%% LaTeX2e file `AlfPreambleL.tex'
%% generated by the `filecontents' environment
%% from source `vdp23' on 2004/09/20.
%%

%% LaTeX2e file `AlfPreambleL'
%% generated by the `filecontents' environment
%% from source `Mazur' on 2002/10/09.
%%

%% LaTeX2e file `AlfPreambleL'
%% generated by the `filecontents' environment
%% from source `Periodic' on 1999/01/08.
%%

%%-------------AlfPreambleL-----------
\ifx\preambleloaded\relax
  \endinput\else\let\preambleloaded\relax\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %
% Alf van der Poorten
% ceNTRe for Number Theory Research
% Macquarie University
% NSW 2109 AUSTRALIA
% alf@mpce.mq.edu.au
%

% This file assumes the presence of AmS-LaTeX 2e
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\mathsurround=1pt


\def\C{{\mathbb C}} \def\N{{\mathbb N}} \def\L{{\mathbb L}} \def\K{{\mathbb K}}
\def\Z{{\mathbb Z}} \def\Q{{\mathbb Q}} \def\A{\overline{\mathbb Q}}
\def\R{{\mathbb R}}
\def\F{{\mathbb F}} %% means, with subscript, finite field to me
\def\Fb{{\mathbold F}}

\def\goth{\mathfrak}
\def\dint#1{\Vert#1\Vert}
\def\={\equiv}
%\DeclareMathOperator{\arsinh}{arsinh}
%\DeclareMathOperator{\Gal}{Gal}



%\def\({\bigl(} \def\){\bigr)} %%Bloody useful for second parentheses
\def\\{\cr} %This may be a bad thing; check that it does no harm
\def\lt{<}
\def\gt{>}
\def\conj{\overline}
\def\ov{\overline}

\def\legendre#1#2{\genfrac{(}{)}{}{}{#1}{#2}}

\def\acclap#1{\raise\hgtsig\hbox to0pt{$#1$\hss}}
\newdimen\hgtsig
\setbox0=\hbox{$\displaystyle{\sum}$}
\hgtsig=\ht0\relax
\advance\hgtsig by -1.75ex
\def\sumprime{\mathop{{\sum}\acclap'}}

\def\myline{\hrule\vskip2pt\hrule\medskip}


\def\id#1{\langle #1\rangle} %%% ideal, in other words
\def\ideal#1{\langle #1\rangle} %%% ideal, in other words

%--------------Overarrows in Continued Fraction expansions--------
\newbox\boxW\newdimen\dimW
\def\heighten#1{%
\setbox\boxW\hbox{$\displaystyle #1$}%%%
\dimW=1.04\ht\boxW\advance\dimW by 1.00pt
\vbox to \dimW{}}

\def\larr#1{\overleftarrow{{\heighten{#1}}#1}}
\def\rarr#1{\overrightarrow{{\heighten{#1}}#1}}


%------------Taken from George Gr^^8atzer's lattice.sty

\newcommand{\set}[1]{\{#1\}}% set
\newcommand{\setm}[2]{\{\,#1\mid#2\,\}}% set with a middle


% Font commands
\newcommand{\tbf}{\textbf}% text bold
\newcommand{\tit}{\textit}% text italic
\newcommand{\tsl}{\textsl}% text slanted
\newcommand{\tsc}{\textsc}% text small cap
\newcommand{\ttt}{\texttt}% text typewriter
\newcommand{\trm}{\textrm}% text roman
\newcommand{\tsf}{\textsf}% text sans serif
\newcommand{\tup}{\textup}% text upright

\newcommand{\mbf}{\mathbf}% math bold
\providecommand{\mit}{\mathit}% math italic
\newcommand{\msf}{\mathsf}% math sans serif
\newcommand{\mrm}{\mathrm}% math roman
\newcommand{\mtt}{\mathtt}% math typewriter

