CoCalc Shared Fileswww / 257 / notes / macros.texOpen in CoCalc with one click!
Author: William A. Stein
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% macros.tex
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\usepackage[active]{srcltx}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{amsthm}
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\newcommand{\edit}[1]{\footnote{#1}\marginpar{\hfill {\sf\thefootnote}}}
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%\newcommand{\edit}[1]{{\bf [[Todo: #1]]}}
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%\author{William~A. Stein}
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\newcommand{\myhead}[3]{
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\par\noindent
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{Version #2}
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\vspace{10ex}
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\par\noindent
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{\bf \LARGE #1}\\
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\vspace{3ex}
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\par\noindent
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{\large W.\thinspace{}A. Stein}\\
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{\small Department of Mathematics, Harvard University}\vspace{1ex}\\
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#3
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\vspace{2ex}\par
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}
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\newcommand{\myheadauth}[3]{
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\par\noindent
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{Version #2}
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\vspace{10ex}
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\par\noindent
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{\bf \LARGE #1}\\
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\vspace{3ex}
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\par\noindent
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#3
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\vspace{5ex}\par
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}
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\newcommand{\gzero}{\Gamma_0(N)}
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\newcommand{\esM}{\overline{\sM}}
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\newcommand{\sM}{\boldsymbol{\mathcal{M}}}
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\newcommand{\sS}{\boldsymbol{\mathcal{S}}}
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\newcommand{\sB}{\boldsymbol{\mathcal{B}}}
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\newcommand{\eE}{\mathbb{E}}
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\newcommand{\Adual}{A^{\vee}}
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\newcommand{\Bdual}{B^{\vee}}
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\newcommand{\defn}[1]{{\em #1}}
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\newcommand{\solution}[1]{\vspace{1em}%
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\par\noindent{\bf Solution #1.} }
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\newcommand{\todo}[1]{\noindent$\bullet$ {\small \textsf{#1}} $\bullet$\\}
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\newcommand{\done}[1]{\noindent {\small \textsf{Done: #1}}\\}
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\newcommand{\danger}[1]{\marginpar{\small \textsl{#1}}}
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\renewcommand{\div}{\mbox{\rm div}}
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\DeclareMathOperator{\can}{can}
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\DeclareMathOperator{\chr}{char}
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\DeclareMathOperator{\cris}{cris}
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\DeclareMathOperator{\dR}{dR}
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\DeclareMathOperator{\Fil}{Fil}
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\DeclareMathOperator{\ind}{ind}
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\DeclareMathOperator{\im}{im}
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\DeclareMathOperator{\oo}{\infty}
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\DeclareMathOperator{\abs}{abs}
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\DeclareMathOperator{\lcm}{lcm}
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\DeclareMathOperator{\cores}{cores}
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\DeclareMathOperator{\coker}{coker}
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\DeclareMathOperator{\image}{image}
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\DeclareMathOperator{\proj}{proj}
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\DeclareMathOperator{\Br}{Br}
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\DeclareMathOperator{\Ann}{Ann}
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\DeclareMathOperator{\End}{End}
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\DeclareMathOperator{\Tan}{Tan}
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\newcommand{\unity}{\mathbb{1}}
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\DeclareMathOperator{\Vis}{Vis}
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\DeclareMathOperator{\Reg}{Reg}
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%\DeclareMathOperator{\myRes}{Res}
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%\newcommand{\Res}{\myRes}
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\DeclareMathOperator{\Res}{Res}
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\newcommand{\an}{{\rm an}}
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\DeclareMathOperator{\rank}{rank}
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\DeclareMathOperator{\Sel}{Sel}
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\DeclareMathOperator{\Mat}{Mat}
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\DeclareMathOperator{\BSD}{BSD}
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\DeclareMathOperator{\id}{id}
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\DeclareMathOperator{\dz}{dz}
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%\DeclareMathOperator{\Re}{Re}
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\renewcommand{\Re}{\mbox{\rm Re}}
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%\DeclareMathOperator{\Im}{Im}
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\DeclareMathOperator{\Selmer}{Selmer}
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\newcommand{\pfSel}{\widehat{\Sel}}
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\newcommand{\qe}{\stackrel{\mbox{\tiny ?}}{=}}
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\newcommand{\isog}{\simeq}
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\newcommand{\e}{\mathbf{e}}
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\newcommand{\bN}{\mathbf{N}}
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% ---- SHA ----
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\DeclareFontEncoding{OT2}{}{} % to enable usage of cyrillic fonts
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\newcommand{\textcyr}[1]{%
