void
acb_poly_agm1_series(acb_poly_t res, const acb_poly_t z, long n, long prec)
{
if (n == 0)
{
acb_poly_zero(res);
return;
}
acb_poly_fit_length(res, n);
if (z->length == 0)
{
acb_t t;
acb_init(t);
_acb_poly_agm1_series(res->coeffs, t, 1, n, prec);
acb_clear(t);
}
else
{
_acb_poly_agm1_series(res->coeffs, z->coeffs, z->length, n, prec);
}
_acb_poly_set_length(res, n);
_acb_poly_normalise(res);
}
void
acb_poly_revert_series_lagrange_fast(acb_poly_t Qinv,
const acb_poly_t Q, slong n, slong prec)
{
slong Qlen = Q->length;
if (Qlen < 2 || !acb_is_zero(Q->coeffs)
|| acb_contains_zero(Q->coeffs + 1))
{
flint_printf("Exception (acb_poly_revert_series_lagrange_fast). Input \n"
"must have zero constant term and nonzero coefficient of x^1.\n");
abort();
}
if (Qinv != Q)
{
acb_poly_fit_length(Qinv, n);
_acb_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
}
else
{
acb_poly_t t;
acb_poly_init2(t, n);
_acb_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n, prec);
acb_poly_swap(Qinv, t);
acb_poly_clear(t);
}
_acb_poly_set_length(Qinv, n);
_acb_poly_normalise(Qinv);
}
void
acb_poly_inv_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec)
{
if (n == 0)
{
acb_poly_zero(Qinv);
return;
}
if (Q->length == 0)
{
acb_poly_fit_length(Qinv, n);
_acb_vec_indeterminate(Qinv->coeffs, n);
_acb_poly_set_length(Qinv, n);
return;
}
if (Qinv == Q)
{
acb_poly_t t;
acb_poly_init(t);
acb_poly_inv_series(t, Q, n, prec);
acb_poly_swap(Qinv, t);
acb_poly_clear(t);
return;
}
acb_poly_fit_length(Qinv, n);
_acb_poly_inv_series(Qinv->coeffs, Q->coeffs, Q->length, n, prec);
_acb_poly_set_length(Qinv, n);
_acb_poly_normalise(Qinv);
}
void
acb_poly_add_si(acb_poly_t res, const acb_poly_t x, slong y, slong prec)
{
slong len = x->length;
if (len == 0)
{
acb_poly_set_si(res, y);
}
else
{
acb_poly_fit_length(res, len);
if (y >= 0)
acb_add_ui(res->coeffs, x->coeffs, y, prec);
else
acb_sub_ui(res->coeffs, x->coeffs, -y, prec);
if (res != x)
_acb_vec_set(res->coeffs + 1, x->coeffs + 1, len - 1);
_acb_poly_set_length(res, len);
_acb_poly_normalise(res);
}
}
void
acb_dirichlet_hardy_z_series(acb_poly_t res, const acb_poly_t s,
const dirichlet_group_t G, const dirichlet_char_t chi,
slong len, slong prec)
{
if (len == 0)
{
acb_poly_zero(res);
return;
}
acb_poly_fit_length(res, len);
if (s->length == 0)
{
acb_t t;
acb_init(t);
_acb_dirichlet_hardy_z_series(res->coeffs, t, 1, G, chi, len, prec);
acb_clear(t);
}
else
{
_acb_dirichlet_hardy_z_series(res->coeffs, s->coeffs, s->length, G, chi, len, prec);
}
_acb_poly_set_length(res, len);
_acb_poly_normalise(res);
}
void
acb_poly_pow_ui(acb_poly_t res,
const acb_poly_t poly, ulong exp, slong prec)
{
slong flen, rlen;
flen = poly->length;
if (exp == 0)
{
acb_poly_one(res);
}
else if (flen == 0)
{
acb_poly_zero(res);
}
else
{
rlen = exp * (flen - 1) + 1;
if (res != poly)
{
acb_poly_fit_length(res, rlen);
_acb_poly_pow_ui(res->coeffs,
poly->coeffs, flen, exp, prec);
_acb_poly_set_length(res, rlen);
_acb_poly_normalise(res);
}
else
{
acb_poly_t t;
acb_poly_init2(t, rlen);
_acb_poly_pow_ui(t->coeffs,
poly->coeffs, flen, exp, prec);
_acb_poly_set_length(t, rlen);
_acb_poly_normalise(t);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
}
}
void
acb_poly_pow_ui_trunc_binexp(acb_poly_t res,
const acb_poly_t poly, ulong exp, long len, long prec)
{
long flen, rlen;
flen = poly->length;
if (exp == 0 && len != 0)
{
acb_poly_one(res);
}
else if (flen == 0 || len == 0)
