FLINT3.7.0-dev
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ca_asin_logarithm, ca_acos_logarithm, ca_asin_direct, ca_acos_direct, ca_asin, ca_acos

Synopsis#include <flint/ca.h>
void ca_asin_logarithm(ca_t res, const ca_t x, ca_ctx_t ctx)source
void ca_acos_logarithm(ca_t res, const ca_t x, ca_ctx_t ctx)source
void ca_asin_direct(ca_t res, const ca_t x, ca_ctx_t ctx)source
void ca_acos_direct(ca_t res, const ca_t x, ca_ctx_t ctx)source
void ca_asin(ca_t res, const ca_t x, ca_ctx_t ctx)source
void ca_acos(ca_t res, const ca_t x, ca_ctx_t ctx)source

Sets res to the principal branch of asin⁡x\operatorname{asin} x or acos⁡x\operatorname{acos} x.

The logarithm versions use asin⁡x=−ilog⁡(ix+1−x2)\operatorname{asin} x = -i \log(ix + \sqrt{1 - x^2}), the direct versions return the generator of Q(asin⁡x)\mathbb{Q}(\operatorname{asin} x), possibly after transforming the argument; simple algebraic arguments give rational multiples of π\pi. The inverse cosine is computed as acos⁡x=π/2−asin⁡x\operatorname{acos} x = \pi/2 - \operatorname{asin} x. ca_asin and ca_acos use the logarithm forms unless CA_OPT_TRIG_FORM is CA_TRIG_DIRECT.

Cite this page

The FLINT team, “ca_asin_logarithm, ca_acos_logarithm, ca_asin_direct, ca_acos_direct, ca_asin, ca_acos (ca.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/ca/ca_asin_logarithm.html (generated 2026-11-02).