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(./latex_ba33aad8d4cb6e24ab849cac7c3067ab7dfd6e13_p.tex
LaTeX2e <2014/05/01>
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Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
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l.7 \documentclass
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l.8 \usepackage
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l.13 \usepackage
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l.18 \usepackage
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l.20 \usepackage
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l.21 \usepackage
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l.22 \usepackage
                [utf8]{inputenc} %Codage UNICODE (UTF-8)

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l.24 \usepackage
                [T1]{fontenc} %Hyphénation des mots accentués

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l.25 \usepackage
                {lmodern} %Polices vectorielles

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l.27 \usepackage
                {sagetex}

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l.57 \begin{document}
                     
[1]

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l.71 \begin{sagesilent}
                       
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                $
l.75 m = A.minimal_
                   polynomial()

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l.77 \end{sagesilent}
                     
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                $
l.77 \end{sagesilent}
                     
! Undefined control sequence.
l.79 Soit $A=\sage
                  {A}$. Faisons quelques calculs sur la matrice $A$.
! Undefined control sequence.
<recently read> \sage 
                      
l.84 $\det(A)$ & $\sage
                       {A.det()}$ \\
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<recently read> \sage 
                      
l.86 $\chi_A(x)$ & $\sage
                         {A.characteristic_polynomial()}$ \\
! Undefined control sequence.
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l.88 $m_A(x)$ & $\sage
                      {A.minimal_polynomial()}$ \\
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l.90 Forme échelonnée & $\sage
                                {A.echelon_form()}$ \\
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l.92 Diviseurs élémentaires & $\sage
                                      {A.elementary_divisors()}$ \\

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l.97 \begin{equation*}
                      % sagetex works fine for equation and equation* enviro...

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                $
l.98 m_
       A(A) = \sage{m(A)}.
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l.98 m_A(A) = \sage
                   {m(A)}.

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l.99 \end{equation*}
                    
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                $
l.99 \end{equation*}
                    

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l.112 \begin{sagesilent}
                        

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l.114 \end{sagesilent}
                      
! Undefined control sequence.
l.116 Soit maintenant $B=\sage
                              {B}$. Le produit de $A$ par $B$ est
! Undefined control sequence.
l.118 \sage
           {A*B}.
[2]

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l.127 \begin{sagesilent}
                        
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                $
l.128 chi = A.characteristic_
                             polynomial()

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l.131 \end{sagesilent}
                      
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                $
l.131 \end{sagesilent}
                      
! Undefined control sequence.
l.133 ...ire étudier la fonction $\chi_A(x)=\sage
                                                  {chi}$. Commençons par tr...

! Undefined control sequence.
l.133 ...de ce polynôme dans l'intervalle $[\sage
                                                  {xmin}, \sage{xmax}]$.
! Undefined control sequence.
l.133 ...me dans l'intervalle $[\sage{xmin}, \sage
                                                  {xmax}]$.
! Undefined control sequence.
l.138 \sageplot
               [width=8cm]{plot(chi, xmin=xmin, xmax=xmax)}

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l.144 \begin{sageblock}
                       
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                $
l.145 r1,r2,r3 = chi.real_
                          roots()

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l.146 \end{sageblock}
                     
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                $
l.146 \end{sageblock}
                     
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<recently read> \sage 
                      
l.148 ...s réelles de $\chi_A(x)$ qui sont $\sage
                                                  {r1}$, $\sage{r2}$, $\sage...

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<recently read> \sage 
                      
l.148 ... $\chi_A(x)$ qui sont $\sage{r1}$, $\sage
                                                  {r2}$, $\sage{r3}$ et $\sa...

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<recently read> \sage 
                      
l.148 ...qui sont $\sage{r1}$, $\sage{r2}$, $\sage
                                                  {r3}$ et $\sage{r3}$. Ceci...

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<recently read> \sage 
                      
l.148 ...{r1}$, $\sage{r2}$, $\sage{r3}$ et $\sage
                                                  {r3}$. Ceci nous indique q...

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l.152 \sageplot
               [width=8cm]{plot(chi, xmin=30, xmax=34)}
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l.161 \frac{d}{dx}\chi_A(x) = \sage
                                   {derivative(chi)}
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l.165 \int\chi_A(x)dx = \sage
                             {integrate(chi)}.

