; i++) p1[i] = perm[i];

for (j=2; j<=lp; j++) perm_mul(perm,p1);

for (j=2; j<=lp; j++) perm_mul_i(perm,p1);

avma = av;

}

return perm;

Line 221 append_vbs(GEN vbs, GEN D)

Line 227 append_vbs(GEN vbs, GEN D)

l = lg(vbs); maxl = vbs[-1];

if (l == maxl)

{

vbs = (GEN)gprealloc((void*)(vbs-1), (2 + (maxl<<1))*sizeof(GEN),

vbs = (GEN)gprealloc((void*)(vbs-1), (2 + (maxl<<1))*sizeof(GEN));

(2 + maxl)*sizeof(GEN));

*vbs = maxl<<1; vbs++; setlg(vbs, 1);

}

if (DEBUGLEVEL>5) fprintferr("appending D = %Z\n",D);

Line 256 print_block_system(long N,GEN Y,long d,GEN vbs,long ma

Line 261 print_block_system(long N,GEN Y,long d,GEN vbs,long ma

if (DEBUGLEVEL>5) fprintferr("Y = %Z\n",Y);

empty = cgetg(1,t_VEC);

n = new_chunk(N+1);

D = cgetg(N+1, t_VEC); setlg(D,1);

D = cget1(N+1, t_VEC);

t=new_chunk(r+1); k=new_chunk(r+1); Z=cgetg(r+1,t_VEC);

for (ns=0,i=1; i<r; i++)

{

Line 299 print_block_system(long N,GEN Y,long d,GEN vbs,long ma

Line 304 print_block_system(long N,GEN Y,long d,GEN vbs,long ma

perm = cgetg(N+1,t_VEC); i=ns;

{

long av = avma;

gpmem_t av = avma;

if (DEBUGLEVEL>5)

{

for (l=1; l<=ns; l++)

Line 313 print_block_system(long N,GEN Y,long d,GEN vbs,long ma

Line 318 print_block_system(long N,GEN Y,long d,GEN vbs,long ma

for (u=1; u<=N; u++) perm[u]=u;

for (u=1; u<=ns; u++)

for (v=1; v<=t[u]; v++)

perm_mul(perm, cycle_power_to_perm(cyperm,gmael(Z,u,v),e[u][v]));

perm_mul_i(perm, cycle_power_to_perm(cyperm,gmael(Z,u,v),e[u][v]));

vbs = append_vbs(vbs, im_block_by_perm(D,perm));

if (lg(vbs) > maxl) return vbs;

avma = av;

Line 376 cand_for_subfields(GEN A,GEN DATA,GEN *ptlistdelta)

Line 381 cand_for_subfields(GEN A,GEN DATA,GEN *ptlistdelta)

{

long N,m,i,j,d,lf;

GEN M,T,pe,p,pol,fhk,g;

GEN _d_1_term,delta,listdelta,whichdelta,firstroot;

GEN d_1_term,delta,listdelta,whichdelta,firstroot;

pol=(GEN)DATA[1];

p = (GEN)DATA[2];

Line 390 cand_for_subfields(GEN A,GEN DATA,GEN *ptlistdelta)

Line 395 cand_for_subfields(GEN A,GEN DATA,GEN *ptlistdelta)

lf = lg(firstroot);

listdelta = cgetg(lf, t_VEC);

whichdelta = cgetg(N+1, t_VECSMALL);

_d_1_term = gzero;

d_1_term = gzero;

for (i=1; i<=m; i++)

{

GEN Ai = (GEN)A[i], p1 = gun;

for (j=1; j<=d; j++)

p1 = FpXQ_mul(p1, (GEN)fhk[Ai[j]], T,pe);

p1 = Fq_mul(p1, (GEN)fhk[Ai[j]], T,pe);

delta[i] = (long)p1;

if (DEBUGLEVEL>2) fprintferr("delta[%ld] = %Z\n",i,p1);

/* g = prod (X - delta[i])

Line 403 cand_for_subfields(GEN A,GEN DATA,GEN *ptlistdelta)

