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 ff to tan⁡\tan, tanh⁡\tanh, cot⁡\cot, coth⁡\coth, tan⁡(π⋅)\tan(\pi \cdot) or cot⁡(π⋅)\cot(\pi \cdot) of hh modulo xnx^n. Over rings with real precision, an argument with large imaginary part (for tan⁡\tan, cot⁡\cot) or large real part (for tanh⁡\tanh, coth⁡\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 2026-11-02).