void
arb_poly_sinh_cosh_series_exponential(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(s);
arb_poly_zero(c);
return;
}
if (hlen == 0)
{
arb_poly_zero(s);
arb_poly_one(c);
return;
}
arb_poly_fit_length(s, n);
arb_poly_fit_length(c, n);
_arb_poly_sinh_cosh_series_exponential(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(s, n);
_arb_poly_normalise(s);
_arb_poly_set_length(c, n);
_arb_poly_normalise(c);
}
void
arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec, int times_pi)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(s);
arb_poly_zero(c);
return;
}
if (hlen == 0)
{
arb_poly_zero(s);
arb_poly_one(c);
return;
}
arb_poly_fit_length(s, n);
arb_poly_fit_length(c, n);
_arb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs,
h->coeffs, hlen, n, prec, times_pi);
_arb_poly_set_length(s, n);
_arb_poly_normalise(s);
_arb_poly_set_length(c, n);
_arb_poly_normalise(c);
}
void
arb_poly_inv_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec)
{
if (n == 0)
{
arb_poly_zero(Qinv);
return;
}
if (Q->length == 0)
{
arb_poly_fit_length(Qinv, n);
_arb_vec_indeterminate(Qinv->coeffs, n);
_arb_poly_set_length(Qinv, n);
return;
}
if (Qinv == Q)
{
arb_poly_t t;
arb_poly_init(t);
arb_poly_inv_series(t, Q, n, prec);
arb_poly_swap(Qinv, t);
arb_poly_clear(t);
return;
}
arb_poly_fit_length(Qinv, n);
_arb_poly_inv_series(Qinv->coeffs, Q->coeffs, Q->length, n, prec);
_arb_poly_set_length(Qinv, n);
_arb_poly_normalise(Qinv);
}
static void
bsplit(arb_poly_t pol, const arb_t sqrtD,
const slong * qbf, slong a, slong b, slong prec)
{
if (b - a == 0)
{
arb_poly_one(pol);
}
else if (b - a == 1)
{
acb_t z;
acb_init(z);
/* j((-b+sqrt(-D))/(2a)) */
arb_set_si(acb_realref(z), -FLINT_ABS(qbf[3 * a + 1]));
arb_set(acb_imagref(z), sqrtD);
acb_div_si(z, z, 2 * qbf[3 * a], prec);
acb_modular_j(z, z, prec);
if (qbf[3 * a + 1] < 0)
{
/* (x^2 - 2re(j) x + |j|^2) */
arb_poly_fit_length(pol, 3);
arb_mul(pol->coeffs, acb_realref(z), acb_realref(z), prec);
arb_addmul(pol->coeffs, acb_imagref(z), acb_imagref(z), prec);
arb_mul_2exp_si(pol->coeffs + 1, acb_realref(z), 1);
arb_neg(pol->coeffs + 1, pol->coeffs + 1);
arb_one(pol->coeffs + 2);
_arb_poly_set_length(pol, 3);
}
else
{
/* (x-j) */
arb_poly_fit_length(pol, 2);
arb_neg(pol->coeffs, acb_realref(z));
arb_one(pol->coeffs + 1);
_arb_poly_set_length(pol, 2);
}
acb_clear(z);
}
else
{
arb_poly_t tmp;
arb_poly_init(tmp);
bsplit(pol, sqrtD, qbf, a, a + (b - a) / 2, prec);
bsplit(tmp, sqrtD, qbf, a + (b - a) / 2, b, prec);
arb_poly_mul(pol, pol, tmp, prec);
arb_poly_clear(tmp);
}
}
int arb_poly_divrem(arb_poly_t Q, arb_poly_t R,
const arb_poly_t A, const arb_poly_t B, slong prec)
{
const slong lenA = A->length, lenB = B->length;
if (lenB == 0 || arb_contains_zero(B->coeffs + lenB - 1))
{
return 0;
}
if (lenA < lenB)
{
arb_poly_set(R, A);
arb_poly_zero(Q);
return 1;
}
if (Q == A || Q == B)
{
arb_poly_t T;
arb_poly_init(T);
arb_poly_divrem(T, R, A, B, prec);
arb_poly_swap(Q, T);
arb_poly_clear(T);
return 1;
}
if (R == A || R == B)
{
arb_poly_t U;
arb_poly_init(U);
arb_poly_divrem(Q, U, A, B, prec);
arb_poly_swap(R, U);
arb_poly_clear(U);
return 1;
}
arb_poly_fit_length(Q, lenA - lenB + 1);
arb_poly_fit_length(R, lenB - 1);
_arb_poly_divrem(Q->coeffs, R->coeffs, A->coeffs, lenA,
B->coeffs, lenB, prec);
_arb_poly_set_length(Q, lenA - lenB + 1);
_arb_poly_set_length(R, lenB - 1);
_arb_poly_normalise(R);
return 1;
}
void