Line 408 cand_for_subfields(GEN A,GEN DATA,GEN *ptlistdelta)

/* fk[k] belongs to block number whichdelta[k] */

for (j=1; j<=d; j++) whichdelta[Ai[j]] = i;

if (typ(p1) == t_POL) p1 = constant_term(p1);

_d_1_term = addii(_d_1_term, p1);

d_1_term = addii(d_1_term, p1);

}

_d_1_term = centermod(_d_1_term, pe); /* Tr(g) */

d_1_term = centermod(d_1_term, pe); /* Tr(g) */

if (absi_cmp(_d_1_term, (GEN)M[3]) > 0) return gdeux; /* d-1 test */

if (absi_cmp(d_1_term, (GEN)M[3]) > 0) return gdeux; /* d-1 test */

g = FqV_roots_to_pol(delta, T, pe, 0);

g = centermod(polsimplify(g), pe); /* assume g in Z[X] */

if (DEBUGLEVEL>2) fprintferr("pol. found = %Z\n",g);

Line 497 chinese_retrieve_pol(GEN DATA, GEN listdelta)

Line 502 chinese_retrieve_pol(GEN DATA, GEN listdelta)

return FpX_res(FpX_red(S, p), FpX_red((GEN)DATA[1],p), p);

}

/* return P(X + c) using destructive Horner */

static GEN

TR_pol(GEN P, GEN c)

{

GEN Q = dummycopy(P), *R;

long i,k,n;

if (!signe(P)) return Q;

R = (GEN*)(Q+2); n = degpol(P);

if (gcmp1(c))

{

for (i=1; i<=n; i++)

for (k=n-i; k<n; k++)

R[k] = gadd(R[k], R[k+1]);

}

else if (gcmp_1(c))

{

for (i=1; i<=n; i++)

for (k=n-i; k<n; k++)

R[k] = gsub(R[k], R[k+1]);

}

else

{

for (i=1; i<=n; i++)

for (k=n-i; k<n; k++)

R[k] = gadd(R[k], gmul(c, R[k+1]));

}

return Q;

}

/* g in Z[X] potentially defines a subfield of Q[X]/f. It is a subfield iff A

* (cf cand_for_subfields) was a block system; then there

* exists h in Q[X] such that f | g o h. listdelta determines h s.t f | g o h

Line 506 embedding_of_potential_subfields(GEN g,GEN DATA,GEN li

Line 541 embedding_of_potential_subfields(GEN g,GEN DATA,GEN li

{

GEN TR,w0_Q,w0,w1_Q,w1,wpow,h0,gp,T,q2,q,p,ind,maxp,a;

long rt;

ulong av;

gpmem_t av;

T = (GEN)DATA[1]; rt = brent_kung_optpow(degpol(T), 2);

p = (GEN)DATA[2];

Line 535 embedding_of_potential_subfields(GEN g,GEN DATA,GEN li

Line 570 embedding_of_potential_subfields(GEN g,GEN DATA,GEN li

w1_Q = centermod(gmul(w1, resii(ind,q)), q);

if (gegal(w1_Q, w0_Q) || cmpii(q,maxp) > 0)

{

GEN G = gcmp1(ind)? g: ZX_rescale_pol(g,ind);

GEN G = gcmp1(ind)? g: rescale_pol(g,ind);

if (gcmp0(poleval(G, gmodulcp(w1_Q,T)))) break;

}

if (cmpii(q, maxp) > 0)

Line 560 embedding_of_potential_subfields(GEN g,GEN DATA,GEN li

Line 595 embedding_of_potential_subfields(GEN g,GEN DATA,GEN li

w0 = w1; w0_Q = w1_Q; p = q; q = q2;

}

TR = (GEN)DATA[14];

if (!gcmp0(TR)) w1_Q = poleval(w1_Q, gadd(polx[0], TR));

if (!gcmp0(TR)) w1_Q = TR_pol(w1_Q, TR);

return gdiv(w1_Q,ind);

}

static GEN

choose_prime(GEN pol,GEN dpol,long d,GEN *ptff,GEN *ptlistpotbl, long *ptlcm)