{
acb_poly_zero(res);
}
else
{
rlen = poly_pow_length(flen, exp, len);
if (res != poly)
{
acb_poly_fit_length(res, rlen);
_acb_poly_pow_ui_trunc_binexp(res->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_acb_poly_set_length(res, rlen);
_acb_poly_normalise(res);
}
else
{
acb_poly_t t;
acb_poly_init2(t, rlen);
_acb_poly_pow_ui_trunc_binexp(t->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_acb_poly_set_length(t, rlen);
_acb_poly_normalise(t);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
}
}
void
acb_poly_lgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec)
{
acb_poly_fit_length(res, n);
if (f->length == 0 || n == 0)
_acb_vec_indeterminate(res->coeffs, n);
else
_acb_poly_lgamma_series(res->coeffs, f->coeffs, f->length, n, prec);
_acb_poly_set_length(res, n);
_acb_poly_normalise(res);
}
void
acb_poly_set_coeff_si(acb_poly_t poly, slong n, slong x)
{
acb_poly_fit_length(poly, n + 1);
if (n + 1 > poly->length)
{
_acb_vec_zero(poly->coeffs + poly->length, n - poly->length);
poly->length = n + 1;
}
acb_set_si(poly->coeffs + n, x);
_acb_poly_normalise(poly);
}
void
acb_poly_add(acb_poly_t res, const acb_poly_t poly1,
const acb_poly_t poly2, long prec)
{
long max = FLINT_MAX(poly1->length, poly2->length);
acb_poly_fit_length(res, max);
_acb_poly_add(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs,
poly2->length, prec);
_acb_poly_set_length(res, max);
_acb_poly_normalise(res);
}
void
acb_poly_rgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec)
{
if (f->length == 0 || n == 0)
{
acb_poly_zero(res);
}
else
{
acb_poly_fit_length(res, n);
_acb_poly_rgamma_series(res->coeffs, f->coeffs, f->length, n, prec);
_acb_poly_set_length(res, n);
_acb_poly_normalise(res);
}
}
void
acb_poly_atan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (hlen == 0 || n == 0)
{
acb_poly_zero(g);
return;
}
acb_poly_fit_length(g, n);
_acb_poly_atan_series(g->coeffs, h->coeffs, hlen, n, prec);
_acb_poly_set_length(g, n);
_acb_poly_normalise(g);
}
void
acb_poly_interpolate_fast(acb_poly_t poly,
acb_srcptr xs, acb_srcptr ys, slong n, slong prec)
{
if (n == 0)
{
acb_poly_zero(poly);
}
else
{
acb_poly_fit_length(poly, n);
_acb_poly_set_length(poly, n);
_acb_poly_interpolate_fast(poly->coeffs, xs, ys, n, prec);
_acb_poly_normalise(poly);
}
}
void
acb_poly_add_series(acb_poly_t res, const acb_poly_t poly1,
const acb_poly_t poly2, slong len, slong prec)
{
slong len1, len2;
len1 = poly1->length;
len2 = poly2->length;
len1 = FLINT_MIN(len1, len);
len2 = FLINT_MIN(len2, len);
len = FLINT_MAX(len1, len2);
acb_poly_fit_length(res, len);
_acb_poly_add(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec);
_acb_poly_set_length(res, len);
_acb_poly_normalise(res);
}
void
acb_poly_mullow(acb_poly_t res, const acb_poly_t poly1,
const acb_poly_t poly2,
slong n, slong prec)
{
slong len1, len2;
len1 = poly1->length;
len2 = poly2->length;
if (len1 == 0 || len2 == 0 || n == 0)
{
acb_poly_zero(res);
return;
}
n = FLINT_MIN((len1 + len2 - 1), n);
len1 = FLINT_MIN(len1, n);
len2 = FLINT_MIN(len2, n);
if (res == poly1 || res == poly2)
{
acb_poly_t t;
acb_poly_init2(t, n);
_acb_poly_mullow(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, n, prec);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
else
{
acb_poly_fit_length(res, n);
_acb_poly_mullow(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, n, prec);
}
_acb_poly_set_length(res, n);
