Attachment 'devoir.tex'
Downloadlatex error! exitcode was 1 (signal 0), transscript follows: This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=latex) entering extended mode (./latex_7c89e2a2cdac3c3a312520e6415d658330219195_p.tex LaTeX2e <2014/05/01> Babel <3.9l> and hyphenation patterns for 2 languages loaded. (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo)) (/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty (/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def (/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu) (/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu))) No file latex_7c89e2a2cdac3c3a312520e6415d658330219195_p.aux. ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.7 \documentclass {article} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.8 \usepackage {graphicx} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.9 \usepackage {amsmath} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.10 \usepackage {amsfonts} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.11 \usepackage {latexsym} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.12 \usepackage {amssymb} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.13 \usepackage {enumerate} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.18 \usepackage {color} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.20 \usepackage {listings} %Pour insérer du code. ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.21 \usepackage [french]{babel} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.22 \usepackage [utf8]{inputenc} %Codage UNICODE (UTF-8) ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.24 \usepackage [T1]{fontenc} %Hyphénation des mots accentués ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.25 \usepackage {lmodern} %Polices vectorielles ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.27 \usepackage {sagetex} ! LaTeX Error: Can be used only in preamble. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.57 \begin{document} [1] ! LaTeX Error: Environment sagesilent undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.71 \begin{sagesilent} ! Missing $ inserted. <inserted text> $ l.75 m = A.minimal_ polynomial() ! LaTeX Error: \begin{document} on input line 57 ended by \end{sagesilent}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.77 \end{sagesilent} ! Missing $ inserted. <inserted text> $ 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 $\det(A)$ & $\sage {A.det()}$ \\ ! Undefined control sequence. <recently read> \sage l.86 $\chi_A(x)$ & $\sage {A.characteristic_polynomial()}$ \\ ! Undefined control sequence. <recently read> \sage l.88 $m_A(x)$ & $\sage {A.minimal_polynomial()}$ \\ ! Undefined control sequence. <recently read> \sage l.90 Forme échelonnée & $\sage {A.echelon_form()}$ \\ ! Undefined control sequence. <recently read> \sage l.92 Diviseurs élémentaires & $\sage {A.elementary_divisors()}$ \\ ! LaTeX Error: Environment equation* undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.97 \begin{equation*} % sagetex works fine for equation and equation* enviro... ! Missing $ inserted. <inserted text> $ l.98 m_ A(A) = \sage{m(A)}. ! Undefined control sequence. l.98 m_A(A) = \sage {m(A)}. ! LaTeX Error: \begin{document} on input line 57 ended by \end{equation*}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.99 \end{equation*} ! Missing $ inserted. <inserted text> $ l.99 \end{equation*} ! LaTeX Error: Environment sagesilent undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.112 \begin{sagesilent} ! LaTeX Error: \begin{document} on input line 57 ended by \end{sagesilent}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... 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] ! LaTeX Error: Environment sagesilent undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.127 \begin{sagesilent} ! Missing $ inserted. <inserted text> $ l.128 chi = A.characteristic_ polynomial() ! LaTeX Error: \begin{document} on input line 57 ended by \end{sagesilent}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.131 \end{sagesilent} ! Missing $ inserted. <inserted text> $ 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)} ! LaTeX Error: Environment sageblock undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.144 \begin{sageblock} ! Missing $ inserted. <inserted text> $ l.145 r1,r2,r3,r4 = chi.real_ roots() ! LaTeX Error: \begin{document} on input line 57 ended by \end{sageblock}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.146 \end{sageblock} ! Missing $ inserted. <inserted text> $ l.146 \end{sageblock} ! Undefined control sequence. <recently read> \sage l.148 ...s réelles de $\chi_A(x)$ qui sont $\sage {r1}$, $\sage{r2}$, $\sage... ! Undefined control sequence. <recently read> \sage l.148 ... $\chi_A(x)$ qui sont $\sage{r1}$, $\sage {r2}$, $\sage{r3}$ et $\sa... ! Undefined control sequence. <recently read> \sage l.148 ...qui sont $\sage{r1}$, $\sage{r2}$, $\sage {r3}$ et $\sage{r4}$. Ceci... ! Undefined control sequence. <recently read> \sage l.148 ...