CoCalc
Sharedwww / macros.texOpen in CoCalc
Author: William A. Stein
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% macros.tex
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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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\author{W. Stein\footnote{University of California, Berkeley, U.S.A.,
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{\tt was@math.berkeley.edu}}}
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\font\cyr=wncyr10 scaled \magstep 1
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\DeclareMathOperator{\ind}{ind}
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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{\prt}{part}
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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{\Pic}{Pic}
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\DeclareMathOperator{\Vol}{Vol}
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\DeclareMathOperator{\rank}{rank}
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\DeclareMathOperator{\Sel}{Sel}
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\DeclareMathOperator{\BSD}{BSD}
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\DeclareMathOperator{\id}{id}
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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{\Sha}{\mbox{\cyr X}}
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\newcommand{\TS}{Tate-Shafarevich group}
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\newcommand{\Gam}{\Gamma}
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\renewcommand{\Im}{\text{Im}}
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\newcommand{\X}{\mathcal{X}}
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\newcommand{\M}{\mathcal{M}}
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\newcommand{\J}{\mathcal{J}}
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\DeclareMathOperator{\new}{new}
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\DeclareMathOperator{\old}{old}
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\DeclareMathOperator{\Sym}{Sym}
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%\newcommand{\Sym}{\mathcal{S}{\rm ym}}
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\newcommand{\dw}{\delta(w)}
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\newcommand{\dwh}{\widehat{\delta(w)}}
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\newcommand{\dlwh}{\widehat{\delta_\l(w)}}
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\newcommand{\dash}{-\!\!\!\!-\!\!\!\!-\!\!\!\!-}
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\DeclareMathOperator{\tor}{tor}
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\newcommand{\Frobl}{\Frob_{\ell}}
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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{\Spec}{Spec}
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\DeclareMathOperator{\Div}{Div}
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\DeclareMathOperator{\Jac}{Jac}
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\DeclareMathOperator{\res}{res}
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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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\newcommand{\intersect}{\cap}
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\newcommand{\cross}{\times}
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\DeclareMathOperator{\md}{mod}
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\newcommand{\rb}{\overline{\rho}}
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\newcommand{\ra}{\rightarrow}
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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{\hecke}{{\tt Hecke}}
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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{array}{rrr}#1&#2&#3\\#4&#5&#6\\#7&#8&#9
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\end{array}\right)}
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\newcommand{\mtwo}[4]{\left(
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\begin{array}{rr}#1&#2\\#3&#4
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\end{array}\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{\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{\Zpstar}{\Zp^{\star}}
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\newcommand{\comment}[1]{}
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\newcommand{\Q}{\mathbf{Q}}
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\newcommand{\GQ}{G_{\Q}}
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\newcommand{\R}{\mathbf{R}}
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\newcommand{\D}{{\mathbb D}}
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\newcommand{\cC}{\mathcal{C}}
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\newcommand{\cD}{\mathcal{D}}
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\newcommand{\cS}{\mathcal{S}}
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\newcommand{\K}{{\mathbb K}}
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\newcommand{\C}{\mathbf{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}{\mathbf{P}}
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\newcommand{\Qbar}{\overline{\Q}}
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\newcommand{\dual}{\bot}
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\newcommand{\T}{\mathbf{T}}
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\newcommand{\Z}{\mathbf{Z}}
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\newcommand{\F}{\mathbf{F}}
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\newcommand{\Fl}{\F_{\ell}}
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\newcommand{\Fbar}{\overline{{\mathbb F}}}
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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{\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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\DeclareMathOperator{\Aut}{Aut}
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\DeclareMathOperator{\Frob}{Frob}
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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{\Gal}{Gal}
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\DeclareMathOperator{\SL}{SL}
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\DeclareMathOperator{\SO}{SO}
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\newcommand{\cM}{\mathcal{M}}
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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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\DeclareMathOperator{\tr}{tr}
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\DeclareMathOperator{\Tr}{Tr}
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\DeclareMathOperator{\Hom}{Hom}
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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}{PARI}
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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{lemma}[theorem]{Lemma}
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\newtheorem{question}[theorem]{Question}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{algorithm}[theorem]{Algorithm}
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\newtheorem{conjecture}[theorem]{Conjecture}
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\theoremstyle{remark}
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\newtheorem{remark}[theorem]{Remark}
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\newtheorem{example}[theorem]{Example}
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\newtheorem{exercise}[theorem]{Exercise}
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