void fmpq_poly_get_slice(fmpq_poly_t rop, const fmpq_poly_t op, long i, long j)
{
i = FLINT_MAX(i, 0);
j = FLINT_MIN(j, op->length);
if (i < j)
{
long k;
if (rop == op)
{
for (k = 0; k < i; k++)
fmpz_zero(rop->coeffs + k);
for (k = j; k < rop->length; k++)
fmpz_zero(rop->coeffs + k);
fmpq_poly_canonicalise(rop);
}
else
{
fmpq_poly_fit_length(rop, j);
_fmpq_poly_set_length(rop, j);
_fmpz_vec_set(rop->coeffs + i, op->coeffs + i, j - i);
fmpz_set(rop->den, op->den);
fmpq_poly_canonicalise(rop);
}
}
else
{
fmpq_poly_zero(rop);
}
}
void fmpq_poly_set_coeff_mpz(fmpq_poly_t poly, long n, const mpz_t x)
{
long len = poly->length;
const int replace = (n < len && !fmpz_is_zero(poly->coeffs + n));
if (!replace && mpz_sgn(x) == 0)
return;
if (n + 1 > len)
{
fmpq_poly_fit_length(poly, n + 1);
_fmpq_poly_set_length(poly, n + 1);
mpn_zero((mp_ptr) poly->coeffs + len, (n + 1) - len);
}
if (*poly->den == 1L)
{
fmpz_set_mpz(poly->coeffs + n, x);
if (replace)
_fmpq_poly_normalise(poly);
}
else
{
fmpz_set_mpz(poly->coeffs + n, x);
fmpz_mul(poly->coeffs + n, poly->coeffs + n, poly->den);
if (replace)
fmpq_poly_canonicalise(poly);
}
}
void fmpq_poly_sqrt_series(fmpq_poly_t res, const fmpq_poly_t poly, slong n)
{
fmpz *copy;
int alloc;
if (poly->length < 1 || !fmpz_equal(poly->coeffs, poly->den))
{
flint_printf("Exception (fmpq_poly_sqrt_series). Constant term != 1.\n");
abort();
}
if (n < 1)
{
fmpq_poly_zero(res);
return;
}
if (poly->length >= n)
{
copy = poly->coeffs;
alloc = 0;
}
else
{
slong i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < poly->length; i++)
copy[i] = poly->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (res != poly)
{
fmpq_poly_fit_length(res, n);
_fmpq_poly_sqrt_series(res->coeffs, res->den, copy, poly->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_sqrt_series(t->coeffs, t->den, copy, poly->den, n);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(res, n);
fmpq_poly_canonicalise(res);
if (alloc)
flint_free(copy);
}
void fmpq_poly_reverse(fmpq_poly_t res, const fmpq_poly_t poly, slong n)
{
slong len = FLINT_MIN(n, poly->length);
if (len == 0)
{
fmpq_poly_zero(res);
return;
}
fmpq_poly_fit_length(res, n);
_fmpz_poly_reverse(res->coeffs, poly->coeffs, len, n);
fmpz_set(res->den, poly->den);
_fmpq_poly_set_length(res, n);
fmpq_poly_canonicalise(res);
}
void random_fmpq_poly(fmpq_poly_t pol, flint_rand_t state, slong length)
{
fmpz * arr;
slong i;
fmpq_poly_fit_length(pol, length);
arr = fmpq_poly_numref(pol);
for (i = 0; i < length; i++)
fmpz_randbits(arr + i, state, BITS);
fmpz_randbits(fmpq_poly_denref(pol), state, BITS);
_fmpq_poly_set_length(pol, length);
_fmpq_poly_normalise(pol);
fmpq_poly_canonicalise(pol);
}
void
fmpq_poly_interpolate_fmpz_vec(fmpq_poly_t poly,
const fmpz * xs, const fmpz * ys, long n)
{
if (n == 0)
{
fmpq_poly_zero(poly);
}
else if (n == 1)
{
fmpq_poly_set_fmpz(poly, ys);
}
else
{
fmpq_poly_fit_length(poly, n);
_fmpq_poly_interpolate_fmpz_vec(poly->coeffs, poly->den, xs, ys, n);
_fmpq_poly_set_length(poly, n);
fmpq_poly_canonicalise(poly);
}
}
void fmpq_poly_inv_series_newton(fmpq_poly_t Qinv, const fmpq_poly_t Q, long n)
{
fmpz *copy;
int alloc;
if (Q->length >= n)
{
copy = Q->coeffs;
alloc = 0;
}
else
{
long i;
copy = (fmpz *) flint_malloc(n * sizeof(fmpz));
for (i = 0; i < Q->length; i++)
copy[i] = Q->coeffs[i];
for ( ; i < n; i++)
copy[i] = 0;
alloc = 1;
}
if (Qinv != Q)
{
fmpq_poly_fit_length(Qinv, n);
_fmpq_poly_inv_series_newton(Qinv->coeffs, Qinv->den, copy, Q->den, n);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, n);
_fmpq_poly_inv_series_newton(t->coeffs, t->den, copy, Q->den, n);
fmpq_poly_swap(Qinv, t);
fmpq_poly_clear(t);
}
_fmpq_poly_set_length(Qinv, n);
fmpq_poly_canonicalise(Qinv);
if (alloc)
flint_free(copy);
}
void fmpq_poly_randtest_unsigned(fmpq_poly_t poly, flint_rand_t state,
long len, mp_bitcnt_t bits)
{
ulong m;
m = n_randlimb(NULL);
fmpq_poly_fit_length(poly, len);