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{\fontencoding{OT2}\fontfamily{wncyr}\fontseries{m}\fontshape{n}%
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\selectfont #1}}
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\newcommand{\Sha}{{\mbox{\textcyr{Sh}}}}
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%\font\cyr=wncyr10 scaled \magstep 1
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%\font\cyr=wncyr10
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%\newcommand{\Sha}{{\cyr X}}
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\newcommand{\Shaan}{\Sha_{\mbox{\tiny \rm an}}}
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\newcommand{\TS}{Shafarevich-Tate group}
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\newcommand{\Gam}{\Gamma}
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\newcommand{\cF}{\mathcal{F}}
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\newcommand{\cV}{\mathcal{V}}
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\newcommand{\cO}{\mathcal{O}}
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%\newcommand{\Sym}{\mathcal{S}{\rm ym}}
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\DeclareMathOperator{\tor}{tor}
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\newcommand{\tE}{\tilde{E}}
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\renewcommand{\l}{\ell}
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\renewcommand{\t}{\tau}
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\DeclareMathOperator{\cond}{cond}
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\DeclareMathOperator{\Spec}{Spec}
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\DeclareMathOperator{\Div}{Div}
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\DeclareMathOperator{\Coker}{Coker}
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\DeclareMathOperator{\sep}{sep}
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\DeclareMathOperator{\sign}{sign}
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\DeclareMathOperator{\unr}{unr}
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\newcommand{\N}{\mathcal{N}}
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\newcommand{\U}{\mathcal{U}}
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\newcommand{\Kbar}{\overline{K}}
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\newcommand{\Lbar}{\overline{L}}
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\newcommand{\gammabar}{\overline{\gamma}}
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\newcommand{\q}{\mathbf{q}}
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%\renewcommand{\star}{\times}
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\newcommand{\gM}{\mathfrak{M}}
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\newcommand{\gA}{\mathfrak{A}}
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\newcommand{\gP}{\mathfrak{P}}
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\newcommand{\bmu}{\boldsymbol{\mu}}
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\newcommand{\union}{\cup}
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\newcommand{\Tl}{T_{\ell}}
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\newcommand{\into}{\rightarrow}
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\newcommand{\onto}{\rightarrow\!\!\!\!\rightarrow}
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\DeclareMathOperator{\md}{mod}
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\DeclareMathOperator{\tors}{tors}
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\DeclareMathOperator{\Frac}{Frac}
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\DeclareMathOperator{\corank}{corank}
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\newcommand{\ra}{\rightarrow}
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\newcommand{\xra}[1]{\xrightarrow{#1}}
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\newcommand{\la}{\leftarrow}
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\newcommand{\lra}{\longrightarrow}
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\newcommand{\riso}{\xrightarrow{\sim}}
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\newcommand{\da}{\downarrow}
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\newcommand{\ua}{\uparrow}
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\newcommand{\con}{\equiv}
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\newcommand{\Gm}{\mathbb{G}_m}
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\newcommand{\set}[1]{\{#1\}}
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\newcommand{\iv}{^{-1}}
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\newcommand{\alp}{\alpha}
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\newcommand{\bq}{\mathbf{q}}
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\newcommand{\cpp}{{\tt C++}}
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\newcommand{\tensor}{\otimes}
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\newcommand{\bg}{{\tt BruceGenus}}
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\newcommand{\abcd}[4]{\left(
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\begin{smallmatrix}#1&#2\\#3&#4\end{smallmatrix}\right)}
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\newcommand{\mthree}[9]{\left(
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\begin{matrix}#1&#2&#3\\#4&#5&#6\\#7&#8&#9
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\end{matrix}\right)}
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\newcommand{\mtwo}[4]{\left(
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\begin{matrix}#1&#2\\#3&#4
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\end{matrix}\right)}
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\newcommand{\vtwo}[2]{\left(
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\begin{matrix}#1\\#2
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\end{matrix}\right)}
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\newcommand{\smallmtwo}[4]{\left(
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\begin{smallmatrix}#1&#2\\#3&#4
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\end{smallmatrix}\right)}
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\newcommand{\twopii}{2\pi{}i{}}
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\newcommand{\eps}{\varepsilon}
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\newcommand{\vphi}{\varphi}
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\newcommand{\gp}{\mathfrak{p}}
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\newcommand{\W}{\mathcal{W}}
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\newcommand{\oz}{\overline{z}}
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\newcommand{\Zpstar}{\Zp^{\star}}
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\newcommand{\Zhat}{\widehat{\Z}}
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\newcommand{\Zbar}{\overline{\Z}}
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\newcommand{\Zl}{\Z_{\ell}}
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\newcommand{\comment}[1]{}
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\newcommand{\Q}{\mathbb{Q}}
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\newcommand{\GQ}{G_{\Q}}
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\newcommand{\R}{\mathbb{R}}
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\newcommand{\D}{{\mathbf D}}
