remove trailing whitespace

This commit is contained in:
Jason Woofenden 2012-11-07 23:40:59 -05:00
parent e1edc8079f
commit 0b6709392b
104 changed files with 1479 additions and 1479 deletions

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@ -1,4 +1,4 @@
\documentclass{article}
\documentclass{article}
\usepackage{hyperref}
\begin{document}
@ -258,7 +258,7 @@ in Section \ref{follows}.
\paragraph{Proof that $\mathbf{AXY=V \Rightarrow A'X'Y'=VD}$.}
Substituting $A'X'Y'=(AB)(f(B,X))(f(f(X,B),Y))$, we
recall that merges are commutative. So for any two
changesets $P$ and $Q$,
changesets $P$ and $Q$,
$$m(P,Q)=m(Q,P)=Qf(Q,P)=Pf(P,Q)$$
Applying this to the relation above, we see
@ -267,7 +267,7 @@ A'X'Y'&=& AB f(B,X) f(f(X,B),Y) \\
&=&AX f(X,B) f(f(X,B),Y) \\
&=&A X Y f(Y, f(X,B)) \\
&=&A X Y D \\
&=&V D
&=&V D
\end{eqnarray*}
As claimed.
@ -348,7 +348,7 @@ the client's changeset $C$, it does five things:
server's most recent revision number, which we call
$r_H$ ($H$ for HEAD). $C'$ can be computed using
follows (Section \ref{follows}). Remember that the server has a series of
changesets,
changesets,
$$S_0\rightarrow S_1\rightarrow \ldots S_{r_c}\rightarrow S_{r_c+1} \rightarrow \ldots \rightarrow S_{r_H} $$
$C$ is relative to $S_{r_c}$, but we need to compute $C'$ relative to $S_{r_H}$.
We can compute a new $C$ relative to $S_{r_c+1}$ by computing $f(S_{r_c+1},C)$. Similarly we can repeat for

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@ -1,7 +1,7 @@
\documentclass[12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[USenglish]{babel}
\usepackage[USenglish]{babel}
\begin{document}
@ -68,7 +68,7 @@ Here are descriptions of the operations, where capital
letters are variables:
\begin{description}
\item{{\bf :N}} \quad \\
\item{{\bf :N}} \quad \\
Source text has length $N$ (must be first op)
\item{{\bf >N}} \quad \\
Final text is $N$ (positive) characters longer than source

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@ -72,7 +72,7 @@ Here are descriptions of the operations, where capital letters are variables:
"-N" : Skip over (delete) N characters from the source text, none of them newlines
"=N" : Keep N characters from the source text, none of them newlines
"|L+N" : Insert N characters from the source text, containing L newlines. The last
character inserted MUST be a newline, but not the (new) document's final newline.
character inserted MUST be a newline, but not the (new) document's final newline.
"|L-N" : Delete N characters from the source text, containing L newlines. The last
character inserted MUST be a newline, but not the (old) document's final newline.
"|L=N" : Keep N characters from the source text, containing L newlines. The last character