Some trivial typo fixes.

git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/CartGrid3D/trunk@167 c78560ca-4b45-4335-b268-5f3340f3cb52

1 files changed, 5 insertions, 4 deletions

diff --git a/doc/rotating_sym.tex b/doc/rotating_sym.tex
index e5ef6b7..02c9371 100644
--- a/doc/rotating_sym.tex
+++ b/doc/rotating_sym.tex
@@ -44,7 +44,7 @@
 These notes describe the implentation of rotating symmetry conditions
 for \emph{bitant} and \emph{quadrant} domains in \texttt{CartGrid3D}.
 For these particular domain types, the condition that fields on the
-grid are have a rotational symmetry in a plane along one of the
+grid have a rotational symmetry in a plane along one of the
 coordinate axes can be simply implemented with minor extensions to the
 already existing symmetry mechanism, which copies the components of
 a given field to the required ghost-zones with a possible plus-minus
@@ -146,7 +146,8 @@ rotation.\\
 
 The first of these issues is not difficult to resolve. As an example,
 consider the half-plane rotational symmetry about the $z$-axis applied
-in the $x=0$ plane, as depicted in Figure \ref{fig:rs_grid}. The has
+in the $x=0$ plane, as depicted in Figure \ref{fig:rs_grid}. The
+Figure has
 $j=0\ldots m$ in the $y$ direction, an arbitrary number of points in the
 $x$ and $z$ directions, and some ghostzones whose $j$ coordinates are
 labelled $j=-1,-2,\ldots$. Then for the ghost-zone point $(n-i, -j,
@@ -361,7 +362,7 @@ symmetries.}
 We note the following useful fact: The transformation factor $s_i$ for
 a rotation about the axis $i$ is given by $s_j \times s_k$ where
 $i\neq j\neq k$. For example, for a rotation about the $z$-axis, the
-transformation factor for the is given by
+transformation factor is given by
 \begin{equation}
   s_x \times s_y = -1 \times -1 = 1.
 \end{equation}
@@ -447,7 +448,7 @@ standard reflection symmetry is applied to one of the half-planes,
 while the physical fields are assumed to rotate in the other plane. To
 set up such a grid which rotates about the $z$-axis and which is
 reflection symmetric in the $z=0$ plane, the following parameters
-could be used:
+would be used:
 \begin{verbatim}
   grid::domain = "quadrant_rotate_reflect"
   grid::quadrant_direction = "x"