{

ulong av;

gpmem_t av;

long j,k,oldllist,llist,r,lcm,oldlcm,N,pp;

GEN p,listpotbl,oldlistpotbl,ff,oldff,n,oldn;

byteptr di=diffptr;

long j,k,oldllist,llist,r,lcm,oldlcm,pp,minp, N = degpol(pol), m = N/d;

if (DEBUGLEVEL) timer2();

GEN p,listpotbl,oldlistpotbl,ff,oldff,n,oldn;

di++; p = stoi(2); N = degpol(pol);

while (p[2]<=N) p[2] += *di++;

minp = N*(m-1)/2;

if (DEBUGLEVEL) (void)timer2();

di++; p = stoi(2);

while (p[2]<=minp)

NEXT_PRIME_VIADIFF(p[2], di);

oldllist = 100000;

oldlcm = 0;

oldlistpotbl = oldff = oldn = NULL; pp = 0; /* gcc -Wall */

av = avma;

for(k=1; k<11 || !oldn; k++,p[2]+= *di++,avma = av)

for(k=1; k<11 || !oldn; k++,avma = av)

{

while (!smodis(dpol,p[2])) p[2] += *di++;

while (!smodis(dpol,p[2]))

NEXT_PRIME_VIADIFF(p[2], di);

if (k > 50) err(talker,"sorry, too many block systems in nfsubfields");

ff=(GEN)factmod(pol,p)[1]; r=lg(ff)-1;

ff=(GEN)factmod0(pol,p)[1]; r=lg(ff)-1;

if (r == 1 || r == N) continue;

if (r == 1 || r == N) goto repeat;

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 (lcm < oldlcm) goto repeat; /* false when oldlcm = 0 */

if (r >= BIL) { err(warner,"subfields: overflow in calc_block"); continue; }

if (r >= BIL) { err(warner,"subfields: overflow in calc_block"); goto repeat; }

if (DEBUGLEVEL) fprintferr("p = %ld,\tlcm = %ld,\torbits: %Z\n",p[2],lcm,n);

if (oldn && gegal(n,oldn)) continue;

if (oldn && gegal(n,oldn)) goto repeat;

listpotbl = potential_block_systems(N,d,n, oldllist);

if (!listpotbl) { oldlistpotbl = NULL; pp = p[2]; break; }

Line 601 choose_prime(GEN pol,GEN dpol,long d,GEN *ptff,GEN *pt

Line 639 choose_prime(GEN pol,GEN dpol,long d,GEN *ptff,GEN *pt

{

if (DEBUGLEVEL) msgtimer("#pbs >= %ld [aborted]",oldllist);

for (j=1; j<llist; j++) free((void*)listpotbl[j]);

free((void*)(listpotbl-1)); continue;

free((void*)(listpotbl-1)); goto repeat;

}

oldllist = llist; oldlistpotbl = listpotbl;

pp = p[2]; oldff = ff; oldlcm = lcm; oldn = n;

if (DEBUGLEVEL) msgtimer("#pbs = %ld",llist);

av = avma;

repeat:

NEXT_PRIME_VIADIFF(p[2], di);

}

if (DEBUGLEVEL)

if (DEBUGLEVEL) fprintferr("Chosen prime: p = %ld\n",pp);

{

fprintferr("Chosen prime: p = %ld\n",pp);

if (DEBUGLEVEL>2)

fprintferr("Potential block systems of size %ld: %Z\n", d,oldlistpotbl);

flusherr();

}

if (oldff) oldff = lift_intern(oldff);

*ptlistpotbl=oldlistpotbl; *ptff=oldff; *ptlcm=oldlcm; return stoi(pp);

}

Line 625 bound_for_coeff(long m,GEN rr, GEN *maxroot)

Line 658 bound_for_coeff(long m,GEN rr, GEN *maxroot)

long i,r1, lrr=lg(rr);