_acb_poly_normalise(res);
}
void acb_poly_compose(acb_poly_t res,
const acb_poly_t poly1, const acb_poly_t poly2, slong prec)
{
const slong len1 = poly1->length;
const slong len2 = poly2->length;
if (len1 == 0)
{
acb_poly_zero(res);
}
else if (len1 == 1 || len2 == 0)
{
acb_poly_set_acb(res, poly1->coeffs);
}
else
{
const slong lenr = (len1 - 1) * (len2 - 1) + 1;
if (res != poly1 && res != poly2)
{
acb_poly_fit_length(res, lenr);
_acb_poly_compose(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, prec);
}
else
{
acb_poly_t t;
acb_poly_init2(t, lenr);
_acb_poly_compose(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, prec);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
_acb_poly_set_length(res, lenr);
_acb_poly_normalise(res);
}
}
void
acb_poly_mullow_classical(acb_poly_t res, const acb_poly_t poly1,
const acb_poly_t poly2,
slong n, slong prec)
{
slong len_out;
if (poly1->length == 0 || poly2->length == 0 || n == 0)
{
acb_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
if (n > len_out)
n = len_out;
if (res == poly1 || res == poly2)
{
acb_poly_t t;
acb_poly_init2(t, n);
_acb_poly_mullow_classical(t->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, n, prec);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
else
{
acb_poly_fit_length(res, n);
_acb_poly_mullow_classical(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, n, prec);
}
_acb_poly_set_length(res, n);
_acb_poly_normalise(res);
}
void
acb_hypgeom_pfq_series_direct(acb_poly_t res,
const acb_poly_struct * a, long p,
const acb_poly_struct * b, long q,
const acb_poly_t z, int regularized,
long n, long len, long prec)
{
acb_poly_t s, t, err;
arb_poly_t C, T;
long i;
int is_real;
/* default algorithm to choose number of terms */
if (n < 0)
{
n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec);
}
acb_poly_init(s);
acb_poly_init(t);
acb_poly_init(err);
arb_poly_init(C);
arb_poly_init(T);
acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec);
if (acb_poly_length(t) != 0)
{
is_real = acb_poly_is_real(z);
for (i = 0; i < p; i++)
is_real = is_real && acb_poly_is_real(a + i);
for (i = 0; i < q; i++)
is_real = is_real && acb_poly_is_real(b + i);
acb_poly_majorant(T, t, MAG_BITS);
acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS);
arb_poly_mullow(T, T, C, len, MAG_BITS);
/* create polynomial of errors */
acb_poly_fit_length(err, len);
for (i = 0; i < FLINT_MIN(len, T->length); i++)
{
arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i);
if (!is_real)
arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i);
}
_acb_poly_set_length(err, len);
_acb_poly_normalise(err);
acb_poly_add(s, s, err, prec);
}
acb_poly_set(res, s);
acb_poly_clear(s);
acb_poly_clear(t);
acb_poly_clear(err);
arb_poly_clear(C);
arb_poly_clear(T);
}
static void
evaluate(acb_poly_t A, acb_srcptr a, slong p, const acb_t z, slong n, slong prec)
{
acb_poly_fit_length(A, p + 1);
if (p == 1)
{
acb_add_ui(A->coeffs, a, n, prec);
if (z != NULL)
acb_mul(A->coeffs, A->coeffs, z, prec);
}
else if (p == 2)
{
acb_add(A->coeffs, a + 0, a + 1, prec);
acb_add_ui(A->coeffs + 1, A->coeffs, 2 * n, prec);
acb_add_ui(A->coeffs, A->coeffs, n, prec);
acb_mul_ui(A->coeffs, A->coeffs, n, prec);
acb_addmul(A->coeffs, a + 0, a + 1, prec);
if (z != NULL)
{
acb_mul(A->coeffs, A->coeffs, z, prec);
acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec);
}
}
else if (p == 3)
{
acb_t t, u;
acb_init(t);
acb_init(u);
