CoCalc Public Fileswww / tables / macros.tex
Author: William A. Stein
1% macros.tex
2\usepackage{amsmath}
3\usepackage{amsfonts}
4\usepackage{amssymb}
5\usepackage{amsthm}
6
7\author{William A. Stein\footnote{University of California, Berkeley, U.S.A.,
8{\tt was@math.berkeley.edu}}}
9
10\font\cyr=wncyr10 scaled \magstep 1
11
13\par\noindent
14{Preprint (\today), Version #2}
15\vspace{10ex}
16\par\noindent
17{\bf \LARGE #1}\\
18\vspace{3ex}
19\par\noindent
20{\large W.A. Stein}\\
21{\small Department of Mathematics, University of California, Berkeley,
22CA 94720, USA}\vspace{1ex}\\
23#3
24\vspace{2ex}\par
25}
26
28\par\noindent
29{Preprint (\today), Version #2}
30\vspace{10ex}
31\par\noindent
32{\bf \LARGE #1}\\
33\vspace{3ex}
34\par\noindent
35#3
36\vspace{5ex}\par
37}
38
39\newcommand{\defn}[1]{{\bf #1}}
40\newcommand{\solution}[1]{\vspace{1em}%
41  \par\noindent{\bf Solution #1.} }
42\newcommand{\todo}[1]{\noindent$\bullet$ {\small \textsf{#1}} $\bullet$\\}
43\newcommand{\done}[1]{\noindent {\small \textsf{Done: #1}}\\}
44\newcommand{\danger}[1]{\marginpar{\small \textsl{#1}}}
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47\DeclareMathOperator{\abs}{abs}
48\DeclareMathOperator{\lcm}{lcm}
49\DeclareMathOperator{\cores}{cores}
50\DeclareMathOperator{\coker}{coker}
51\DeclareMathOperator{\image}{image}
52\DeclareMathOperator{\prt}{part}
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54\DeclareMathOperator{\Ann}{Ann}
55\DeclareMathOperator{\End}{End}
56\DeclareMathOperator{\Eis}{Eis}
57\DeclareMathOperator{\Pic}{Pic}
58\DeclareMathOperator{\Vol}{Vol}
59\DeclareMathOperator{\rank}{rank}
60\DeclareMathOperator{\Sel}{Sel}
61\DeclareMathOperator{\Mat}{Mat}
62\DeclareMathOperator{\BSD}{BSD}
63\DeclareMathOperator{\id}{id}
64\DeclareMathOperator{\dz}{dz}
65%\DeclareMathOperator{\Re}{Re}
66%\DeclareMathOperator{\Im}{Im}
67\DeclareMathOperator{\Selmer}{Selmer}
68\newcommand{\pfSel}{\widehat{\Sel}}
69\newcommand{\qe}{\stackrel{\mbox{\tiny ?}}{=}}
70\newcommand{\isog}{\simeq}
71\newcommand{\e}{\mathbf{e}}
72\newcommand{\bN}{\mathbf{N}}
73\newcommand{\Sha}{\mbox{\cyr X}}
74\newcommand{\TS}{Tate-Shafarevich group}
75\newcommand{\Gam}{\Gamma}
76\renewcommand{\Im}{\text{Im}}
77\newcommand{\X}{\mathcal{X}}
78\newcommand{\cH}{\mathcal{H}}
79\newcommand{\cA}{\mathcal{A}}
80\newcommand{\ds}{\displaystyle}
81\newcommand{\M}{\mathcal{M}}
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86\DeclareMathOperator{\Morph}{Morph}
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88\DeclareMathOperator{\Sym}{Sym}
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102\DeclareMathOperator{\Jac}{Jac}
103\DeclareMathOperator{\res}{res}
104\DeclareMathOperator{\Ker}{Ker}
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106\DeclareMathOperator{\unr}{unr}
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112\newcommand{\q}{\mathbf{q}}
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115\newcommand{\gA}{\mathfrak{A}}
116\newcommand{\gP}{\mathfrak{P}}
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136\newcommand{\pni}{\par\noindent}
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138\newcommand{\iv}{^{-1}}
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140\newcommand{\bq}{\mathbf{q}}
141\newcommand{\hecke}{{\tt HECKE}}
142\newcommand{\lidia}{{\tt LiDIA}}
143\newcommand{\cpp}{{\tt C++}}
144\newcommand{\tensor}{\otimes}
145\newcommand{\bg}{{\tt BruceGenus}}
146\newcommand{\abcd}[4]{\left(
147        \begin{smallmatrix}#1&#2\\#3&#4\end{smallmatrix}\right)}
148%\newcommand{\mthree}[9]{\left(
149%        \begin{array}{rrr}#1&#2&#3\\#4&#5&#6\\#7&#8&#9
150%        \end{array}\right)}
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152        \begin{matrix}#1&#2&#3\\#4&#5&#6\\#7&#8&#9