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l.170 \begin{sagesilent}
                        
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l.173 g = (x+1)^
                (1/x)

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l.175 \end{sagesilent}
                      
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                $
l.175 \end{sagesilent}
                      
! Undefined control sequence.
l.178 \lim_{x\to 0+}\sage
                         {f} = \sage{limit(f, x = 0, dir='above')}
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l.178 \lim_{x\to 0+}\sage{f} = \sage
                                    {limit(f, x = 0, dir='above')}
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l.181 \lim_{x\to 0}\sage
                        {g} = \sage{limit(g, x = 0)}
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l.181 \lim_{x\to 0}\sage{g} = \sage
                                   {limit(g, x = 0)}
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l.184 \lim_{x\to \sage
                      {oo}}\sage{h} = \sage{limit(h, x = oo)}
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l.184 \lim_{x\to \sage{oo}}\sage
                                {h} = \sage{limit(h, x = oo)}
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l.184 \lim_{x\to \sage{oo}}\sage{h} = \sage
                                           {limit(h, x = oo)}
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l.187 \lim_{x\to \sage
                      {-oo}}\sage{h} = \sage{limit(h, x = -oo)}
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l.187 \lim_{x\to \sage{-oo}}\sage
                                 {h} = \sage{limit(h, x = -oo)}
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l.187 \lim_{x\to \sage{-oo}}\sage{h} = \sage
                                            {limit(h, x = -oo)}
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l.190 \lim_{x\to 0}\sage
                        {1/x} = \sage{limit(1/x, x = 0)}
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l.190 \lim_{x\to 0}\sage{1/x} = \sage
                                     {limit(1/x, x = 0)}
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l.193 \lim_{x\to 0+}\sage
                         {1/x} = \sage{limit(1/x, x = 0, dir='above')}
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l.193 \lim_{x\to 0+}\sage{1/x} = \sage
                                      {limit(1/x, x = 0, dir='above')}
[3]

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l.203 \begin{sagesilent}
                        
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                $
l.206 g = S.cayley_
                   graph()

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l.207 \end{sagesilent}
                      
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                $
l.207 \end{sagesilent}
                      
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l.209 ...yley du groupe symétrique d'ordre $\sage
                                                  {n}$. Les couleurs des ar...

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<recently read> \sage 
                      
l.209 ...ndent aux générateurs suivants : $\sage
                                                  {S.gens()}$.
! Undefined control sequence.
l.211 \sageplot
               [width=6cm]{g.plot(color_by_label=True, vertex_size=0.01)}
! Missing $ inserted.
<inserted text> 
                $
l.211 \sageplot[width=6cm]{g.plot(color_
                                        by_label=True, vertex_size=0.01)}
! Extra }, or forgotten $.
l.211 ...t(color_by_label=True, vertex_size=0.01)}
                                                  
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                $
l.212 
      

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l.213 \begin{sagesilent}
                        
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                $
l.216 g = S.cayley_
                   graph()

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l.217 \end{sagesilent}
                      
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                $
l.217 \end{sagesilent}
                      
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l.219 ...yley du groupe symétrique d'ordre $\sage
                                                  {n}$. Les couleurs des ar...

! Undefined control sequence.
<recently read> \sage 
                      
l.219 ...ndent aux générateurs suivants : $\sage
                                                  {S.gens()}$.
! Undefined control sequence.
l.221 \sageplot
               [width=8cm]{g.plot(color_by_label=True, vertex_size=0.01)}
! Missing $ inserted.
<inserted text> 
                $
l.221 \sageplot[width=8cm]{g.plot(color_
                                        by_label=True, vertex_size=0.01)}
! Extra }, or forgotten $.
l.221 ...t(color_by_label=True, vertex_size=0.01)}
                                                  
! Missing $ inserted.
<inserted text> 
                $
l.222 
      

Overfull \hbox (132.09656pt too wide) in paragraph at lines 226--227
\OT1/cmr/m/n/12 tion disponible dans l'arborescence de sage : \OT1/cmtt/m/n/12 
sage-4.1/examples/latex[]embed/sagetexpackage.pdf\OT1/cmr/m/n/12 . 

Overfull \hbox (42.00279pt too wide) in paragraph at lines 240--242
\OT1/cmtt/m/n/12 http://www.ctan.org/tex-archive/help/Catalogue/entries/sagetex
.html 
[4] (./latex_ba33aad8d4cb6e24ab849cac7c3067ab7dfd6e13_p.aux)

LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.

 )
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### bottom level
(see the transcript file for additional information)
Output written on latex_ba33aad8d4cb6e24ab849cac7c3067ab7dfd6e13_p.dvi (4 pages
, 6928 bytes).
Transcript written on latex_ba33aad8d4cb6e24ab849cac7c3067ab7dfd6e13_p.log.

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