python, hg: tow outside the environment.

they've served us well, and can ride off into the sunset.

1 files changed, 0 insertions, 142 deletions

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-\section{\module{cmath} ---
-         Mathematical functions for complex numbers}
-
-\declaremodule{builtin}{cmath}
-\modulesynopsis{Mathematical functions for complex numbers.}
-
-This module is always available.  It provides access to mathematical
-functions for complex numbers.  The functions are:
-
-\begin{funcdesc}{acos}{x}
-Return the arc cosine of \var{x}.
-There are two branch cuts:
-One extends right from 1 along the real axis to \infinity, continuous
-from below.
-The other extends left from -1 along the real axis to -\infinity,
-continuous from above.
-\end{funcdesc}
-
-\begin{funcdesc}{acosh}{x}
-Return the hyperbolic arc cosine of \var{x}.
-There is one branch cut, extending left from 1 along the real axis
-to -\infinity, continuous from above.
-\end{funcdesc}
-
-\begin{funcdesc}{asin}{x}
-Return the arc sine of \var{x}.
-This has the same branch cuts as \function{acos()}.
-\end{funcdesc}
-
-\begin{funcdesc}{asinh}{x}
-Return the hyperbolic arc sine of \var{x}.
-There are two branch cuts, extending left from \plusminus\code{1j} to
-\plusminus-\infinity\code{j}, both continuous from above.
-These branch cuts should be considered a bug to be corrected in a
-future release.
-The correct branch cuts should extend along the imaginary axis,
-one from \code{1j} up to \infinity\code{j} and continuous from the
-right, and one from -\code{1j} down to -\infinity\code{j} and
-continuous from the left.
-\end{funcdesc}
-
-\begin{funcdesc}{atan}{x}
-Return the arc tangent of \var{x}.
-There are two branch cuts:
-One extends from \code{1j} along the imaginary axis to
-\infinity\code{j}, continuous from the left.
-The other extends from -\code{1j} along the imaginary axis to
--\infinity\code{j}, continuous from the left.
-(This should probably be changed so the upper cut becomes continuous
-from the other side.)
-\end{funcdesc}
-
-\begin{funcdesc}{atanh}{x}
-Return the hyperbolic arc tangent of \var{x}.
-There are two branch cuts:
-One extends from 1 along the real axis to \infinity, continuous
-from above.
-The other extends from -1 along the real axis to -\infinity,
-continuous from above.
-(This should probably be changed so the right cut becomes continuous from
-the other side.)
-\end{funcdesc}
-
-\begin{funcdesc}{cos}{x}
-Return the cosine of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{cosh}{x}
-Return the hyperbolic cosine of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{exp}{x}
-Return the exponential value \code{e**\var{x}}.
-\end{funcdesc}
-
-\begin{funcdesc}{log}{x\optional{, base}}
-Returns the logarithm of \var{x} to the given \var{base}.
-If the \var{base} is not specified, returns the natural logarithm of \var{x}.
-There is one branch cut, from 0 along the negative real axis to
--\infinity, continuous from above.
-\versionchanged[\var{base} argument added]{2.4}
-\end{funcdesc}
-
-\begin{funcdesc}{log10}{x}
-Return the base-10 logarithm of \var{x}.
-This has the same branch cut as \function{log()}.
-\end{funcdesc}
-
-\begin{funcdesc}{sin}{x}
-Return the sine of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{sinh}{x}
-Return the hyperbolic sine of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{sqrt}{x}
-Return the square root of \var{x}.
-This has the same branch cut as \function{log()}.
-\end{funcdesc}
-
-\begin{funcdesc}{tan}{x}
-Return the tangent of \var{x}.
-\end{funcdesc}
-
-\begin{funcdesc}{tanh}{x}
-Return the hyperbolic tangent of \var{x}.
-\end{funcdesc}
-
-The module also defines two mathematical constants:
-
-\begin{datadesc}{pi}
-The mathematical constant \emph{pi}, as a real.
-\end{datadesc}
-
-\begin{datadesc}{e}
-The mathematical constant \emph{e}, as a real.
-\end{datadesc}
-
-Note that the selection of functions is similar, but not identical, to
-that in module \refmodule{math}\refbimodindex{math}.  The reason for having
-two modules is that some users aren't interested in complex numbers,
-and perhaps don't even know what they are.  They would rather have
-\code{math.sqrt(-1)} raise an exception than return a complex number.
-Also note that the functions defined in \module{cmath} always return a
-complex number, even if the answer can be expressed as a real number
-(in which case the complex number has an imaginary part of zero).
-
-A note on branch cuts: They are curves along which the given function
-fails to be continuous.  They are a necessary feature of many complex
-functions.  It is assumed that if you need to compute with complex
-functions, you will understand about branch cuts.  Consult almost any
-(not too elementary) book on complex variables for enlightenment.  For
-information of the proper choice of branch cuts for numerical
-purposes, a good reference should be the following:
-
-\begin{seealso}
-  \seetext{Kahan, W:  Branch cuts for complex elementary functions;
-           or, Much ado about nothing's sign bit.  In Iserles, A.,
-           and Powell, M. (eds.), \citetitle{The state of the art in
-           numerical analysis}. Clarendon Press (1987) pp165-211.}
-\end{seealso}