From 379a86f6dac10d94313b052884fa5b2bdbbf7d2c Mon Sep 17 00:00:00 2001
From: Sven Verdoolaege <skimo@kotnet.org>
Date: Sun, 11 Mar 2007 19:08:48 +0100
Subject: [PATCH] doc: fix primal decomposition example + clean-ups

---
 doc/implementation.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/doc/implementation.tex b/doc/implementation.tex
index d443644..f33642e 100644
--- a/doc/implementation.tex
+++ b/doc/implementation.tex
@@ -623,7 +623,7 @@ an explicitly marked $\vec y$.
 \POS"a"\ar@{--}@[|(3)]"b"
 \POS"b"\ar@{--}@[|(3)]"c"
 \POS"c"\ar@{-}@[|(3)]"a"
-\POS(3.5,-.5)*{\bullet},*+!D{\vec y}
+\POS(4.7,-2.5)*{\bullet},*+!R{\vec y}
 \end{xy}
 & =
 \intercol=0.48cm
@@ -635,7 +635,7 @@ an explicitly marked $\vec y$.
 \POS"c"\ar@{-}@[|(3)]"a"
 \POS"a"\ar@{--}@[|(3)]"w"
 \POS"c"\ar@{--}@[|(3)]"w"
-\POS(3.5,-.5)*{\bullet},*+!D{\vec y}
+\POS(4.7,-2.5)*{\bullet},*+!R{\vec y}
 \end{xy}
 -
 \begin{xy}
@@ -646,7 +646,7 @@ an explicitly marked $\vec y$.
 \POS"a"\ar@{-}@[|(3)]"b"
 \POS"a"\ar@{--}@[|(3)]"w"
 \POS"b"\ar@{--}@[|(3)]"w"
-\POS(3.5,-.5)*{\bullet},*+!D{\vec y}
+\POS(4.7,-2.5)*{\bullet},*+!R{\vec y}
 \end{xy}
 \end{align*}
 \caption{Examples of decompositions in primal space.}
@@ -682,7 +682,7 @@ i.e., a facet of $K'$, or an ``internal'' facet.
 If, on the other hand, $\alpha_j = 0$, then $\vec n_{ij} = \vec n_{0j}$.
 If $\sp{n_{ij}}y > 0$, then the facet is closed.
 Otherwise it is open.
-That is, the two (or more) occurrences of external facets are either all open
+It follows that the two (or more) occurrences of external facets are either all open
 or all closed, while for internal facets, exactly one is closed.
 
 First consider the facet not containing $\vec u_0 = \vec w$.
@@ -705,7 +705,7 @@ Figure~\ref{fig:w:opposite} shows the possible configurations
 for the case that $\alpha_i \alpha_j > 0$.
 If exactly one of $\vec n_{0i}$ and $\vec n_{0j}$ is closed, then
 $\vec y$ lies in region~3 or region~5 and therefore $\vec n_{ij}$ is closed iff
-$\vec n_{0j}$.
+$\vec n_{0j}$ is closed.
 Otherwise, as explained above, we choose $\vec n_{ij}$ to be closed if $i < j$.
 
 \begin{figure}
-- 
2.11.4.GIT