GEN p1,b1,b2,B,M, C = matpascal(m-1);

for (r1=0; typ(rr[r1+1]) == t_REAL; r1++) /* empty */;

for (r1=1; r1 < lrr; r1++)

if (typ(rr[r1]) != t_REAL) break;

r1--;

rr = gabs(rr,0); *maxroot = vecmax(rr);

for (i=1; i<lrr; i++)

Line 689 interpol(GEN H, GEN T, GEN p)

Line 724 interpol(GEN H, GEN T, GEN p)

{

d = constant_term(H[i]); /* -D[i] */

p1 = FpXQX_mul(p1,gadd(X,d), T,p);

p2 = FpXQ_mul(p2, gadd(a,d), T,p);

p2 = Fq_mul(p2, gadd(a,d), T,p);

}

p2 = FpXQ_inv(p2, T,p);

return FpXQX_FpXQ_mul(p1,p2, T,p);

Line 732 struct poldata

Line 767 struct poldata

static GEN

compute_data(GEN DATA, struct poldata PD, long d, GEN ff, GEN T,GEN p)

{

long i,j,l,e,N;

long i,j,l,e,N, lff = lg(ff);

GEN den,roo,pe,p1,p2,fk,fhk,MM,maxroot,pol,interp,bezoutC;

GEN ffL,den,roo,pe,p1,p2,fk,fhk,MM,maxroot,pol,interp,bezoutC;

if (DEBUGLEVEL>1) { fprintferr("Entering compute_data()\n\n"); flusherr(); }

pol = PD.pol; N = degpol(pol);

Line 743 compute_data(GEN DATA, struct poldata PD, long d, GEN

Line 778 compute_data(GEN DATA, struct poldata PD, long d, GEN

{

GEN Xm1 = gsub(polx[varn(pol)], gun);

GEN TR = addis((GEN)DATA[14],1);

GEN mTR = negi(TR), mun = negi(gun);

DATA[14] = (long)TR;

pol = poleval(pol, gsub(polx[varn(pol)], TR));

pol = TR_pol(pol, mTR);

p1 = dummycopy(roo); l = lg(p1);

for (i=1; i<l; i++) p1[i] = ladd(TR, (GEN)p1[i]);

roo = p1;

Line 758 compute_data(GEN DATA, struct poldata PD, long d, GEN

Line 794 compute_data(GEN DATA, struct poldata PD, long d, GEN

{

if (degpol(interp[i]) > 0) /* do not turn polun[0] into gun */

{

p1 = poleval((GEN)interp[i], Xm1);

p1 = TR_pol((GEN)interp[i], mun);

interp[i] = (long)FpXQX_red(p1, NULL,p);

}

if (degpol(bezoutC[i]) > 0)

{

p1 = poleval((GEN)bezoutC[i], Xm1);

p1 = TR_pol((GEN)bezoutC[i], mun);

bezoutC[i] = (long)FpXQX_red(p1, NULL,p);

}

p1 = cgetg(lff, t_VEC);

for (i=1; i<lff; i++)

p1[i] = (long)FpX_red(TR_pol((GEN)ff[i], mTR), p);

ff = p1;

}

else

{

GEN firstroot;

GEN firstroot = cgetg(lff, t_VECSMALL);

long r = lg(ff);

DATA = cgetg(15,t_VEC);

DATA[2] = (long)p;

DATA[4] = (long)T;

interp = cgetg(r, t_VEC);

interp = cgetg(lff, t_VEC);

firstroot = cgetg(r, t_VECSMALL);

fk = cgetg(N+1,t_VEC);

for (l=1,j=1; j<r; j++)

for (l=1,j=1; j<lff; j++)

{ /* compute roots and fix ordering (Frobenius cycles) */

p1 = Fp_factor_irred((GEN)ff[j], p, (GEN)DATA[4]);

p1 = Fp_factor_irred((GEN)ff[j], p,T);

interp[j] = (long)interpol(p1,T,p);

firstroot[j] = l;

for (i=1; i<lg(p1); i++,l++) fk[l] = p1[i];

