1\documentclass{article}
2\usepackage{a4wide}
3\usepackage{amsmath}
4\usepackage{ifthen}
5\usepackage{calc}
6
7\title{Test de primitives amstex}
8\date{}
9\numberwithin{equation}{section}
10\renewcommand{\theequation}{\thesection.\alph{equation}}
11
12\begin{document}
13\maketitle
14
15\part{Some tests}
16\section{Matrices}
17\section*{Toutes les r\'ef\'erences}
18Les num\'eros sont~:
19
20\begin{tabular}{*{5}{|c}|}\hline
21\ref{bigmat} & \ref{dessus} & \ref{dessous} & \ref{t_2_formula}\\ \hline
22\end{tabular}
23
24\subsection{Simple}
25\begin{gather}
26\begin{matrix} 1 & 0\\ 0 & 1\end{matrix}
27\quad
28\begin{pmatrix} 1 & 0\\ 0 & 1\end{pmatrix}
29\quad
30\begin{Vmatrix} 1 & 0\\ 0 & 1\\ 1 & 2\end{Vmatrix}
31\end{gather}
32
33\subsection{Compliqu\'e}
34\setcounter{MaxMatrixCols}{20}
35\newcounter{x}
36\newcommand{\row}[1]{%
37\hdotsfor{#1} &
38\setcounter{x}{#1}\addtocounter{x}{1}\thex
39\setcounter{x}{-\value{x}}\addtocounter{x}{20} &
40\hdotsfor{\value{x}}}
41\begin{equation}
42\begin{pmatrix}
431 & \hdotsfor{19}\\
44\row{1}\\
45\row{2}\\
46\row{3}\\
47\row{4}\\
48\row{5}\\
49\row{6}\\
50\row{7}\\
51\row{8}\\
52\row{9}\\
53\row{10}\\
54\row{11}\\
55\row{12}\\
56\row{13}\\
57\row{14}\\
58\row{15}\\
59\row{16}\\
60\row{17}\\
61\row{18}\\
62\hdotsfor{19} & 20
63\end{pmatrix}\label{bigmat}
64\end{equation}
65
66\section{Environement \texttt{cases}}
67To summarize, we obtain the following exact representation for the
68inverse of~$x^2e^x+1$:
69\[\begin{cases}
70Y(x) = y(\log x),\quad&\text{$y_{\phantom{0}}$ inverse of~$2\log
71x+x+\log(1+e^{-x}/x^2)$},\\
72y[x+\log(1+y_0^{-2}(x)e^{-y_0(x)})] = y_0(x),\quad&\text{$y_0$
73inverse of~$x+2\log x$,}\\
74y_0(x) = y_1(\log x),\quad&\text{$y_1$ inverse of~$\log x+\log(1+2\log x/x)$},\\
75y_1(x) = \exp(y_2(x)),\quad&\text{$y_2$ inverse of~$x+\log(1+2xe^{-x})$},\\
76y_2[x+\log(1+2y_3(x)e^{-y_3(x)})] = y_3(x),&\text{$y_3$ inverse
77of~$x$.}
78  \end{cases}
79\]
80
81\section{Test d'alignement}
82Now the $\phi_i$s are very easy to compute:
83\begin{align*}
84\phi_1&  =  y_0 = 1/t_2,\\
85\phi_2&  = \phi_1(y_0(x+g))-\phi_1 = {t_3t_2^2\over(1+2t_2)}
86-{1+4t_2+2t_2^2\over2(1+2t_2)^3}t_2^4t_3^2+O(t_3^3),\\
87\phi_3&  = \phi_2(y_0(x+g))-\phi_2 = -{1+4t_2+2t_2^2\over(1+2t_2)^3}t_2^4t_3^2+O(t_3^3),
88\end{align*}
89
90A similar treatment applies to~(\ref{bigmat}), and leads to
91\begin{alignat*}{5}
92x+\log(1+2xe^{-x})&  =  1/t_1(y_3(x+g))&&  =  x+2xe^{-x}-2x^2e^{-2x}+O(x^3e^{-3x}),\\
93\exp[-x+\log(1+2xe^{-x})]&  =  t_2(y_3(x+g))&&  =  e^{-x}-2xe^{-2x}+4x^2e^{-3x}+O(x^3e^{-4x}).
