From: Richard B. Kreckel
Date: Thu, 8 Dec 2011 16:59:16 +0000 (+0000)
Subject: Documentation: Update branch cut convention
X-Git-Tag: release_1-6-3~69
X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=commitdiff_plain;h=a104ecb34a015fc40a4bdc16ae6ea038ecb8c55d
Documentation: Update branch cut convention
Now that C++11 is out, there is no more need for oracling
about how it might eventually standardize the branch cuts of
elementary and inverse trigonometric and hyperbolic functions.
---
diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi
index 0ab43f6b..a767d57c 100644
--- a/doc/tutorial/ginac.texi
+++ b/doc/tutorial/ginac.texi
@@ -5912,20 +5912,19 @@ GiNaC contains the following predefined mathematical functions:
@end cartouche
@cindex branch cut
-For functions that have a branch cut in the complex plane GiNaC follows
-the conventions for C++ as defined in the ANSI standard as far as
-possible. In particular: the natural logarithm (@code{log}) and the
-square root (@code{sqrt}) both have their branch cuts running along the
-negative real axis where the points on the axis itself belong to the
-upper part (i.e. continuous with quadrant II). The inverse
-trigonometric and hyperbolic functions are not defined for complex
-arguments by the C++ standard, however. In GiNaC we follow the
-conventions used by CLN, which in turn follow the carefully designed
-definitions in the Common Lisp standard. It should be noted that this
-convention is identical to the one used by the C99 standard and by most
-serious CAS. It is to be expected that future revisions of the C++
-standard incorporate these functions in the complex domain in a manner
-compatible with C99.
+For functions that have a branch cut in the complex plane, GiNaC
+follows the conventions of C/C++ for systems that do not support a
+signed zero. In particular: the natural logarithm (@code{log}) and
+the square root (@code{sqrt}) both have their branch cuts running
+along the negative real axis. The @code{asin}, @code{acos}, and
+@code{atanh} functions all have two branch cuts starting at +/-1 and
+running away towards infinity along the real axis. The @code{atan} and
+@code{asinh} functions have two branch cuts starting at +/-i and
+running away towards infinity along the imaginary axis. The
+@code{acosh} function has one branch cut starting at +1 and running
+towards -infinity. These functions are continuous as the branch cut
+is approached coming around the finite endpoint of the cut in a
+counter clockwise direction.
@node Multiple polylogarithms, Complex expressions, Built-in functions, Methods and functions
@c node-name, next, previous, up