Line 799 compute_data(GEN DATA, struct poldata PD, long d, GEN

Line 837 compute_data(GEN DATA, struct poldata PD, long d, GEN

e = logint(shifti(vecmax(MM),20), p, &pe); /* overlift 2^20 [for d-1 test] */

DATA[3] = (long)pe;

DATA[6] = (long)roots_from_deg1(fk);

#if 0

fhk = hensel_lift_fact(pol,fk,(GEN)DATA[4],p,pe,e);

#else

/* first lift in Zp to precision p^e */

ffL = hensel_lift_fact(pol,ff, NULL,p,pe,e);

fhk = NULL;

for (l=i=1; i<lff; i++)

{ /* lift factorization of ff[i] in Qp[X] / T */

GEN L = (GEN)ffL[i];

long di = degpol(L);

p2 = cgetg(di+1, t_VEC);

for (j=1; j<=di; j++) p2[j] = fk[l++];

p1 = hensel_lift_fact(L,p2,T,p,pe,e);

fhk = fhk? concatsp(fhk, p1): p1;

}

#endif

DATA[5] = (long)roots_from_deg1(fhk);

p1 = gmul(stoi(N), gsqrt(gpuigs(stoi(N-1),N-1),DEFAULTPREC));

Line 831 _subfield(GEN g, GEN h)

Line 885 _subfield(GEN g, GEN h)

static GEN

subfields_of_given_degree(struct poldata PD,long d)

{

ulong av,av2;

gpmem_t av, av2;

long llist,i,nn;

long llist,i,nn,v;

GEN listpotbl,ff,A,CSF,ESF,LSB,p,T,DATA,listdelta;

GEN pol = PD.pol, dpol = PD.dis;

Line 840 subfields_of_given_degree(struct poldata PD,long d)

Line 894 subfields_of_given_degree(struct poldata PD,long d)

av = avma;

p = choose_prime(pol,dpol,degpol(pol)/d,&ff,&listpotbl,&nn);

if (!listpotbl) { avma=av; return cgetg(1,t_VEC); }

T = lift_intern(ffinit(p,nn, fetch_var()));

v = fetch_var(); name_var(v,"y");

T = lift_intern(ffinit(p,nn, v));

DATA = NULL; LSB = cgetg(1,t_VEC);

i = 1; llist = lg(listpotbl);

CHANGE:

Line 871 CHANGE:

Line 926 CHANGE:

LSB = gerepileupto(av2, concat(LSB, _subfield(CSF,ESF)));

}

delete_var();

(void)delete_var();

for (i=1; i<llist; i++) free((void*)listpotbl[i]);

free((void*)(listpotbl-1));

if (DEBUGLEVEL) fprintferr("\nSubfields of degree %ld: %Z\n",d, LSB);

Line 887 fix_var(GEN x, long v)

Line 942 fix_var(GEN x, long v)

return x;

}

extern GEN get_nfpol(GEN x, GEN *nf);

extern GEN vandermondeinverseprep(GEN T, GEN L);

extern GEN ZX_disc_all(GEN x, ulong bound);

extern GEN indexpartial(GEN P, GEN DP);

void

subfields_poldata(GEN T, struct poldata *PD)

{

int i, n;

GEN nf,L,dis;

GEN L, z, prep, den;

long prec;

GEN nf, dis;

T = get_nfpol(T, &nf);

PD->pol = dummycopy(T); /* may change variable number later */

if (nf)

{

PD->den = (GEN)nf[4];

PD->den = Q_denom((GEN)nf[7]);

PD->roo = (GEN)nf[6];

PD->dis = mulii(absi((GEN)nf[3]), sqri((GEN)nf[4]));

return;

}

else

/* copy-paste from galconj.c:galoisborne. Merge as soon as possible */

/* start of copy-paste */

n = degpol(T);

prec = 1;

for (i = 2; i < lgef(T); i++)

if (lg(T[i]) > prec)

prec = lg(T[i]);

/*prec++;*/

if (DEBUGLEVEL>=4) gentimer(3);

L = roots(T, prec);

if (DEBUGLEVEL>=4) genmsgtimer(3,"roots");

for (i = 1; i <= n; i++)