_fmpq_poly_set_length(poly, len);
if (m & 1UL)
{
_fmpz_vec_randtest_unsigned(poly->coeffs, state, len, bits);
}
else
{
fmpz_t x;
fmpz_init(x);
fmpz_randtest_unsigned(x, state, bits / 2);
_fmpz_vec_randtest_unsigned(poly->coeffs, state, len, (bits + 1) / 2);
_fmpz_vec_scalar_mul_fmpz(poly->coeffs, poly->coeffs, len, x);
fmpz_clear(x);
}
if (m & 2UL)
{
fmpz_randtest_not_zero(poly->den, state, FLINT_MAX(bits, 1));
fmpz_abs(poly->den, poly->den);
fmpq_poly_canonicalise(poly);
}
else
{
fmpz_set_ui(poly->den, 1);
_fmpq_poly_normalise(poly);
}
}
int
main(void)
{
int i, result;
ulong cflags = UWORD(0);
FLINT_TEST_INIT(state);
flint_printf("sqrt_series....");
fflush(stdout);
/* Check aliasing of a and c */
for (i = 0; i < 50 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b;
slong n = n_randint(state, 50) + 1;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_randtest_not_zero(a, state, n_randint(state, 50) + 1, 50);
fmpq_poly_set_coeff_ui(a, 0, UWORD(1));
fmpq_poly_canonicalise(a);
fmpq_poly_sqrt_series(b, a, n);
fmpq_poly_sqrt_series(a, a, n);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(b) ? 0 : 2;
result = (fmpq_poly_equal(a, b) && !cflags);
if (!result)
{
flint_printf("FAIL:\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
}
/* Check sqrt(a)^2 = a */
for (i = 0; i < 50 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b, c;
slong n = n_randint(state, 80) + 1;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(c);
fmpq_poly_randtest_not_zero(a, state, n_randint(state, 80) + 1, 80);
fmpq_poly_set_coeff_ui(a, 0, UWORD(1));
fmpq_poly_sqrt_series(b, a, n);
fmpq_poly_mullow(c, b, b, n);
fmpq_poly_truncate(a, n);
cflags |= fmpq_poly_is_canonical(b) ? 0 : 1;
result = (fmpq_poly_equal(c, a) && !cflags);
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), fmpq_poly_debug(a), flint_printf("\n\n");
flint_printf("b = "), fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("c = "), fmpq_poly_debug(c), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
ulong cflags = UWORD(0);
FLINT_TEST_INIT(state);
flint_printf("asinh_series....");
fflush(stdout);
/* Check aliasing of a and c */
for (i = 0; i < 20 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b;
slong n = n_randint(state, 50) + 1;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_randtest_not_zero(a, state, n_randint(state, 50) + 1, 50);
fmpq_poly_set_coeff_ui(a, 0, UWORD(0));
fmpq_poly_canonicalise(a);
fmpq_poly_asinh_series(b, a, n);
fmpq_poly_asinh_series(a, a, n);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(b) ? 0 : 2;
result = (fmpq_poly_equal(a, b) && !cflags);
if (!result)
{
flint_printf("FAIL:\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
}
/* Check asinh(A) = atanh(A/sqrt(1+A^2)) */
for (i = 0; i < 20 * flint_test_multiplier(); i++)
{
fmpq_poly_t A, B, asinhA, atanhB;
slong n = n_randint(state, 80) + 1;
fmpq_poly_init(A);
fmpq_poly_init(B);
fmpq_poly_init(asinhA);
fmpq_poly_init(atanhB);
fmpq_poly_randtest_not_zero(A, state, n_randint(state, 80) + 1, 80);
fmpq_poly_set_coeff_ui(A, 0, UWORD(0));
fmpq_poly_mullow(B, A, A, n);
fmpq_poly_set_coeff_ui(B, 0, UWORD(1));
fmpq_poly_invsqrt_series(B, B, n);
fmpq_poly_mullow(B, A, B, n);
fmpq_poly_asinh_series(asinhA, A, n);
fmpq_poly_atanh_series(atanhB, B, n);
cflags |= fmpq_poly_is_canonical(asinhA) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(atanhB) ? 0 : 2;
result = (fmpq_poly_equal(asinhA, atanhB) && !cflags);
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("A = "), fmpq_poly_debug(A), flint_printf("\n\n");
flint_printf("B = "), fmpq_poly_debug(B), flint_printf("\n\n");
flint_printf("asinh(A) = "), fmpq_poly_debug(asinhA), flint_printf("\n\n");
flint_printf("atanh(B) = "), fmpq_poly_debug(atanhB), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_poly_clear(A);
fmpq_poly_clear(B);
fmpq_poly_clear(asinhA);
fmpq_poly_clear(atanhB);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
ulong cflags = 0UL;