\newcommand{\B}{\boldsymbol}
   % Bold math symbol, use as \B{a}
\DeclareMathAlphabet{\Bi}{OT1}{cmm}{b}{it}  %Bold Math Italic
\newcommand{\MC}[1]{\mathcal{#1}}
   % Euler Script - only caps, use as \MC{A}
\newcommand{\D}[1]{\mathbb{#1}}
   % Doubled - blackboard bold - only caps, use as \D{A}
\newcommand{\E}[1]{\mathcal{#1}}% same as \C
   % Euler Script - only caps, use as \E{A}
\newcommand{\MF}[1]{\mathfrak{#1}}% Fraktur, use as \MF{a}
\newcommand{\Ms}[1]{\mathsf{#1}}% sans serif, use as \Ms{a}

% Miscellaneous
\newcommand{\nl}{\newline}
\newcommand{\ol}[1]{\overline{#1}}
\newcommand{\ul}[1]{\underline{#1}}
\providecommand{\bysame}{\makebox[3em]{\hrulefill}\thinspace}
\newcommand{\q}{\quad}% spacing
\newcommand{\qq}{\qquad}% more spacing
\newcommand{\iso}{\cong}% isomorphic
\def\con#1=#2(#3){#1\equiv#2\pod{#3}}
   %congruence, use it as \con a=b(\theta)%
\newenvironment{enumeratei}{\begin{enumerate}[\upshape (i)]}%
                            {\end{enumerate}}
   %produces (i), (ii), etc. Cross-reference with \eqref.
\newenvironment{enumeratea}{\begin{enumerate}[\upshape (a)]}%
                            {\end{enumerate}}
   %produces (a), (b), etc. Cross-reference with \eqref.
\begin{comment}
\theoremstyle{plain}
\newtheorem*{namedtheorem}{\theoremname}
\newcommand{\theoremname}{testing}
\newenvironment{named}[1]{\renewcommand{\theoremname}{#1}
   \begin{namedtheorem}}
   {\end{namedtheorem}}

\theoremstyle{definition}
\newtheorem*{namedremark}{\remarkname}
\newcommand{\remarkname}{testing}
\newenvironment{renamed}[1]{\renewcommand{\remarkname}{#1}
   \begin{namedremark}}
   {\end{namedremark}}
\end{comment}
%-------------------------------------------



%%-------------- Continued Fractions -----------------------------
\def\CF#1{{\def\\{\mathrel{,}}\def\;{\mathrel{;}}
\def\dots{\ldots}\def\dotss{\ldots\ldots}[\,#1\,]}}
\def\lCF#1{{\def\\{\mathrel{,}}\def\;{\mathrel{;}}
\def\dots{\ldots}\def\dotss{\ldots\ldots}[\,#1\,,}}
\def\rCF#1{{\def\\{\mathrel{,}}\def\;{\mathrel{;}}
\def\dots{\ldots}\def\dotss{\ldots\ldots}#1\,]}}
\def\cCF#1{{\def\\{\mathrel{,}}\def\;{\mathrel{;}}
\def\dots{\ldots}\def\dotss{\ldots\ldots}#1\,}}

%%------- David Cantor's suggestion ---------
%infinite continued fraction:
\def\cfraci#1#2{#1_0+{
\let\ds\displaystyle
\def\vl{\ds1\vrule width0pt depth.5ex height2ex\over}
\vl{\ds#1_1 + {\vl{\ds#1_2 +{\vl\hskip.5em\ddots}}}}}}
%---------------end continued fraction-----------------------------

%--------divides--------
\def\exactlydivides{{\mathchoice{\mathrel{\bigm\|}}%
{\mathrel{\bigm\|}}{\mathrel{\|}}%
{\mathrel{\|}}}}
\def\ediv{\exactlydivides}
\def\divides{{\mathchoice{\mathrel{\bigm|}}{\mathrel{\bigm|}}{\mathrel{|}}%
{\mathrel{|}}}}
\def\Div{\divides}
\def\notdivides{\mathrel{\kern-3pt\not\!\kern3.5pt\bigm|}}
\def\ndiv{\notdivides}
\def\nDiv{\notdivides}
%------------end divides-------

%----A damned useful definition of \house for the size of algebraic numbers
\newbox\boxA
\newbox\boxB
\newdimen\dimA
\newdimen\dimB
\newdimen\dimC

