ca_log

The following simplifications are made automatically: $\log 1 = 0$; $\log(e^z) = z + 2 \pi i k$, $\log(\sqrt{z}) = \frac{1}{2} \log z + 2 \pi i k$ and $\log(z^a) = a \log z + 2 \pi i k$ with the integer $k$ determined numerically; $\log x = \log(-x) + \pi i$ for negative real $x$; and logarithms of roots of unity are rational multiples of $\pi i$. Integer relations between logarithms in one field, such as $\log 8 = 3 \log 2$, are found when the field is created (see Formal fields and the ideal of relations).

For special values and zero, $\log 0 = -\infty$ (Unknown if it cannot be decided whether $x = 0$), the logarithm of any infinity is $+\infty$, and Undefined and Unknown map to themselves.

@misc{flint-doc-ca-ca-log,
  author       = {{The FLINT team}},
  title        = {{ca\_log (ca.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/ca/ca_log.html},
  note         = {Generated 2026-11-02}
}