printf("sinh_series....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing of a and c */
for (i = 0; i < 200; i++)
{
fmpq_poly_t a, b;
long n = n_randint(state, 50) + 1;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_randtest_not_zero(a, state, n_randint(state, 50) + 1, 50);
fmpq_poly_set_coeff_ui(a, 0, 0UL);
fmpq_poly_canonicalise(a);
fmpq_poly_sinh_series(b, a, n);
fmpq_poly_sinh_series(a, a, n);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(b) ? 0 : 2;
result = (fmpq_poly_equal(a, b) && !cflags);
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
printf("cflags = %lu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
}
/* Check asinh(sinh(a)) = a */
for (i = 0; i < 200; i++)
{
fmpq_poly_t a, sinha, asinhsinha;
long n = n_randint(state, 80) + 1;
fmpq_poly_init(a);
fmpq_poly_init(sinha);
fmpq_poly_init(asinhsinha);
fmpq_poly_randtest_not_zero(a, state, n_randint(state, 60) + 1, 80);
fmpq_poly_set_coeff_ui(a, 0, 0UL);
fmpq_poly_sinh_series(sinha, a, n);
fmpq_poly_asinh_series(asinhsinha, sinha, n);
fmpq_poly_truncate(a, n);
cflags |= fmpq_poly_is_canonical(sinha) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(asinhsinha) ? 0 : 2;
result = (fmpq_poly_equal(asinhsinha, a) && !cflags);
if (!result)
{
printf("FAIL:\n");
printf("a = "), fmpq_poly_debug(a), printf("\n\n");
printf("sinh(a) = "), fmpq_poly_debug(sinha), printf("\n\n");
printf("asinh(sinh(a)) = "), fmpq_poly_debug(asinhsinha), printf("\n\n");
printf("cflags = %lu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(sinha);
fmpq_poly_clear(asinhsinha);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
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;
}
int
main(void)
{
int i, result;
flint_rand_t state;
ulong cflags = 0UL;
printf("exp_series....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing of a and c */
for (i = 0; i < 200; i++)
{
fmpq_poly_t a, b;
long n = n_randint(state, 50) + 1;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_randtest_not_zero(a, state, n_randint(state, 50) + 1, 50);
fmpq_poly_set_coeff_ui(a, 0, 0UL);
fmpq_poly_canonicalise(a);
fmpq_poly_exp_series(b, a, n);
fmpq_poly_exp_series(a, a, n);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(b) ? 0 : 2;
result = (fmpq_poly_equal(a, b) && !cflags);
if (!result)
{
printf("FAIL:\n");
fmpq_poly_debug(a), printf("\n\n");
fmpq_poly_debug(b), printf("\n\n");
printf("cflags = %lu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
}
/* Check exp(a+b) = exp(a) * exp(b) */
for (i = 0; i < 500; i++)
{
fmpq_poly_t a, b, ab, expa, expb, expab, expa_expb;
long n = n_randint(state, 80) + 1;
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(ab);
fmpq_poly_init(expa);
fmpq_poly_init(expb);
fmpq_poly_init(expab);
fmpq_poly_init(expa_expb);
fmpq_poly_randtest_not_zero(a, state, n_randint(state, 60) + 1, 80);
fmpq_poly_set_coeff_ui(a, 0, 0UL);
fmpq_poly_randtest_not_zero(b, state, n_randint(state, 60) + 1, 80);
fmpq_poly_set_coeff_ui(b, 0, 0UL);
fmpq_poly_add(ab, a, b);
fmpq_poly_exp_series(expab, ab, n);
fmpq_poly_exp_series(expa, a, n);
fmpq_poly_exp_series(expb, b, n);
fmpq_poly_mullow(expa_expb, expa, expb, n);
cflags |= fmpq_poly_is_canonical(expa) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(expb) ? 0 : 2;
cflags |= fmpq_poly_is_canonical(expab) ? 0 : 4;
result = (fmpq_poly_equal(expab, expa_expb) && !cflags);
if (!result)
{
printf("FAIL:\n");
printf("a = "), fmpq_poly_debug(a), printf("\n\n");
printf("b = "), fmpq_poly_debug(b), printf("\n\n");
printf("exp(a) = "), fmpq_poly_debug(expa), printf("\n\n");
printf("exp(b) = "), fmpq_poly_debug(expb), printf("\n\n");
printf("exp(ab) = "), fmpq_poly_debug(expab), printf("\n\n");
printf("cflags = %lu\n\n", cflags);
abort();
}
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(ab);
fmpq_poly_clear(expa);
fmpq_poly_clear(expb);
fmpq_poly_clear(expab);
fmpq_poly_clear(expa_expb);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