{r1}$, $\sage{r2}$, $\sage{r3}$ et $\sage {r4}$. Ceci nous indique q... ! Undefined control sequence. l.152 \sageplot [width=8cm]{plot(chi, xmin=30, xmax=34)} ! Undefined control sequence. l.161 \frac{d}{dx}\chi_A(x) = \sage {derivative(chi)} ! Undefined control sequence. l.165 \int\chi_A(x)dx = \sage {integrate(chi)}. ! LaTeX Error: Environment sagesilent undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.170 \begin{sagesilent} ! Missing $ inserted. <inserted text> $ l.173 g = (x+1)^ (1/x) ! LaTeX Error: \begin{document} on input line 57 ended by \end{sagesilent}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.175 \end{sagesilent} ! Missing $ inserted. <inserted text> $ l.175 \end{sagesilent} ! Undefined control sequence. l.178 \lim_{x\to 0+}\sage {f} = \sage{limit(f, x = 0, dir='above')} ! Undefined control sequence. l.178 \lim_{x\to 0+}\sage{f} = \sage {limit(f, x = 0, dir='above')} ! Undefined control sequence. l.181 \lim_{x\to 0}\sage {g} = \sage{limit(g, x = 0)} ! Undefined control sequence. l.181 \lim_{x\to 0}\sage{g} = \sage {limit(g, x = 0)} ! Undefined control sequence. l.184 \lim_{x\to \sage {oo}}\sage{h} = \sage{limit(h, x = oo)} ! Undefined control sequence. l.184 \lim_{x\to \sage{oo}}\sage {h} = \sage{limit(h, x = oo)} ! Undefined control sequence. l.184 \lim_{x\to \sage{oo}}\sage{h} = \sage {limit(h, x = oo)} ! Undefined control sequence. l.187 \lim_{x\to \sage {-oo}}\sage{h} = \sage{limit(h, x = -oo)} ! Undefined control sequence. l.187 \lim_{x\to \sage{-oo}}\sage {h} = \sage{limit(h, x = -oo)} ! Undefined control sequence. l.187 \lim_{x\to \sage{-oo}}\sage{h} = \sage {limit(h, x = -oo)} ! Undefined control sequence. l.190 \lim_{x\to 0}\sage {1/x} = \sage{limit(1/x, x = 0)} ! Undefined control sequence. l.190 \lim_{x\to 0}\sage{1/x} = \sage {limit(1/x, x = 0)} ! Undefined control sequence. l.193 \lim_{x\to 0+}\sage {1/x} = \sage{limit(1/x, x = 0, dir='above')} ! Undefined control sequence. l.193 \lim_{x\to 0+}\sage{1/x} = \sage {limit(1/x, x = 0, dir='above')} [3] ! LaTeX Error: Environment sagesilent undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.203 \begin{sagesilent} ! Missing $ inserted. <inserted text> $ l.206 g = S.cayley_ graph() ! LaTeX Error: \begin{document} on input line 57 ended by \end{sagesilent}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.207 \end{sagesilent} ! Missing $ inserted. <inserted text> $ l.207 \end{sagesilent} ! Undefined control sequence. <recently read> \sage l.209 ...yley du groupe symétrique d'ordre $\sage {n}$. Les couleurs des arÃ... ! Undefined control sequence. <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)} ! Missing $ inserted. <inserted text> $ l.212 ! LaTeX Error: Environment sagesilent undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.213 \begin{sagesilent} ! Missing $ inserted. <inserted text> $ l.216 g = S.cayley_ graph() ! LaTeX Error: \begin{document} on input line 57 ended by \end{sagesilent}. See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ... l.217 \end{sagesilent} ! Missing $ inserted. <inserted text> $ l.217 \end{sagesilent} ! Undefined control sequence. <recently read> \sage l.219 ...yley du groupe symétrique d'ordre $\sage {n}$. Les couleurs des arÃ... ! 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_7c89e2a2cdac3c3a312520e6415d658330219195_p.aux) LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. ) (\end occurred inside a group at level 3) ### simple group (level 3) entered at line 221 ({) ### simple group (level 2) entered at line 211 ({) ### semi simple group (level 1) entered at line 57 (\begingroup) ### bottom level (see the transcript file for additional information) Output written on latex_7c89e2a2cdac3c3a312520e6415d658330219195_p.dvi (4 pages , 6932 bytes). Transcript written on latex_7c89e2a2cdac3c3a312520e6415d658330219195_p.log.
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