FLINT3.7.0-dev
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_gr_poly_sin_cos_series, gr_poly_sin_cos_series, _gr_poly_sin_cos_pi_series, gr_poly_sin_cos_pi_series, _gr_poly_sin_series, gr_poly_sin_series, _gr_poly_sin_pi_series, gr_poly_sin_pi_series, _gr_poly_cos_series, gr_poly_cos_series, _gr_poly_cos_pi_series, gr_poly_cos_pi_series

Synopsis#include <flint/gr_poly.h>
int _gr_poly_sin_cos_series(gr_ptr s, gr_ptr c, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_sin_cos_series(gr_poly_t s, gr_poly_t c, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_sin_cos_pi_series(gr_ptr s, gr_ptr c, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_sin_cos_pi_series(gr_poly_t s, gr_poly_t c, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_sin_series(gr_ptr s, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_sin_series(gr_poly_t s, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_sin_pi_series(gr_ptr s, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_sin_pi_series(gr_poly_t s, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_cos_series(gr_ptr c, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_cos_series(gr_poly_t c, const gr_poly_t h, slong n, gr_ctx_t ctx)source
int _gr_poly_cos_pi_series(gr_ptr c, gr_srcptr h, slong hlen, slong n, gr_ctx_t ctx)source
int gr_poly_cos_pi_series(gr_poly_t c, const gr_poly_t h, slong n, gr_ctx_t ctx)source

Set s = \sin(h) and c = \cos(h) modulo x^n, or \sin(\pi h) and \cos(\pi h) for the pi versions. The default algorithm is the basecase for \mathit{hlen} < 20 and below a ring-dependent cutoff (500 over finite rings, \min(500, 20 + 100000/p) over rings with real precision p, 25 otherwise), and Newton iteration above it.

Cite this page

The FLINT team, “_gr_poly_sin_cos_series, gr_poly_sin_cos_series, _gr_poly_sin_cos_pi_series, gr_poly_sin_cos_pi_series, _gr_poly_sin_series, gr_poly_sin_series, _gr_poly_sin_pi_series, gr_poly_sin_pi_series, _gr_poly_cos_series, gr_poly_cos_series, _gr_poly_cos_pi_series, gr_poly_cos_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_sin_cos_series.html (generated 2026-10-20).