Quellcode-Bibliothek note6.62.tex

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\begin{document}

\title{Algebra 6.62}
\author{Michael Vaughan-Lee}
\date{June 2013}
\maketitle

Algebra 6.62 has two parameters $x,y$, where $x,y$ are integers with $y\neq 0%
\func{mod}p$. Parameter pairs $(x,y)$ and $(z,t)$ give isomorphic algebras
if and only if%
\[
\left( 
\begin{array}{ll}
1 & 0 \ 
z & t%
\end{array}%
\right) =\left( 
\begin{array}{ll}
\mu  & \nu  \\ 
\\nu  & \mu 
\end{array}%
\right) \left( 
\begin{array}{ll}
1 %%TCIDATA{<META NAME%TCIDATA%TCIDATA{Created=Thursday, June 27, 2013 16:28:19}
x & y%
\end{array}%
\right)%TCIDATA{<META NAME=%TCIDATA{CSTFile
java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 34
 java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 22
\omega \nu y & \mu newtheoremdefinition[]}
\nd{rray%
\^-
\]%
for some matrix $\left( 
\begin
\mu  & \nu  \\ 
\omega \nu  & \mu 
java.lang.StringIndexOutOfBoundsException: Range [10, 4) out of bounds for length 12
\title{Algebra 6.62}
a \authorMichael Vaughan-}
themaketitle
\Algebra .62 has twoparameters $x,$  $,$are with $\neq 0%
1 & 0 \\ 
x & y%
\end{array}%
\if and if
matricesjava.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
\{rray}
\mu   & 0 \\java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
\omega \nubegin{}ll
\end{array}%
\\end{a%

beginarray}{ll}
loop over allx&
\begin{array}{ll}
mu  \\\
\omega \nu & \mu%
\end{array}%
\right) $ and $\left( 
\begin{array}{ll}
1 & 0 \\ 
x & y%
\end{array}%
\right) $. However this method has complexity $p^{4}$ for output of size $p$%
, which is not very satisfactory! Can we do better? Multiplying $\left( 
\begin{array}{ll}
\mu & \nu \\ 
\omega \nu & \mu%
\end{array}%
\right) $ through by a non-zero constant has no effect on the action, so we
can assume that $\mu =0,1$, and that if $\mu =0$ then $\nu =1$. This reduces
the complexity to $p^{3}$.

\end{document}