153        \end{matrix}\right)}
154%\newcommand{\mtwo}[4]{\left(
155%        \begin{array}{rr}#1&#2\\#3&#4
156%        \end{array}\right)}
157\newcommand{\mtwo}[4]{\left(
158        \begin{matrix}#1&#2\\#3&#4
159        \end{matrix}\right)}
160\newcommand{\smallmtwo}[4]{\left(
161        \begin{smallmatrix}#1&#2\\#3&#4
162        \end{smallmatrix}\right)}
163\newcommand{\eps}{\varepsilon}
164\newcommand{\vphi}{\varphi}
165\newcommand{\gp}{\mathfrak{p}}
166\newcommand{\W}{\mathcal{W}}
167\newcommand{\oz}{\overline{z}}
168\newcommand{\Zpstar}{\Zp^{\star}}
169\newcommand{\Zhat}{\widehat{\Z}}
170\newcommand{\comment}[1]{}
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172\newcommand{\GQ}{G_{\Q}}
173\newcommand{\R}{\mathbf{R}}
174\newcommand{\D}{{\mathbb D}}
175\newcommand{\cC}{\mathcal{C}}
176\newcommand{\cD}{\mathcal{D}}
177\newcommand{\cS}{\mathcal{S}}
178\newcommand{\Sbar}{\overline{S}}
179\newcommand{\K}{{\mathbb K}}
180\newcommand{\C}{\mathbf{C}}
181\newcommand{\Cp}{{\mathbb C}_p}
182\newcommand{\Sets}{\mbox{\rm\bf Sets}}
183\newcommand{\bcC}{\boldsymbol{\mathcal{C}}}
184\renewcommand{\P}{\mathbf{P}}
185\newcommand{\Qbar}{\overline{\Q}}
186\newcommand{\kbar}{\overline{k}}
187\newcommand{\dual}{\bot}
188\newcommand{\T}{\mathbf{T}}
189\newcommand{\calT}{\mathcal{T}}
190\newcommand{\cT}{\mathcal{T}}
191\newcommand{\cbT}{\mathbf{\mathcal{T}}}
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201\newcommand{\Qp}{\Q_p}
202\newcommand{\Ql}{\Q_{\ell}}
203\newcommand{\Qlbar}{\overline{\Q}_{\ell}}
204\newcommand{\Qlnr}{\Q_{\ell}^{\text{nr}}}
205\newcommand{\Qltm}{\Q_{\ell}^{\text{tame}}}
206\newcommand{\Qv}{\Q_v}
207\newcommand{\Qpbar}{\Qbar_p}
208\newcommand{\Zp}{\Z_p}
209\newcommand{\Fp}{\F_p}
210\newcommand{\Fq}{\F_q}
211\newcommand{\Fqbar}{\overline{\F}_q}
214\renewcommand{\O}{\mathcal{O}}
215\newcommand{\A}{\mathcal{A}}
216\newcommand{\Og}{O_{\gamma}}
217\newcommand{\isom}{\cong}
218\newcommand{\ncisom}{\approx}   % noncanonical isomorphism
219\DeclareMathOperator{\Aut}{Aut}
220\DeclareMathOperator{\Frob}{Frob}
221\DeclareMathOperator{\Ver}{Ver}
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223\DeclareMathOperator{\disc}{disc}
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227\DeclareMathOperator{\PGL}{PGL}
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234\newcommand{\cB}{\mathcal{B}}
235\newcommand{\cE}{\mathcal{E}}
236
237\newcommand{\sltwoz}{\SL_2(\Z)}
238\newcommand{\sltwo}{\SL_2}
239\newcommand{\gltwoz}{\GL_2(\Z)}
240\newcommand{\mtwoz}{M_2(\Z)}
241\newcommand{\gltwoq}{\GL_2(\Q)}
242\newcommand{\gltwo}{\GL_2}
243\newcommand{\gln}{\GL_n}
244\newcommand{\psltwoz}{\PSL_2(\Z)}
245\newcommand{\psltwo}{\PSL_2}
246\newcommand{\h}{\mathfrak{h}}
247\renewcommand{\a}{\mathfrak{a}}
248\newcommand{\p}{\mathfrak{p}}
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259                        \end{smallmatrix}\right)}
260\newcommand{\smallone}{\left(\begin{smallmatrix}1&0\\0&1
261                        \end{smallmatrix}\right)}
262\newcommand{\pari}{PARI}
263
264%%%% Theoremstyles
265\theoremstyle{plain}
266\newtheorem{theorem}{Theorem}[section]
267\newtheorem{proposition}[theorem]{Proposition}
268\newtheorem{corollary}[theorem]{Corollary}
269\newtheorem{lemma}[theorem]{Lemma}
270\newtheorem{conjecture}[theorem]{Conjecture}
271
272\theoremstyle{definition}
273\newtheorem{definition}[theorem]{Definition}
274\newtheorem{algorithm}[theorem]{Algorithm}
275\newtheorem{question}[theorem]{Question}
276
277\theoremstyle{remark}
278\newtheorem{goal}[theorem]{Goal}
279\newtheorem{remark}[theorem]{Remark}
280\newtheorem{example}[theorem]{Example}
281\newtheorem{exercise}[theorem]{Exercise}
282
283
284
285