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\newcommand{\cC}{\mathcal{C}}
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\newcommand{\cD}{\mathcal{D}}
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\newcommand{\cP}{\mathcal{P}}
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\newcommand{\cS}{\mathcal{S}}
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\newcommand{\Sbar}{\overline{S}}
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\newcommand{\K}{{\mathbb K}}
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\newcommand{\C}{\mathbb{C}}
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\newcommand{\Cp}{{\mathbb C}_p}
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\newcommand{\Sets}{\mbox{\rm\bf Sets}}
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\newcommand{\bcC}{\boldsymbol{\mathcal{C}}}
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\renewcommand{\P}{\mathbb{P}}
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\newcommand{\Qbar}{\overline{\Q}}
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\newcommand{\kbar}{\overline{k}}
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\newcommand{\dual}{\bot}
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\newcommand{\T}{\mathbb{T}}
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\newcommand{\calT}{\mathcal{T}}
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\newcommand{\cT}{\mathcal{T}}
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\newcommand{\cbT}{\mathbb{\mathcal{T}}}
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\newcommand{\cU}{\mathcal{U}}
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\newcommand{\Z}{\mathbb{Z}}
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\newcommand{\F}{\mathbb{F}}
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\newcommand{\Fl}{\F_{\ell}}
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\newcommand{\Fell}{\Fl}
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\newcommand{\Flbar}{\overline{\F}_{\ell}}
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\newcommand{\Flnu}{\F_{\ell^{\nu}}}
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\newcommand{\Fbar}{\overline{\F}}
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\newcommand{\Fpbar}{\overline{\F}_p}
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\newcommand{\fbar}{\overline{f}}
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\newcommand{\Qp}{\Q_p}
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\newcommand{\Ql}{\Q_{\ell}}
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\newcommand{\Qell}{\Q_{\ell}}
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\newcommand{\Qlbar}{\overline{\Q}_{\ell}}
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\newcommand{\Qlnr}{\Q_{\ell}^{\text{nr}}}
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\newcommand{\Qlur}{\Q_{\ell}^{\text{ur}}}
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\newcommand{\Qltm}{\Q_{\ell}^{\text{tame}}}
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\newcommand{\Qv}{\Q_v}
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\newcommand{\Qpbar}{\Qbar_p}
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\newcommand{\Zp}{\Z_p}
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\newcommand{\Fp}{\F_p}
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\newcommand{\Fq}{\F_q}
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\newcommand{\Fqbar}{\overline{\F}_q}
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\newcommand{\Ad}{Ad}
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\newcommand{\adz}{\Ad^0}
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\renewcommand{\O}{\mathcal{O}}
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\newcommand{\A}{\mathcal{A}}
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\newcommand{\Og}{O_{\gamma}}
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\newcommand{\isom}{\cong}
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\newcommand{\ncisom}{\approx} % noncanonical isomorphism
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\DeclareMathOperator{\ab}{ab}
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\DeclareMathOperator{\Aut}{Aut}
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\DeclareMathOperator{\Frob}{Frob}
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\DeclareMathOperator{\Fr}{Fr}
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\DeclareMathOperator{\Ver}{Ver}
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\DeclareMathOperator{\Norm}{Norm}
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\DeclareMathOperator{\norm}{norm}
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\DeclareMathOperator{\disc}{disc}
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\DeclareMathOperator{\ord}{ord}
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\DeclareMathOperator{\GL}{GL}
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\DeclareMathOperator{\PSL}{PSL}
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\DeclareMathOperator{\PGL}{PGL}
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\DeclareMathOperator{\Gal}{Gal}
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\DeclareMathOperator{\SL}{SL}
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\DeclareMathOperator{\SO}{SO}
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\newcommand{\galq}{\Gal(\Qbar/\Q)}
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\newcommand{\rhobar}{\overline{\rho}}
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\newcommand{\cM}{\mathcal{M}}
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\newcommand{\cB}{\mathcal{B}}
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\newcommand{\cE}{\mathcal{E}}
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\newcommand{\cR}{\mathcal{R}}
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\newcommand{\et}{\text{\rm\'et}}
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\newcommand{\sltwoz}{\SL_2(\Z)}
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\newcommand{\sltwo}{\SL_2}
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\newcommand{\gltwoz}{\GL_2(\Z)}
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\newcommand{\mtwoz}{M_2(\Z)}
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\newcommand{\gltwoq}{\GL_2(\Q)}
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\newcommand{\gltwo}{\GL_2}
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\newcommand{\gln}{\GL_n}
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\newcommand{\psltwoz}{\PSL_2(\Z)}
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\newcommand{\psltwo}{\PSL_2}
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\newcommand{\h}{\mathfrak{h}}
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\renewcommand{\a}{\mathfrak{a}}
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\newcommand{\p}{\mathfrak{p}}
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\newcommand{\m}{\mathfrak{m}}
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\newcommand{\trho}{\tilde{\rho}}
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\newcommand{\rhol}{\rho_{\ell}}
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\newcommand{\rhoss}{\rho^{\text{ss}}}
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\DeclareMathOperator{\tr}{tr}
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\DeclareMathOperator{\order}{order}
