FLINT3.7.0-dev
/

ca_pow_fmpq, ca_pow_fmpz, ca_pow_ui, ca_pow_si, ca_pow

Synopsis#include <flint/ca.h>
void ca_pow_fmpq(ca_t res, const ca_t x, const fmpq_t y, ca_ctx_t ctx)source
void ca_pow_fmpz(ca_t res, const ca_t x, const fmpz_t y, ca_ctx_t ctx)source
void ca_pow_ui(ca_t res, const ca_t x, ulong y, ca_ctx_t ctx)source
void ca_pow_si(ca_t res, const ca_t x, slong y, ca_ctx_t ctx)source
void ca_pow(ca_t res, const ca_t x, const ca_t y, ca_ctx_t ctx)source

Sets res to x^y, with the principal branch x^y = \exp(y \log x) for non-integer y.

Integer powers of rational numbers and of number field elements are computed exactly unless the size of the result would exceed about CA_OPT_PREC_LIMIT bits; in generic fields, x^n is expanded by repeated multiplication for |n| \le CA_OPT_POW_LIMIT. Exponents n/2 are computed via ca_sqrt, and (z^a)^b is simplified to z^{ab} when this is valid. Otherwise the result is the generator of a new field \mathbb{Q}(x^y), which requires that x is proved nonzero unless y is a positive rational number; if that fails, the result is Unknown.

For special bases and integer exponents n: \tilde \infty^n is \tilde \infty, 0 or Undefined for n > 0, n < 0 and n = 0; (c \infty)^n = c^n \infty for n > 0, 0 for n < 0 and Undefined for n = 0; 0^n = \tilde \infty for n < 0. Non-integer powers involving special values give Unknown.

Cite this page

The FLINT team, “ca_pow_fmpq, ca_pow_fmpz, ca_pow_ui, ca_pow_si, ca_pow (ca.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/ca/ca_pow_fmpq.html (generated 2026-10-20).