X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fsam.git;a=blobdiff_plain;f=chapters%2FBackground%2FRationals.tex;h=da4f77a68ab8b38a8466236dbbe85a16dbdbc0bb;hp=8b137891791fe96927ad78e64b0aad7bded08bdc;hb=689e433b348588e05f47d23385dbf05d239c95d2;hpb=9fcf44a0c34f393689118e913a2d17d907036c85

diff --git a/chapters/Background/Rationals.tex b/chapters/Background/Rationals.tex
index 8b13789..da4f77a 100644
--- a/chapters/Background/Rationals.tex
+++ b/chapters/Background/Rationals.tex
@@ -1 +1,15 @@
-
+	\begin{align}
+		Q &= \frac{N}{D} 
+	\end{align}			
+	\begin{itemize}
+		\item $N$ and $D$ are arbitrary precision integers
+	\end{itemize}
+	\begin{align}
+		N &= \sum_{i=0}^{S} d_i \beta^{i}
+	\end{align}	
+	\begin{itemize}
+		\item $d_i$ are fixed size integers, $\beta = 2^{64}$
+		\item Size $S$ grows as needed
+		\item Operations are always exact
+		\item Implemented by GNU Multiple Precision Library
+	\end{itemize}