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\DeclareMathOperator{\ur}{ur}
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\DeclareMathOperator{\Tr}{Tr}
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\DeclareMathOperator{\Hom}{Hom}
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\DeclareMathOperator{\Mor}{Mor}
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\DeclareMathOperator{\HH}{H}
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\renewcommand{\H}{\HH}
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\DeclareMathOperator{\Ext}{Ext}
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\DeclareMathOperator{\Tor}{Tor}
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\newcommand{\smallzero}{\left(\begin{smallmatrix}0&0\\0&0
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\end{smallmatrix}\right)}
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\newcommand{\smallone}{\left(\begin{smallmatrix}1&0\\0&1
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\end{smallmatrix}\right)}
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\newcommand{\pari}{{\sc Pari}}
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\newcommand{\magma}{{\sc Magma}}
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\newcommand{\hecke}{{\sc Hecke}}
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\newcommand{\lidia}{{\sc LiDIA}}
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%%%% Theoremstyles
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\theoremstyle{plain}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{claim}[theorem]{Claim}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{conjecture}[theorem]{Conjecture}
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\newtheorem{hypothesis}[theorem]{Hypothesis}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{question}[theorem]{Question}
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\newtheorem{problem}[theorem]{Problem}
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\newtheorem{alg}[theorem]{Algorithm}
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\newtheorem{openproblem}[theorem]{Open Problem}
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%\theoremstyle{remark}
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\newtheorem{goal}[theorem]{Goal}
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\newtheorem{remark}[theorem]{Remark}
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\newtheorem{remarks}[theorem]{Remarks}
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\newtheorem{example}[theorem]{Example}
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\newtheorem{exercise}[theorem]{Exercise}
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\numberwithin{equation}{section}
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\numberwithin{figure}{section}
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\numberwithin{table}{section}
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% bulleted list environment
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\newenvironment{bulletlist}
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{
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\begin{list}
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{$\bullet$}
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{
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\setlength{\itemsep}{.5ex}
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\setlength{\parsep}{0ex}
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\setlength{\parskip}{0ex}
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\setlength{\topsep}{.5ex}
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}
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}
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{
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\end{list}
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}
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%end newenvironment
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% bulleted list environment
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\newenvironment{dashlist}
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{
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\begin{list}
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{---}
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{
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\setlength{\itemsep}{.5ex}
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\setlength{\parsep}{0ex}
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\setlength{\parskip}{0ex}
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\setlength{\topsep}{.5ex}
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}
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}
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{
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\end{list}
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}
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%end newenvironment
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% numbered list environment
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\newcounter{listnum}
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\newenvironment{numlist}
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{
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\begin{list}
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{{\em \thelistnum.}}{
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\usecounter{listnum}
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\setlength{\itemsep}{.5ex}
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\setlength{\parsep}{0ex}
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\setlength{\parskip}{0ex}
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\setlength{\topsep}{.5ex}
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}
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}
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{
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\end{list}
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}
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%end newenvironment
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\newcommand{\hd}[1]{\vspace{1ex}\noindent{\bf #1} }
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\newcommand{\nf}[1]{\underline{#1}}
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\newcommand{\cbar}{\overline{c}}
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\DeclareMathOperator{\rad}{rad}
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\newenvironment{algorithm}[1]{%
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\begin{alg}[#1]\index{algorithm!#1}\sf
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}%
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{\end{alg}}
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\newenvironment{steps}%
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{\begin{enumerate}\setlength{\itemsep}{0.1ex}}{\end{enumerate}}
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%\usepackage[hypertex]{hyperref}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: t
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%%% End:
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