std::vector<mpz_class> renf_elem_class::num_vector() const noexcept
{
mpz_class x;
std::vector<mpz_class> res;
if (nf == nullptr)
{
fmpz_get_mpz(x.__get_mp(), fmpq_numref(b));
res.push_back(x);
}
else
{
fmpq_poly_t f;
fmpq_poly_init(f);
nf_elem_get_fmpq_poly(f, a->elem, nf->renf_t()->nf);
for (size_t i = 0; i < fmpq_poly_length(f); i++)
{
fmpz_get_mpz(x.__get_mp(), fmpq_poly_numref(f) + i);
res.push_back(x);
}
size_t deg = fmpq_poly_degree(nf->renf_t()->nf->pol);
for (size_t i = fmpq_poly_length(f); i < deg; i++)
res.push_back(mpz_class(0));
fmpq_poly_clear(f);
}
return res;
}
int main(int argc, char* argv[]) {
int i, j, k;
int levels[argc-1];
fmpq_poly_t Pn, Ep;
long deg;
char *strf;
acb_ptr nodes;
acb_ptr weights;
int solvable;
int validate_extension, validate_weights;
int valid;
int comp_nodes, comp_weights;
int target_prec;
int nrprintdigits;
int loglevel;
if(argc <= 1) {
printf("Compute a nested generalized Kronrod extension of a Gauss rule\n");
printf("Syntax: kes [-ve] [-vw] [-cn] [-cw] [-dc D] [-dp D] [-l L] n p1 p2 ... pk\n");
printf("Options:\n");
printf(" -ve Validate the polynomial extension by nodes\n");
printf(" -vw Validate the polynomial extension by weights\n");
printf(" -cn Compute the nodes\n");
printf(" -cw Compute the weights\n");
printf(" -dc Compute nodes and weights up to this number of decimal digits\n");
printf(" -dp Print this number of decimal digits\n");
printf(" -l Set the log level\n");
return EXIT_FAILURE;
}
target_prec = 53;
nrprintdigits = 20;
loglevel = 8;
comp_nodes = 0;
comp_weights = 0;
validate_extension = 0;
validate_weights = 0;
k = 0;
for(i = 1; i < argc; i++) {
if (!strcmp(argv[i], "-ve")) {
validate_extension = 1;
} else if (!strcmp(argv[i], "-vw")) {
validate_weights = 1;
} else if (!strcmp(argv[i], "-cn")) {
comp_nodes = 1;
} else if (!strcmp(argv[i], "-cw")) {
comp_weights = 1;
} else if (!strcmp(argv[i], "-dc")) {
/* 'digits' is in base 10 and log(10)/log(2) = 3.32193 */
target_prec = 3.32193 * atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-dp")) {
nrprintdigits = atoi(argv[i+1]);
i++;
} else if (!strcmp(argv[i], "-l")) {
loglevel = atoi(argv[i+1]);
i++;
} else {
levels[k] = atoi(argv[i]);
k++;
}
}
/* Compute extension */
fmpq_poly_init(Pn);
polynomial(Pn, levels[0]);
printf("Starting with polynomial:\n");
strf = fmpq_poly_get_str_pretty(Pn, "t");
flint_printf("P : %s\n", strf);
printf("Extension levels are:");
for(i = 0; i < k; i++) {
printf(" %i", levels[i]);
}
printf("\n");
fmpq_poly_init(Ep);
solvable = find_multi_extension(Ep, Pn, k, levels, validate_extension, loglevel);
fmpq_poly_mul(Pn, Pn, Ep);
fmpq_poly_canonicalise(Pn);
if(solvable) {
if(! fmpq_poly_is_squarefree(Pn)) {
printf("=====> FINAL POLYNOMIAL NOT SQF <=====");
}
if(loglevel >= 2) {
printf("-------------------------------------------------\n");
printf("Ending with final polynomial:\n");
strf = fmpq_poly_get_str_pretty(Pn, "t");
flint_printf("P : %s\n", strf);
}
deg = fmpq_poly_degree(Pn);
nodes = _acb_vec_init(deg);
weights = _acb_vec_init(deg);
if(comp_weights || validate_weights) {
compute_nodes_and_weights(nodes, weights, Pn, target_prec, loglevel);
} else if(comp_nodes) {
compute_nodes(nodes, Pn, target_prec, loglevel);
}
valid = 1;
if(validate_weights) {
valid = validate_extension_by_weights(weights, deg, target_prec, loglevel);
}
if(! valid) {
printf("**************************************\n");
printf("*** EXTENSION WITH INVALID WEIGHTS ***\n");
printf("**************************************\n");
}
/* Print roots and weights */
if((validate_weights && valid) || ! validate_weights) {
if(comp_nodes) {
printf("-------------------------------------------------\n");
printf("The nodes are:\n");
for(j = 0; j < deg; j++) {
printf("| ");
acb_printd(nodes + j, nrprintdigits);
printf("\n");
}
}
if(comp_weights) {
printf("-------------------------------------------------\n");
printf("The weights are:\n");
for(j = 0; j < deg; j++) {
printf("| ");
acb_printd(weights + j, nrprintdigits);
printf("\n");
}
}
}
_acb_vec_clear(nodes, deg);
_acb_vec_clear(weights, deg);
}
flint_free(strf);
fmpq_poly_clear(Pn);
