Define minimum and maximum of complex values.

git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/LocalReduce/trunk@71 7daa882c-dc44-4453-834e-278d26b18e6a

1 files changed, 7 insertions, 1 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
index bb001c8..217e360 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -170,7 +170,13 @@ $$ \mathrm{maxabs} := \max_i |a_i| $$
 Note that the above definitions are for both real and complex values.
 For $n=0$, the result of the reduction operation is $0$, except for
 $\mathrm{product}$, which is $1$, $\mathrm{min}$, which is $+\infty$,
-and $\mathrm{max}$, which is $-\infty$.
+and $\mathrm{max}$, which is $-\infty$.  We define the minimum of
+complex values by
+$$
+\min \left( a+ib, x+iy \right) := \min \left( a,x \right) + i \min
+\left (b,y \right)
+$$
+and define the maximum equivalently.
 
 \subsection{High-level Reduction Operations}
 The following high-level reduction operations are also implemented.