static GEN
fix_var(GEN x, long v)
{
long i, l = lg(x);
if (!v) return x;
for (i=1; i<l; i++) { GEN t = gel(x,i); setvarn(t[1],v); setvarn(t[2],v); }
return x;
}
static void
init_primedata(primedata *S)
{
long i, j, l, lff = lg(S->ff), v = fetch_var(), N = degpol(S->pol);
GEN T, p = S->p;
if (S->lcm == degpol(S->ff[lff-1]))
{
T = shallowcopy((GEN)S->ff[lff-1]);
setvarn(T, v);
}
else
T = init_Fq(p, S->lcm, v);
name_var(v,"y");
S->T = T;
S->firstroot = cgetg(lff, t_VECSMALL);
S->interp = cgetg(lff, t_VEC);
S->fk = cgetg(N+1, t_VEC);
for (l=1,j=1; j<lff; j++)
{ /* compute roots and fix ordering (Frobenius cycles) */
GEN F = FpX_factorff_irred(gel(S->ff,j), T, p);
gel(S->interp,j) = interpol(F,T,p);
S->firstroot[j] = l;
for (i=1; i<lg(F); i++,l++) S->fk[l] = F[i];
}
S->Trk = init_traces(S->ff, T,p);
S->bezoutC = get_bezout(S->pol, S->ff, p);
}
static void
subfields_poldata(GEN T, poldata *PD)
{
GEN nf,L,dis;
T = shallowcopy(get_nfpol(T, &nf));
PD->pol = T; setvarn(T, 0);
if (nf)
{
PD->den = Q_denom(gel(nf,7));
PD->roo = gel(nf,6);
PD->dis = mulii(absi(gel(nf,3)), sqri(gel(nf,4)));
}
else
{
PD->den = initgaloisborne(T,NULL,ZX_get_prec(T), &L,NULL,&dis);
PD->roo = L;
PD->dis = absi(dis);
}
}
engine_RawRingElementArrayOrNull rawRoots(const RingElement *p, long prec,
int unique) {
const Ring *R = p->get_ring();
const PolynomialRing *P = R->cast_to_PolynomialRing();
if (P == 0) {
ERROR("expected a polynomial ring");
return NULL;
}
const int n = P->n_vars();
if (n != 1) {
ERROR("expected a univariate polynomial ring");
return NULL;
}
const Ring *K = P->getCoefficients();
int degree = 0;
for (Nterm *t = p->get_value(); t != NULL; t = t->next) {
degree = max(degree, abs(*(t->monom)));
}
if (prec == -1) {
prec = (K->get_precision() == 0 ? 53 : K->get_precision());
}
engine_RawRingElementArrayOrNull result = nullptr;
/* Start PARI computations. */
pari_CATCH(e_STACK) {
#ifdef NDEBUG
/*
* Every time the stack is changed PARI writes a message to the file pari_errfile
* which by default is /dev/stderr. To avoid showing this message to the user we
* redirect to /dev/null before the PARI's stack is modified.
*/
FILE *tmp, *dev_null = fopen("/dev/null", "w");
if (dev_null != NULL) {
tmp = pari_errfile;
pari_errfile = dev_null;
}
#endif
allocatemem(0); // passing 0 will double the current stack size.
#ifdef NDEBUG
/*
* We set pari_errfile back to the default value just in case PARI crashes.
