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LaTeX Error: Command \t already defined. Or name \end... illegal, see p.192 of the manual. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.20 \newcommand{\t}{{}^t\!} Your command was ignored. Type I to replace it with another command, or to continue without it. \c@remarques=\count282 \c@lemmes=\count283 \c@corollaires=\count284 \c@theoremes=\count285 \c@exemples=\count286 \c@exercices=\count287 \c@definitions=\count288 \c@methodes=\count289 (/usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def File: l3backend-pdftex.def 2021-03-18 L3 backend support: PDF output (pdfTeX) \l__color_backend_stack_int=\count290 \l__pdf_internal_box=\box49 ) (./cours-théorique.aux) Runaway argument? {id=25,dest={72656D617 ! File ended while scanning use of \BKM@entry. \par l.93 \begin{document} I suspect you have forgotten a `}', causing me to read past where you wanted me to stop. 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Underfull \hbox (badness 10000) in paragraph at lines 100--101 [] [1 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}pdfTeX warning (ext4): desti nation with the same identifier (name{remarque1.3}) has been already used, dupl icate ignored ...shipout:D \box_use:N \l_shipout_box l.153 \end{demo} pdfTeX warning (ext4): destination with the same identifier (na me{remarque1.3}) has been already used, duplicate ignored ...shipout:D \box_use:N \l_shipout_box l.153 \end{demo} pdfTeX warning (ext4): destination with the same identifier (na me{remarque1.3}) has been already used, duplicate ignored ...shipout:D \box_use:N \l_shipout_box l.153 \end{demo} ]pdfTeX warning (ext4): destination with the same identifier (n ame{remarque1.3}) has been already used, duplicate ignored \relax l.158 \begin {align*} Underfull \hbox (badness 10000) in paragraph at lines 158--158 [] Underfull \hbox (badness 10000) in paragraph at lines 172--173 [] Underfull \hbox (badness 10000) in paragraph at lines 206--207 [] [2]pdfTeX warning (ext4): destination with the same identifier (name{remarque1. 3}) has been already used, duplicate ignored \relax l.216 S oient $\bc_1, \bc_2$ deux bases. Underfull \hbox (badness 10000) in paragraph at lines 224--224 [] Underfull \hbox (badness 10000) in paragraph at lines 243--243 [] [3] Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 274. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 274. pdfTeX warning (ext4): destination with the same identifier (name{remarque2.3}) has been already used, duplicate ignored \relax l.274 \begin{remarque}[$\K=\R$] pdfTeX warning (ext4): destination with the same identifier (name{remarque2.3}) has been already used, duplicate ignored \relax l.284 P our $\K=\R$, on dit que \emph{deux bases $\bc_1$ et $\bc_2$ ont la m... pdfTeX warning (ext4): destination with the same identifier (name{remarque2.3}) has been already used, duplicate ignored \relax l.303 O n suppose $\K=\R$ et \emph{$E$ euclidien}. [4] Underfull \hbox (badness 10000) in paragraph at lines 323--323 [] ! Undefined control sequence. Déterminant de $M \in \mc _n(\K )$ $\det M$ l.342 ...©terminant de $M \in \mc_n(\K)$ $\det M$] The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `\in' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `subscript' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `\mathop' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `\mathgroup' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `\symoperators' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `\nmlimits@' on input line 342. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 342. pdfTeX warning (ext4): destination with the same identifier (name{remarque3.3}) has been already used, duplicate ignored \relax l.342 ...©terminant de $M \in \mc_n(\K)$ $\det M$] ! Undefined control sequence. ...em} {\it Déterminant de $M \in \mc _n(\K )$ $\det M$} l.342 ...©terminant de $M \in \mc_n(\K)$ $\det M$] The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...em} {\it Déterminant de $M \in \mc _n(\K )$ $\det M$}}{\thepa... l.342 ...©terminant de $M \in \mc_n(\K)$ $\det M$] The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \hbox (badness 10000) in paragraph at lines 342--343 [] pdfTeX warning (ext4): destination with the same identifier (name{remarque3.3}) has been already used, duplicate ignored \relax l.349 O n a donc $\det M = \det f_M$ [5pdfTeX warning (ext4): destination with the same identifier (name{section*.23}) has been already used, duplicate ignore d ...shipout:D \box_use:N \l_shipout_box l.357 \end{align*} ] ! Undefined control sequence. l.361 Soit $u\in \lc (E)$ et $\bc$ une base de $E$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \det (\Mat _{\bc } u) &= \det u \\ l.365 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \det (\Mat _{\bc } u) &= \det u \\ l.365 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \hbox (badness 10000) in paragraph at lines 369--369 [] ! Undefined control sequence. \det \Mat _{\bc } u &= \begin {pmatrix} \decomp {u(\epsilon _1)}... l.373 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \det \Mat _{\bc } u &= \begin {pmatrix} \decomp {u(\epsilon _1)}... l.373 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \det \Math _{\bc } u &= \sum _{\sigma \in S_n} \epsilon (\sigma ... l.378 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \det \Math _{\bc } u &= \sum _{\sigma \in S_n} \epsilon (\sigma ... l.378 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. pdfTeX warning (ext4): destination with the same identifier (name{remarque2.3}) has been already used, duplicate ignored \relax l.387 $ \det: \mc_n(\K) \to \K$ est un invariant de similitude [6] ! Undefined control sequence. l.387 $\det: \mc _n(\K) \to \K$ est un invariant de similitude The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. pdfTeX warning (ext4): destination with the same identifier (name{remarque4.3}) has been already used, duplicate ignored \relax l.393 \begin {enumerate} Underfull \hbox (badness 10000) in paragraph at lines 393--393 [] Underfull \hbox (badness 10000) in paragraph at lines 400--400 [] Underfull \hbox (badness 10000) in paragraph at lines 415--415 [] ! Undefined control sequence. l.416 \item Soient $u, v\in \lc (E)$ alors \begin{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.420 \item Soient $M, N\in \mc _n(\K)$ alors \begin{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Underfull \hbox (badness 10000) in paragraph at lines 429--429 [] [7] Underfull \hbox (badness 10000) in paragraph at lines 441--441 [] Underfull \hbox (badness 10000) in paragraph at lines 447--450 [] pdfTeX warning (ext4): destination with the same identifier (name{remarque1.3}) has been already used, duplicate ignored \relax l.459 ...n{exercice}[Déterminant d'une symétrie] ! Undefined control sequence. Exercice \theexercice \hspace {1em} {\it Déterminant d'une symé... l.459 ...n{exercice}[Déterminant d'une symétrie] The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ...ndcsname }\fi Exercice \theexercice \hspace {1em} {\it Déterm... l.459 ...n{exercice}[Déterminant d'une symétrie] The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.460 Soit $s\in \lc (E)$ tel que $s\circ \s = \de_E$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.460 Soit $s\in \lc(E)$ tel que $s\circ \s = \de_E$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.460 ...t $s\in \lc(E)$ tel que $s\circ \s = \de _E$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.479 $E = \Ker (s-\id)\oplus\Ker(s+\id)$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.479 $E = \Ker(s-\id)\oplus\Ker (s+\id)$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \det s &= \det \Mat _{\bc } s \\ &= \det \begin {pmatrix} 1 & \d... l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \Ker l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \Ker l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... {si } \dim \Ker (s + \id ) \in 2\N +1 \\ 1 &\text {sinon} \en... l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \det s &= \det \Mat _{\bc } s \\ &= \det \begin {pmatrix} 1 & \d... l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \Ker l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. \Ker l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. ... {si } \dim \Ker (s + \id ) \in 2\N +1 \\ 1 &\text {sinon} \en... l.489 \end{align*} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. [8]pdfTeX warning (ext4): destination with the same identifier (name{remarque5. 3}) has been already used, duplicate ignored \relax l.493 \begin {enumerate} Underfull \hbox (badness 10000) in paragraph at lines 493--493 [] Underfull \hbox (badness 10000) in paragraph at lines 500--500 [] ! Undefined control sequence. l.515 Soit $M\in \mc _n(\K)$ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. LaTeX Warning: Command \t invalid in math mode on input line 519. LaTeX Warning: Command \t invalid in math mode on input line 519. ! Please use \mathaccent for accents in math mode. \add@accent ... \let \ignorespaces \relax \accent #1 #2\egroup \spacefactor ... l.519 \end{align*} I'm changing \accent to \mathaccent here; wish me luck. (Accents are not the same in formulas as they are in text.) ! Missing { inserted. \edef l.519 \end{align*} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing `I}' now.) ! You can't use `\spacefactor' in math mode. \add@accent ... \accent #1 #2\egroup \spacefactor \accent@spacefactor l.519 \end{align*} Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Missing } inserted. } l.519 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. Missing character: There is no ç in font cmex10! LaTeX Warning: Command \t invalid in math mode on input line 519. LaTeX Warning: Command \t invalid in math mode on input line 519. ! Please use \mathaccent for accents in math mode. \add@accent ... \let \ignorespaces \relax \accent #1 #2\egroup \spacefactor ... l.519 \end{align*} I'm changing \accent to \mathaccent here; wish me luck. (Accents are not the same in formulas as they are in text.) ! Missing { inserted. \edef l.519 \end{align*} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing `I}' now.) ! You can't use `\spacefactor' in math mode. \add@accent ... \accent #1 #2\egroup \spacefactor \accent@spacefactor l.519 \end{align*} Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Missing } inserted. } l.519 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. Missing character: There is no ç in font cmex10! LaTeX Warning: Command \t invalid in math mode on input line 529. LaTeX Warning: Command \t invalid in math mode on input line 529. ! Please use \mathaccent for accents in math mode. \add@accent ... \let \ignorespaces \relax \accent #1 #2\egroup \spacefactor ... l.529 \end{align*} I'm changing \accent to \mathaccent here; wish me luck. (Accents are not the same in formulas as they are in text.) ! Missing { inserted. \edef l.529 \end{align*} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing `I}' now.) ! You can't use `\spacefactor' in math mode. \add@accent ... \accent #1 #2\egroup \spacefactor \accent@spacefactor l.529 \end{align*} Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Missing } inserted. } l.529 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. Missing character: There is no ç in font cmex10! LaTeX Warning: Command \t invalid in math mode on input line 529. LaTeX Warning: Command \t invalid in math mode on input line 529. ! Please use \mathaccent for accents in math mode. \add@accent ... \let \ignorespaces \relax \accent #1 #2\egroup \spacefactor ... l.529 \end{align*} I'm changing \accent to \mathaccent here; wish me luck. (Accents are not the same in formulas as they are in text.) ! Missing { inserted. \edef l.529 \end{align*} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing `I}' now.) ! You can't use `\spacefactor' in math mode. \add@accent ... \accent #1 #2\egroup \spacefactor \accent@spacefactor l.529 \end{align*} Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Missing } inserted. } l.529 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. Missing character: There is no ç in font cmex10! [9] LaTeX Warning: Command \t invalid in math mode on input line 536. LaTeX Warning: Command \t invalid in math mode on input line 536. ! Please use \mathaccent for accents in math mode. \add@accent ... \let \ignorespaces \relax \accent #1 #2\egroup \spacefactor ... l.536 \end{align*} I'm changing \accent to \mathaccent here; wish me luck. (Accents are not the same in formulas as they are in text.) ! Missing { inserted. \edef l.536 \end{align*} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing `I}' now.) ! You can't use `\spacefactor' in math mode. \add@accent ... \accent #1 #2\egroup \spacefactor \accent@spacefactor l.536 \end{align*} Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Missing } inserted. } l.536 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. Missing character: There is no ç in font cmex10! LaTeX Warning: Command \t invalid in math mode on input line 536. LaTeX Warning: Command \t invalid in math mode on input line 536. ! Please use \mathaccent for accents in math mode. \add@accent ... \let \ignorespaces \relax \accent #1 #2\egroup \spacefactor ... l.536 \end{align*} I'm changing \accent to \mathaccent here; wish me luck. (Accents are not the same in formulas as they are in text.) ! Missing { inserted. \edef l.536 \end{align*} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing `I}' now.) ! You can't use `\spacefactor' in math mode. \add@accent ... \accent #1 #2\egroup \spacefactor \accent@spacefactor l.536 \end{align*} Sorry, but I'm not programmed to handle this case; I'll just pretend that you didn't ask for it. If you're in the wrong mode, you might be able to return to the right one by typing `I}' or `I$' or `I\par'. ! Missing } inserted. } l.536 \end{align*} I've put in what seems to be necessary to fix the current column of the current alignment. Try to go on, since this might almost work. Missing character: There is no ç in font cmex10! ! Misplaced \noalign. \hline ->\noalign {\ifnum 0=`}\fi \hrule \@height \arrayrulewidth \futurelet... l.544 Soit $M = \begin{pmatrix} \hline L_1 \hline \\ \vdots \hline L_n \hli... I expect to see \noalign only after the \cr of an alignment. Proceed, and I'll ignore this case. ! Missing $ inserted. $ l.544 Soit $M = \begin{pmatrix} \hline L_1 \hline \\ \vdots \hline L_n \hli... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.544 Soit $M = \begin{pmatrix} \hline L_1 \hline \\ \vdots \hline L_n \hli... I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! You can't use `\hrule' here except with leaders. \hrule l.544 Soit $M = \begin{pmatrix} \hline L_1 \hline \\ \vdots \hline L_n \hli... To put a horizontal rule in an hbox or an alignment, you should use \leaders or \hrulefill (see The TeXbook). ! Missing number, treated as zero. \futurelet l.544 Soit $M = \begin{pmatrix} \hline L_1 \hline \\ \vdots \hline L_n \hli... A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) ! Illegal unit of measure (pt inserted).