arb_poly_zeta_series(arb_poly_t res, const arb_poly_t f, const arb_t a, int deflate, long n, long prec)
{
if (n == 0)
{
arb_poly_zero(res);
return;
}
arb_poly_fit_length(res, n);
if (f->length == 0)
{
arb_t t;
arb_init(t);
_arb_poly_zeta_series(res->coeffs, t, 1, a, deflate, n, prec);
arb_clear(t);
}
else
{
_arb_poly_zeta_series(res->coeffs, f->coeffs, f->length, a, deflate, n, prec);
}
_arb_poly_set_length(res, n);
_arb_poly_normalise(res);
}
void
arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, long n, long prec)
{
if (n == 0 || B->length == 0)
{
printf("arb_poly_inv_series: require n > 0 and nonzero input\n");
abort();
}
if (A->length == 0)
{
arb_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
arb_poly_t t;
arb_poly_init(t);
arb_poly_div_series(t, A, B, n, prec);
arb_poly_swap(Q, t);
arb_poly_clear(t);
return;
}
arb_poly_fit_length(Q, n);
_arb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec);
_arb_poly_set_length(Q, n);
_arb_poly_normalise(Q);
}
void
arb_poly_rising_ui_series(arb_poly_t res, const arb_poly_t f, ulong r, slong trunc, slong prec)
{
slong len;
if ((f->length == 0 && r != 0) || trunc == 0)
{
arb_poly_zero(res);
return;
}
if (r == 0)
{
arb_poly_one(res);
return;
}
len = poly_pow_length(f->length, r, trunc);
if (f == res)
{
arb_poly_t tmp;
arb_poly_init(tmp);
arb_poly_rising_ui_series(tmp, f, r, len, prec);
arb_poly_swap(tmp, res);
arb_poly_clear(tmp);
}
else
{
arb_poly_fit_length(res, len);
_arb_poly_rising_ui_series(res->coeffs, f->coeffs, f->length, r, len, prec);
_arb_poly_set_length(res, len);
_arb_poly_normalise(res);
}
}
void
arb_poly_mul(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2, slong prec)
{
slong len_out;
if ((poly1->length == 0) || (poly2->length == 0))
{
arb_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
if (res == poly1 || res == poly2)
{
arb_poly_t temp;
arb_poly_init2(temp, len_out);
_arb_poly_mul(temp->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, prec);
arb_poly_swap(res, temp);
arb_poly_clear(temp);
}
else
{
arb_poly_fit_length(res, len_out);
_arb_poly_mul(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, prec);
}
_arb_poly_set_length(res, len_out);
_arb_poly_normalise(res);
}
void
arb_poly_majorant(arb_poly_t res, const arb_poly_t poly, slong prec)
{
arb_poly_fit_length(res, poly->length);
_arb_poly_majorant(res->coeffs, poly->coeffs, poly->length, prec);
_arb_poly_set_length(res, poly->length);
}
void
arb_poly_binomial_transform(arb_poly_t b, const arb_poly_t a, slong len, slong prec)
{
if (len == 0 || a->length == 0)
{
arb_poly_zero(b);
return;
}
if (b == a)
{
arb_poly_t c;
arb_poly_init2(c, len);
_arb_poly_binomial_transform(c->coeffs, a->coeffs, a->length, len, prec);
arb_poly_swap(b, c);
arb_poly_clear(c);
}
else
{
arb_poly_fit_length(b, len);
_arb_poly_binomial_transform(b->coeffs, a->coeffs, a->length, len, prec);
}
_arb_poly_set_length(b, len);
_arb_poly_normalise(b);
}
void
arb_poly_revert_series(arb_poly_t Qinv,
const arb_poly_t Q, slong n, slong prec)
{
slong Qlen = Q->length;
if (Qlen < 2 || !arb_is_zero(Q->coeffs)
|| arb_contains_zero(Q->coeffs + 1))
{
flint_printf("Exception (arb_poly_revert_series). Input must \n"
"have zero constant term and nonzero coefficient of x^1.\n");
abort();
}
if (Qinv != Q)
{
arb_poly_fit_length(Qinv, n);
_arb_poly_revert_series(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
}
else
{
arb_poly_t t;
arb_poly_init2(t, n);
