[Rd] branch cuts of log() and sqrt()
Robin Hankin
r.hankin at noc.soton.ac.uk
Tue Dec 18 12:19:43 CET 2007
Dear developers
Neither Math.Rd nor Log.Rd mention the branch cuts
that appear for complex arguments. I think it's important
to include such information.
Please find following two context diffs for Log.Rd and Math.Rd.
[The pedants amongst us will observe that
both sqrt() and log() have a branch point at complex
infinity, which is not mentioned in the patch. Comments
anyone?]
rksh
245-10:~/scratch/R-devel/src/library/base/man% diff -c Log.Rd
new_Log.Rd
*** Log.Rd Fri Jul 27 16:51:42 2007
--- new_Log.Rd Tue Dec 18 08:57:03 2007
***************
*** 66,71 ****
--- 66,75 ----
\code{logb} is a wrapper for \code{log} for compatibility with
S. If
(S3 or S4) methods are set for \code{log} they will be dispatched.
Do not set S4 methods on \code{logb} itself.
+
+ For complex arguments, the branch cut is standard: there is a branch
+ point at zero and a cut along the negative real axis; continuity
+ is from above.
}
\section{S4 methods}{
\code{exp}, \code{expm1}, \code{log}, \code{log10}, \code{log2} and
245-10:~/scratch/R-devel/src/library/base/man%
245-10:~/scratch/R-devel/src/library/base/man% diff -c Math.Rd
new_Math.Rd
*** Math.Rd Fri Jul 27 16:51:44 2007
--- new_Math.Rd Tue Dec 18 09:01:35 2007
***************
*** 22,32 ****
\details{
These are generic functions: methods can be defined for them
individually or via the \code{\link[base:groupGeneric]{Math}}
! group generic. For complex arguments (and the default method),
\code{z},
! \code{abs(z) == \link{Mod}(z)} and \code{sqrt(z) == z^0.5}.
\code{abs(x)} returns an \code{\link{integer}} vector when \code
{x} is
\code{integer} or \code{\link{logical}}.
}
\section{S4 methods}{
Both are S4 generic and members of the
--- 22,39 ----
\details{
These are generic functions: methods can be defined for them
individually or via the \code{\link[base:groupGeneric]{Math}}
! group generic.
\code{abs(x)} returns an \code{\link{integer}} vector when \code
{x} is
\code{integer} or \code{\link{logical}}.
+
+ For complex arguments (and the default method), \code{z},
+ \code{abs(z) == \link{Mod}(z)} and \code{sqrt(z) == z^0.5}.
+
+ The branch cut of \code{sqrt()} is standard: there is a branch point
+ at zero and a cut along the negative real axis; continuity is from
+ above.
+
}
\section{S4 methods}{
Both are S4 generic and members of the
245-10:~/scratch/R-devel/src/library/base/man%
--
Robin Hankin
Uncertainty Analyst and Neutral Theorist,
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
tel 023-8059-7743
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