\def\house#1{%%% constructed by Ross Talent, by the way
%Sadly this fails in LaTex
\setbox\boxA\hbox{$\displaystyle #1$}%%%
\dimA=1.04\wd\boxA\advance\dimA by 2pt
\dimB=1.04\ht\boxA\advance\dimB by 2pt
\dimC=0.05\wd\boxA
\hskip\dimC\hskip1pt\hbox to \dimA
{\vrule\vbox to \dimB{\hsize=\dimA
%\hrule\vfill \line{\hfil \box\boxA\hfil}}\vrule} %Corrected
\hrule\vfill \centerline{\box\boxA}}\vrule}
\hskip 0.8pt\hskip1pt\hskip\dimC}
%-------------end \house---------------

%-------------Abbreviations
\def\poly {polynomial}
\def\ep {exponential polynomial}
\def\gps {generalised power sum}
\def\rs {recurrence sequence}
\def\cf {continued fraction}
\def\pq {partial quotient}
\def\cq {complete quotient}
\def\ap {approximation}
\def\ex{expansion}
\def\cv {convergent}
\def\cfe{continued fraction expansion}
%\DeclareMathOperator{\Norm}{Norm}
%\DeclareMathOperator{\Trace}{Trace}
%\DeclareMathOperator{\Jac}{Jac}

\def\fl#1{\left\lfloor#1\right\rfloor}
\def\cl#1{\left\lceil#1\right\rceil}


%------------Current time; this may be system dependent!
\newcount\hours
\newcount\minutes
\def \SetTime{\hours=\time
\global\divide\hours by 60
\minutes=\hours
\multiply\minutes by 60
\advance\minutes by-\time
\global\multiply\minutes by-1 }
\SetTime
\def \now{\number\hours:\ifnum\minutes<10 0\fi\number\minutes}
\def \Now{\today\ $[$\now$]$}
%--------------------end time----------------------------------

%-----needed for the ceNTRe logo----------
%---to avoid this uncomment the logo below

%
% Handling PostScript Graphics
%
%

%---For use with Textures on a Macintosh ONLY!!--%
\newif\ifMacTextures
\MacTexturestrue

\ifMacTextures

\gdef\EPSF#1by#2(#3){%
\vbox to #2{\hrule width #1 height 0pt depth 0pt%
\vfill\special{illustration #3}}}%


\gdef\scaledEPSF#1by#2(#3 scaled #4){{%
\dimen0=#1 \dimen1=#2%
\divide\dimen0 by 1000 \multiply\dimen0 by #4%
\divide\dimen1 by 1000 \multiply\dimen1 by #4%
\EPSF \dimen0 by \dimen1 (#3 scaled #4)}}%
\else
%
%---For use with dvips by Tomas Rokicki, ONLY!!--%
\input epsf

\gdef\EPSF#1by#2(#3){%
\vbox to #2{\hrule width #1 height 0pt depth 0pt\vfill \epsfbox{#3}}}%

\gdef\EPSF#1by#2(#3){\epsfbox{#3}}%

\gdef\scaledEPSF#1by#2(#3 scaled #4){{%
\dimen0=#1 \dimen1=#2%
\divide\dimen0 by 1000 \multiply\dimen0 by #4%
\divide\dimen1 by 1000 \multiply\dimen1 by #4%
\epsfxsize=\dimen0\epsfbox{#3}}}%
\fi
\MacTexturesfalse


%This stuff is needed for the ceNTRe logo
%The availability of the ps file logo.art
%in the working directory is essential

\def\centrelogo{\scaledEPSF 2.5in by 1.4in (logo.art scaled 650)}
\def\expcentrelogo{\scaledEPSF 2.5in by 1.4in (logoexp.art scaled 650)}

\def\smallcentrelogo{\scaledEPSF 2.5in by 1.4in (logo.art scaled 325)}

\font \logofont=cmss8
\def\ceNTRelogo{\vtop{\baselineskip10truept
\hsize= 0.8125in \smallcentrelogo \logofont
\smallskip
\centerline{ceNTRe}
%\centerline{1 Bimbil Place, Killara}
\centerline{Sydney, Australia 2071}} }

%--uncomment the \def\ceNTRelogo to disappear the logo,
%--or comment it to reappear it
%\def\ceNTRelogo{\relax}

\endinput
%-------------end of file AlfPreamble.tex------------------