fmpq_poly_clear(Ep);
return EXIT_SUCCESS;
}
void nf_elem_rep_mat_fmpz_mat_den(fmpz_mat_t res, fmpz_t den, const nf_elem_t a, const nf_t nf)
{
if (nf->flag & NF_LINEAR)
{
fmpz_set(fmpz_mat_entry(res, 0, 0), LNF_ELEM_NUMREF(a));
fmpz_set(den, LNF_ELEM_DENREF(a));
}
else if (nf->flag & NF_QUADRATIC)
{
nf_elem_t t;
const fmpz * const anum = QNF_ELEM_NUMREF(a);
const fmpz * const aden = QNF_ELEM_DENREF(a);
fmpz * const tnum = QNF_ELEM_NUMREF(t);
fmpz * const tden = QNF_ELEM_DENREF(t);
nf_elem_init(t, nf);
nf_elem_mul_gen(t, a, nf);
if (fmpz_equal(tden, aden))
{
fmpz_set(fmpz_mat_entry(res, 0, 0), anum);
fmpz_set(fmpz_mat_entry(res, 0, 1), anum + 1);
fmpz_set(fmpz_mat_entry(res, 1, 0), tnum);
fmpz_set(fmpz_mat_entry(res, 1, 1), tnum + 1);
fmpz_set(den, tden);
}
else
{
fmpz_lcm(den, tden, aden);
fmpz_divexact(fmpz_mat_entry(res, 0, 0), den, aden);
fmpz_mul(fmpz_mat_entry(res, 0, 1), anum + 1, fmpz_mat_entry(res, 0, 0));
fmpz_mul(fmpz_mat_entry(res, 0, 0), anum, fmpz_mat_entry(res, 0, 0));
fmpz_divexact(fmpz_mat_entry(res, 1, 0), den, tden);
fmpz_mul(fmpz_mat_entry(res, 1, 1), tnum + 1, fmpz_mat_entry(res, 1, 0));
fmpz_mul(fmpz_mat_entry(res, 1, 0), tnum, fmpz_mat_entry(res, 1, 0));
}
nf_elem_clear(t, nf);
}
else
{
slong i, j;
nf_elem_t t;
slong d = fmpq_poly_degree(nf->pol);
nf_elem_init(t, nf);
nf_elem_set(t, a, nf);
if (NF_ELEM(a)->length == 0)
{
fmpz_mat_zero(res);
fmpz_one(den);
}
else if (NF_ELEM(a)->length == 1)
{
fmpz_mat_zero(res);
for (i = 0; i <= d - 1; i++)
{
fmpz_set(fmpz_mat_entry(res, i, i), fmpq_poly_numref(NF_ELEM(a)));
}
fmpz_set(den, fmpq_poly_denref(NF_ELEM(a)));
}
else
{
/* Special case if defining polynomial is monic and integral and the element also has trivial denominator */
if (nf->flag & NF_MONIC && fmpz_is_one(fmpq_poly_denref(nf->pol)) && fmpz_is_one(fmpq_poly_denref(NF_ELEM(a))))
{
fmpz_one(den);
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 1; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
}
else
{
/* Now the general case. For 0 <= j < d - 2 we store the
* denominator for row j at res[d - 1, j]. At the end we
* divide the lcm of all of them by the corresponding
* denominator of the row to get the correct multiplier for
* row.
*/
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, 0, i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, 0, i));
fmpz_set(fmpz_mat_entry(res, d - 1, 0), fmpq_poly_denref(NF_ELEM(a)));
for (j = 1; j <= d - NF_ELEM(a)->length; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i < j; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
for (i = 0; i <= NF_ELEM(a)->length - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, j + i), fmpq_poly_numref(NF_ELEM(a)) + i);
for (i = j + NF_ELEM(a)->length; i <= d - 1; i++)
fmpz_zero(fmpz_mat_entry(res, j, i));
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(a)));
}
for (j = d - NF_ELEM(a)->length + 1; j <= d - 2; j++)
{
nf_elem_mul_gen(t, t, nf);
for (i = 0; i <= d - 1; i++)
fmpz_set(fmpz_mat_entry(res, j, i), fmpq_poly_numref(NF_ELEM(t)) + i);
fmpz_set(fmpz_mat_entry(res, d - 1, j), fmpq_poly_denref(NF_ELEM(t)));
}
nf_elem_mul_gen(t, t, nf);
/* Now compute the correct denominator */
fmpz_set(fmpz_mat_entry(res, d - 1, d - 1), fmpq_poly_denref(NF_ELEM(t)));
fmpz_set(den, fmpq_poly_denref(NF_ELEM(t)));
for (j = 0; j <= d - 2; j++)
fmpz_lcm(den, den, fmpz_mat_entry(res, d - 1, j));
for (j = 0; j <= d - 2; j++)
{
if (!fmpz_equal(den, fmpz_mat_entry(res, d - 1, j)))
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, j), den, fmpz_mat_entry(res, d - 1, j));
for (i = 0; i <= d - 1; i++)
fmpz_mul(fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, j, i), fmpz_mat_entry(res, d - 1, j));
}
}
if (fmpz_equal(den, fmpz_mat_entry(res, d - 1, d - 1)))
{
for (i = 0; i < d; i++)
fmpz_set(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i);
}
else
{
fmpz_divexact(fmpz_mat_entry(res, d - 1, d - 1), den, fmpq_poly_denref(NF_ELEM(t)));
for (i = 0; i < d; i++)
fmpz_mul(fmpz_mat_entry(res, d - 1, i), fmpq_poly_numref(NF_ELEM(t)) + i, fmpz_mat_entry(res, d - 1, d - 1));
}
}
}
nf_elem_clear(t, nf);
}
}