{

z = (GEN) L[i];

PD->den = initgaloisborne(T,NULL,ZX_get_prec(T), &L,NULL,&dis);

if (signe(z[2]))

PD->roo = L;

break;

PD->dis = absi(dis);

L[i] = z[1];

}

if (DEBUGLEVEL>=4) gentimer(3);

prep=vandermondeinverseprep(T, L);

/* end of copy-paste */

{

GEN res = divide_conquer_prod(gabs(prep,prec), mpmul);

disable_dbg(0);

dis = ZX_disc_all(T, 1+logint(res,gdeux,NULL));

disable_dbg(-1);

den = indexpartial(T,dis);

}

PD->den = den;

PD->roo = L;

PD->dis = absi(dis);

}

GEN

subfields(GEN nf,GEN d)

{

ulong av = avma;

gpmem_t av = avma;

long di,N,v0;

long di, N, v0;

GEN LSB,pol;

GEN LSB, pol, G;

struct poldata PD;

pol = get_nfpol(nf, &nf); /* in order to treat trivial cases */

Line 958 subfields(GEN nf,GEN d)

Line 977 subfields(GEN nf,GEN d)

if (di==1) return gerepilecopy(av, _subfield(polx[v0], pol));

if (di < 1 || di > N || N % di) return cgetg(1,t_VEC);

subfields_poldata(nf, &PD);

/* much easier if nf is Galois (WSS) */

G = galoisconj4(nf? nf: pol, NULL, 1, 0);

if (typ(G) != t_INT)

{ /* Bingo */

GEN L = galoissubgroups(G), F;

long k,i, l = lg(L), o = N/di;

F = cgetg(l, t_VEC);

k = 1;

for (i=1; i<l; i++)

{

GEN H = (GEN)L[i];

if (group_order(H) == o)

F[k++] = (long) lift_intern(galoisfixedfield(G, (GEN)H[1], 0, v0));

}

setlg(F, k);

return gerepilecopy(av, F);

}

subfields_poldata(nf? nf:pol, &PD);

pol = PD.pol;

setvarn(pol, 0);

LSB = subfields_of_given_degree(PD, di);

Line 968 subfields(GEN nf,GEN d)

Line 1005 subfields(GEN nf,GEN d)

static GEN

subfieldsall(GEN nf)

{

ulong av = avma;

gpmem_t av = avma;

long N,ld,i,v0;

long N, ld, i, v0;

GEN pol,dg,LSB,NLSB;

GEN G, pol, dg, LSB, NLSB;

struct poldata PD;

/* much easier if nf is Galois (WSS) */

G = galoisconj4(nf, NULL, 1, 0);

if (typ(G) != t_INT)

{

pol = get_nfpol(nf, &nf);

return gerepilecopy(av, lift_intern( galoissubfields(G, 0, varn(pol)) ));

}

subfields_poldata(nf, &PD);

pol = PD.pol;

Line 986 subfieldsall(GEN nf)

Line 1031 subfieldsall(GEN nf)

setvarn(pol, 0);

for (i=2; i<ld; i++)

{

ulong av1 = avma;

gpmem_t av1 = avma;

NLSB = subfields_of_given_degree(PD, N / itos((GEN)dg[i]));

if (lg(NLSB) > 1) LSB = concatsp(LSB,NLSB); else avma = av1;

}

Line 1002 subfields0(GEN nf,GEN d)

Line 1047 subfields0(GEN nf,GEN d)

return d? subfields(nf,d): subfieldsall(nf);

}

/* irreducible (unitary) polynomial of degree n over Fp[v] */

GEN

ffinit(GEN p,long n,long v)

{

long av = avma;

GEN pol;

if (n<=0) err(talker,"non positive degree in ffinit");

if (typ(p) != t_INT) err(typeer,"ffinit");

if (v<0) v = 0;

for(;; avma = av)

{

pol = gadd(gpowgs(polx[v],n), FpX_rand(n-1,v, p));

if (FpX_is_irred(pol, p)) break;

}

return gerepileupto(av, FpX(pol,p));

}

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