*/
if (dev_null != NULL) {
pari_errfile = tmp;
fclose(dev_null);
}
#endif
} pari_RETRY {
const pari_sp av = avma;
GEN q = cgetg(2 + degree + 1, t_POL);
setsigne(q, 1);
setvarn(q, 0);
for (int i = 0; i < degree + 1; ++i) {
gel(q, 2 + i) = gen_0;
}
switch (K->ringID()) {
case M2::ring_ZZ:
ZZ_GMP:
for (Nterm *t = p->get_value(); t != NULL; t = t->next) {
gel(q, 2 + abs(*(t->monom))) =
mpz_get_GEN(reinterpret_cast<const mpz_ptr>(t->coeff.poly_val));
}
break;
case M2::ring_QQ:
for (Nterm *t = p->get_value(); t != NULL; t = t->next) {
gel(q, 2 + abs(*(t->monom))) =
mpq_get_GEN(reinterpret_cast<const mpq_ptr>(t->coeff.poly_val));
}
break;
case M2::ring_RR:
pari_CATCH(e_OVERFLOW) {
ERROR("coefficient is NaN or Infinity");
avma = av;
return NULL;
}
pari_TRY {
for (Nterm *t = p->get_value(); t != NULL; t = t->next) {
gel(q, 2 + abs(*(t->monom))) =
dbltor(*reinterpret_cast<double *>(t->coeff.poly_val));
}
}
pari_ENDCATCH
break;
case M2::ring_CC:
pari_CATCH(e_OVERFLOW) {
ERROR("coefficient is NaN or Infinity");
avma = av;
return NULL;
}
pari_TRY {
for (Nterm *t = p->get_value(); t != NULL; t = t->next) {
GEN z = cgetg(3, t_COMPLEX);
gel(z, 1) = dbltor(reinterpret_cast<complex *>(t->coeff.poly_val)->re);
gel(z, 2) = dbltor(reinterpret_cast<complex *>(t->coeff.poly_val)->im);
gel(q, 2 + abs(*(t->monom))) = z;
}
}
pari_ENDCATCH
break;
case M2::ring_RRR:
for (Nterm *t = p->get_value(); t != NULL; t = t->next) {
gel(q, 2 + abs(*(t->monom))) =
mpfr_get_GEN(reinterpret_cast<const mpfr_ptr>(t->coeff.poly_val));
}
break;
case M2::ring_CCC:
for (Nterm *t = p->get_value(); t != NULL; t = t->next) {
gel(q, 2 + abs(*(t->monom))) =
mpc_get_GEN(reinterpret_cast<const mpc_ptr>(t->coeff.poly_val));
}
break;
case M2::ring_old:
if (K->is_ZZ()) {
goto ZZ_GMP;
}
default:
ERROR("expected coefficient ring of the form ZZ, QQ, RR or CC");
return NULL;
}
if (unique) {
q = RgX_div(q, RgX_gcd_simple(q, RgX_deriv(q)));
}
GEN roots = cleanroots(q, nbits2prec(prec));
const size_t num_roots = lg(roots) - 1;
result = getmemarraytype(engine_RawRingElementArray, num_roots);
result->len = static_cast<int>(num_roots);
ring_elem m2_root;
if (prec <= 53) {
const RingCC *CC = dynamic_cast<const RingCC *>(IM2_Ring_CCC(prec));
for (int i = 0; i < num_roots; ++i) {
const pari_sp av2 = avma;
GEN pari_root = gel(roots, 1 + i);
const complex root = {rtodbl(greal(pari_root)),
rtodbl(gimag(pari_root))};
CC->ring().to_ring_elem(m2_root, root);
result->array[i] = RingElement::make_raw(CC, m2_root);
avma = av2;
}
} else {
const RingCCC *CCC = dynamic_cast<const RingCCC *>(IM2_Ring_CCC(prec));
for (int i = 0; i < num_roots; ++i) {
const pari_sp av2 = avma;
mpc_t root;
auto root1 = reinterpret_cast<mpfc_t*>(&root);
pari_mpc_init_set_GEN(root, gel(roots, 1 + i), GMP_RNDN);
// CCC->ring().to_ring_elem(m2_root, **reinterpret_cast<mpfc_t*>(&root));
CCC->ring().to_ring_elem(m2_root, **root1);
result->array[i] = RingElement::make_raw(CCC, m2_root);
avma = av2;
}
}
/* End PARI computations. */
avma = av;
}
pari_ENDCATCH
return result;
}