acb_add(t, a + 0, a + 1, prec);
acb_add(t, t, a + 2, prec);
acb_mul(u, a + 0, a + 1, prec);
acb_mul(A->coeffs, u, a + 2, prec);
acb_addmul(u, a + 0, a + 2, prec);
acb_addmul(u, a + 1, a + 2, prec);
/*
(a0 + n)(a1 + n)(a2 + n) = a0 a1 a2 + (a0 a1 + a0 a2 + a1 a2) n + (a0 + a1 + a2) n^2 + n^3
(a0 a1 + a0 a2 + a1 a2) + 2 (a0 + a1 + a2) n + 3 n^2
(a0 + a1 + a2) + 3n
1
*/
acb_addmul_ui(A->coeffs, u, n, prec);
acb_addmul_ui(A->coeffs, t, n * n, prec);
acb_add_ui(A->coeffs, A->coeffs, n * n * n, prec);
acb_set(A->coeffs + 1, u);
acb_addmul_ui(A->coeffs + 1, t, 2 * n, prec);
acb_add_ui(A->coeffs + 1, A->coeffs + 1, 3 * n * n, prec);
acb_add_ui(A->coeffs + 2, t, 3 * n, prec);
if (z != NULL)
{
acb_mul(A->coeffs + 0, A->coeffs + 0, z, prec);
acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec);
acb_mul(A->coeffs + 2, A->coeffs + 2, z, prec);
}
acb_clear(t);
acb_clear(u);
}
else if (p != 0)
{
flint_abort();
}
if (z != NULL)
acb_set(A->coeffs + p, z);
else
acb_one(A->coeffs + p);
_acb_poly_set_length(A, p + 1);
_acb_poly_normalise(A);
}
void
acb_hypgeom_pfq_series_direct(acb_poly_t res,
const acb_poly_struct * a, long p,
const acb_poly_struct * b, long q,
const acb_poly_t z, int regularized,
long n, long len, long prec)
{
acb_poly_t s, t, err;
arb_poly_t C, T;
long i;
int is_real;
int terminating;
/* default algorithm to choose number of terms */
if (n < 0)
{
n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec);
}
terminating = 0;
/* check if it terminates due to a root of the numerator */
for (i = 0; i < p; i++)
{
if (acb_poly_length(a + i) == 0 && n > 0)
{
terminating = 1;
}
else if (acb_poly_length(a + i) == 1)
{
acb_srcptr c = acb_poly_get_coeff_ptr(a + i, 0);
if (acb_is_int(c) && arb_is_negative(acb_realref(c)) &&
arf_cmpabs_ui(arb_midref(acb_realref(c)), n) < 0)
{
terminating = 1;
}
}
}
/* check if it terminates (to order n) due to z */
/* the following tests could be made stronger... */
if (z->length == 0 && n >= 1)
{
terminating = 1;
}
else if (!terminating && z->length > 0 && acb_is_zero(z->coeffs) && n >= len)
{
if (regularized)
{
terminating = 1;
}
else
{
terminating = 1;
for (i = 0; i < q; i++)
{
acb_srcptr c = acb_poly_get_coeff_ptr(b + i, 0);
if (!arb_is_positive(acb_realref(c)) && acb_contains_int(c))
terminating = 0;
}
}
}
acb_poly_init(s);
acb_poly_init(t);
acb_poly_init(err);
arb_poly_init(C);
arb_poly_init(T);
acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec);
if (!terminating)
{
is_real = acb_poly_is_real(z);
for (i = 0; i < p; i++)
is_real = is_real && acb_poly_is_real(a + i);
for (i = 0; i < q; i++)
is_real = is_real && acb_poly_is_real(b + i);
acb_poly_majorant(T, t, MAG_BITS);
acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS);
if (!_arb_vec_is_finite(T->coeffs, T->length) ||
!_arb_vec_is_finite(C->coeffs, C->length))
{
arb_poly_fit_length(T, len);
_arb_vec_indeterminate(T->coeffs, len);
_arb_poly_set_length(T, len);
}
else
{
arb_poly_mullow(T, T, C, len, MAG_BITS);
}
/* create polynomial of errors */
acb_poly_fit_length(err, len);
for (i = 0; i < FLINT_MIN(len, T->length); i++)
{
arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i);
if (!is_real)
arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i);
}
_acb_poly_set_length(err, len);
_acb_poly_normalise(err);
acb_poly_add(s, s, err, prec);
}
acb_poly_set(res, s);
acb_poly_clear(s);
acb_poly_clear(t);
acb_poly_clear(err);
arb_poly_clear(C);
arb_poly_clear(T);
}