94\end{alignat*}
95
96\subsection{\texttt{gather}, \texttt{multline}}
97or one of the following (successive) refinements:
98\begin{gather}\label{dessus}
99\exp(e^U)\left[1-\frac{2e^{-U^{1/2}}}{U^{1/2}+4}
100+\frac{2e^{-2U^{1/2}}}{(U^{1/2}+4)^2}
101-\frac{4}{3}\frac{e^{-3U^{1/2}}}{(U^{1/2}+4)^3}+O(e^{-4U^{1/2}})\right],\\
102\exp(e^U)\exp\left[-\frac{2e^{-U^{1/2}}}{U^{1/2}+4}\right]\left[1+
103\frac{8-2U^{-1/2}-U^{-1}+U^{-3/2}}{(4+U^{-1/2})^3}
104e^{-U-2U^{1/2}}+O(e^{-2U})\right],\label{dessous}
105\end{gather}
106
107Cette \'equation a le num\'ero~\ref{t_2_formula}, celles d'au dessus les
108num\'ero~\ref{dessus} et~\ref{dessous}.
109\begin{multline}	\label{t_2_formula}
1101/t_2(y_0(x+g)) = y_0(x+\log(1+y_0^{-2}e^{-y_0}))\\
111 = y_0+{e^{-y_0}\over y_0^2(1+2/y_0)}
112-{1+4/y_0+2/y_0^2\over 2y_0^4(1+2/y_0)^3}e^{-2y_0}+O(e^{-3y_0}).
113\end{multline}
114
115\part{Other tests}
116
117\section{Z\'ero}
118
119\begin{equation}
120x^2+y^2 = z^2\label{un:un}
121\end{equation}
122\begin{equation*}
123x^2+y^2 = z^2
124\end{equation*}
125\begin{equation}
126x^2+y^2 = z^2\label{un:deux}
127\end{equation}
128\begin{equation}
129x^2+y^2 = z^2\notag
130\end{equation}
131\begin{equation*}
132\tag{oups}x^2+y^2 = z^2\label{oups}
133\end{equation*}
134Au desus \ref{un:un}, \ref{un:deux} et \ref{oups}.
135Apr\`es
136\theequation
137
138\section{Deux}
139\begin{gather}
140x^2+y^2 = z^2\\
141x^3+y^3 = z^3\\
142x^4+y^4 = z^4\\
143x^5+y^5 = z^5\\
144x^6+y^6 = z^6\\
145x^7+y^7 = z^7
146\end{gather}
147
148\section{Un}
149\begin{gather}
150x^2+y^2 = z^2 \label{eq:r2}\\
151x^3+y^3 = z^3 \notag\\
152x^4+y^4 = z^4 \tag{$*$}\label{foo}\\
153x^5+y^5 = z^5 \tag*{$*$}\\
154x^6+y^6 = z^6 \tag*{\ref{eq:r2}$'$}\\
155x^7+y^7 = z^7
156\end{gather}
157Ben mon vieux pour avoir l'\'equation~\ref{foo}.
158
159\section{Trois}
160\begin{gather*}
161x^2+y^2 = z^2\tag{$+$}\\
162x^3+y^3 = z^3\\
163x^4+y^4 = z^4\\
164x^5+y^5 = z^5\\
165x^6+y^6 = z^6\\
166x^7+y^7 = z^7
167\end{gather*}
168
169\section{Quatre}
170\begin{gather}
171x^2+y^2 = z^2\\
172x^3+y^3 = z^3\\
173x^4+y^4 = z^4\\
174x^5+y^5 = z^5\\
175x^6+y^6 = z^6\\
176x^7+y^7 = z^7
177\end{gather}
178Maintenant~: \theequation.
179
180\section{Cinq}
181\begin{align}
182\tag{a} x^2+y^2 &= z^2 & x^3+y^3 &= z^3\label{a}\\
183\notag x^4+y^4 &= z^4 & x^5+y^5 &= z^5\label{b}\\
184x^6+y^6 &= z^6 & x^7+y^7 &= z^7
185\end{align}
186Au dessus ya l'\'equation~\eqref{a}.
187
188\section{Multline}
189\begin{multline}
190x+1 =\\
191y+2
192\end{multline}
193
194\end{document}
195