_arb_poly_revert_series(t->coeffs, Q->coeffs, Qlen, n, prec);
arb_poly_swap(Qinv, t);
arb_poly_clear(t);
}
_arb_poly_set_length(Qinv, n);
_arb_poly_normalise(Qinv);
}
void
arb_poly_sqrt_series(arb_poly_t g, const arb_poly_t h, long n, long prec)
{
if (n == 0)
{
arb_poly_zero(g);
return;
}
if (g == h)
{
arb_poly_t t;
arb_poly_init(t);
arb_poly_sqrt_series(t, h, n, prec);
arb_poly_swap(g, t);
arb_poly_clear(t);
return;
}
arb_poly_fit_length(g, n);
if (h->length == 0)
_arb_vec_indeterminate(g->coeffs, n);
else
_arb_poly_sqrt_series(g->coeffs, h->coeffs, h->length, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}
void
acb_poly_reciprocal_majorant(arb_poly_t res, const acb_poly_t poly, long prec)
{
arb_poly_fit_length(res, poly->length);
_acb_poly_reciprocal_majorant(res->coeffs, poly->coeffs, poly->length, prec);
_arb_poly_set_length(res, poly->length);
}
void
arb_poly_product_roots(arb_poly_t poly, arb_srcptr xs, slong n, slong prec)
{
arb_poly_fit_length(poly, n + 1);
_arb_poly_product_roots(poly->coeffs, xs, n, prec);
_arb_poly_set_length(poly, n + 1);
}
void
arb_poly_exp_series(arb_poly_t f, const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(f);
return;
}
if (hlen == 0)
{
arb_poly_one(f);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(f, n);
_arb_poly_exp_series(f->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(f, n);
_arb_poly_normalise(f);
}
void
arb_poly_cosh_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(g);
return;
}
if (hlen == 0)
{
arb_poly_one(g);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(g, n);
_arb_poly_cosh_series(g->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}
void
arb_poly_integral(arb_poly_t res, const arb_poly_t poly, slong prec)
{
arb_poly_fit_length(res, poly->length + 1);
_arb_poly_integral(res->coeffs, poly->coeffs, poly->length + 1, prec);
_arb_poly_set_length(res, poly->length + 1);
_arb_poly_normalise(res);
}
void
arb_poly_inv_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec)
{
arb_poly_fit_length(res, poly->length);
_arb_poly_inv_borel_transform(res->coeffs, poly->coeffs, poly->length, prec);
_arb_poly_set_length(res, poly->length);
_arb_poly_normalise(res);
}
void
arb_poly_set(arb_poly_t dest, const arb_poly_t src)
{
slong len = arb_poly_length(src);
arb_poly_fit_length(dest, len);
_arb_vec_set(dest->coeffs, src->coeffs, len);
_arb_poly_set_length(dest, len);
}
void
arb_poly_compose_series(arb_poly_t res,
const arb_poly_t poly1,
const arb_poly_t poly2, slong n, slong prec)
{
slong len1 = poly1->length;
slong len2 = poly2->length;
slong lenr;
if (len2 != 0 && !arb_is_zero(poly2->coeffs))
{
flint_printf("exception: compose_series: inner "
"polynomial must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
arb_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
arb_poly_set_arb(res, poly1->coeffs);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
arb_poly_fit_length(res, lenr);
_arb_poly_compose_series(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, prec);
_arb_poly_set_length(res, lenr);
_arb_poly_normalise(res);
}
else
{
arb_poly_t t;
arb_poly_init2(t, lenr);
_arb_poly_compose_series(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, prec);
_arb_poly_set_length(t, lenr);
_arb_poly_normalise(t);
arb_poly_swap(res, t);
arb_poly_clear(t);
}
}
void
arb_poly_cot_pi_series(arb_poly_t res, const arb_poly_t f, slong len, slong prec)
{
arb_poly_fit_length(res, len);
if (f->length == 0 || len == 0)
