FLINT3.7.0-dev
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_gr_poly_tan_series, gr_poly_tan_series, _gr_poly_tanh_series, gr_poly_tanh_series, _gr_poly_cot_series, gr_poly_cot_series, _gr_poly_coth_series, gr_poly_coth_series, _gr_poly_tan_pi_series, gr_poly_tan_pi_series, _gr_poly_cot_pi_series, gr_poly_cot_pi_series

Synopsis#include <flint/gr_poly.h>
int _gr_poly_tan_series(gr_ptr f, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_tan_series(gr_poly_t f, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_tanh_series(gr_ptr f, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_tanh_series(gr_poly_t f, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_cot_series(gr_ptr f, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_cot_series(gr_poly_t f, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_coth_series(gr_ptr f, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_coth_series(gr_poly_t f, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_tan_pi_series(gr_ptr f, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_tan_pi_series(gr_poly_t f, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_cot_pi_series(gr_ptr f, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_cot_pi_series(gr_poly_t f, const gr_poly_t h, slong n, gr_ctx_t ctx)source

Set f to \tan, \tanh, \cot, \coth, \tan(\pi \cdot) or \cot(\pi \cdot) of h modulo x^n. Over rings with real precision, an argument with large imaginary part (for \tan, \cot) or large real part (for \tanh, \coth) is handled by the exponential algorithm for the sake of relative accuracy; otherwise the basecase is used below a cutoff as for the sine and cosine, and Newton iteration above it.

Cite this page

The FLINT team, “_gr_poly_tan_series, gr_poly_tan_series, _gr_poly_tanh_series, gr_poly_tanh_series, _gr_poly_cot_series, gr_poly_cot_series, _gr_poly_coth_series, gr_poly_coth_series, _gr_poly_tan_pi_series, gr_poly_tan_pi_series, _gr_poly_cot_pi_series, gr_poly_cot_pi_series (gr_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_poly/_gr_poly_tan_series.html (generated 2026-10-20).