_arb_vec_indeterminate(res->coeffs, len);
else
_arb_poly_cot_pi_series(res->coeffs, f->coeffs, f->length, len, prec);
_arb_poly_set_length(res, len);
_arb_poly_normalise(res);
}
void
arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, long n, long prec)
{
if (n == 0)
{
arb_poly_zero(Q);
return;
}
if (B->length == 0)
{
arb_poly_fit_length(Q, n);
_arb_vec_indeterminate(Q->coeffs, n);
_arb_poly_set_length(Q, n);
return;
}
if (A->length == 0)
{
arb_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
arb_poly_t t;
arb_poly_init(t);
arb_poly_div_series(t, A, B, n, prec);
arb_poly_swap(Q, t);
arb_poly_clear(t);
return;
}
arb_poly_fit_length(Q, n);
_arb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec);
_arb_poly_set_length(Q, n);
_arb_poly_normalise(Q);
}
void
arb_poly_set_coeff_arb(arb_poly_t poly, long n, const arb_t x)
{
arb_poly_fit_length(poly, n + 1);
if (n + 1 > poly->length)
{
_arb_vec_zero(poly->coeffs + poly->length, n - poly->length);
poly->length = n + 1;
}
arb_set(poly->coeffs + n, x);
_arb_poly_normalise(poly);
}
void
arb_poly_add(arb_poly_t res, const arb_poly_t poly1,
const arb_poly_t poly2, slong prec)
{
slong max = FLINT_MAX(poly1->length, poly2->length);
arb_poly_fit_length(res, max);
_arb_poly_add(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs,
poly2->length, prec);
_arb_poly_set_length(res, max);
_arb_poly_normalise(res);
}
void
arb_poly_rgamma_series(arb_poly_t res, const arb_poly_t f, long n, long prec)
{
if (f->length == 0 || n == 0)
{
arb_poly_zero(res);
}
else
{
arb_poly_fit_length(res, n);
_arb_poly_rgamma_series(res->coeffs, f->coeffs, f->length, n, prec);
_arb_poly_set_length(res, n);
_arb_poly_normalise(res);
}
}
void
arb_poly_log_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)
{
if (n == 0)
{
arb_poly_zero(res);
return;
}
arb_poly_fit_length(res, n);
if (f->length == 0)
_arb_vec_indeterminate(res->coeffs, n);
else
_arb_poly_log_series(res->coeffs, f->coeffs, f->length, n, prec);
_arb_poly_set_length(res, n);
_arb_poly_normalise(res);
}
void
arb_poly_interpolate_newton(arb_poly_t poly,
arb_srcptr xs, arb_srcptr ys, long n, long prec)
{
if (n == 0)
{
arb_poly_zero(poly);
}
else
{
arb_poly_fit_length(poly, n);
_arb_poly_set_length(poly, n);
_arb_poly_interpolate_newton(poly->coeffs,
xs, ys, n, prec);
_arb_poly_normalise(poly);
}
}
void
arb_poly_log1p_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)
{
slong flen = f->length;
if (flen == 0 || n == 0)
{
arb_poly_zero(res);
return;
}
if (flen == 1 /*&& !arb_contains_si(f->coeffs, -1)*/)
n = 1;
arb_poly_fit_length(res, n);
_arb_poly_log1p_series(res->coeffs, f->coeffs, flen, n, prec);
_arb_poly_set_length(res, n);
_arb_poly_normalise(res);
}
void
arb_poly_pow_ui_trunc_binexp(arb_poly_t res,
const arb_poly_t poly, ulong exp, slong len, slong prec)
{
slong flen, rlen;
flen = poly->length;
if (exp == 0 && len != 0)
{
arb_poly_one(res);
}
else if (flen == 0 || len == 0)
{
arb_poly_zero(res);
}
else
{
rlen = poly_pow_length(flen, exp, len);
if (res != poly)
{
arb_poly_fit_length(res, rlen);
_arb_poly_pow_ui_trunc_binexp(res->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_arb_poly_set_length(res, rlen);
_arb_poly_normalise(res);
}
else
{
arb_poly_t t;
arb_poly_init2(t, rlen);
_arb_poly_pow_ui_trunc_binexp(t->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_arb_poly_set_length(t, rlen);
_arb_poly_normalise(t);
arb_poly_swap(res, t);
arb_poly_clear(t);
}
}
}
