This is TeX, Version 3.141592 (MiKTeX 2.3) (preloaded format=latex 2000.11.28) 19 MAY 2008 14:45 **srank.tex (srank.tex LaTeX2e <2001/06/01> Babel and hyphenation patterns for english, french, german, ngerman, du mylang, nohyphenation, loaded. (C:\CTeX\texmf\tex\latex\base\article.cls Document Class: article 2001/04/21 v1.4e Standard LaTeX document class (C:\CTeX\texmf\tex\latex\base\size12.clo File: size12.clo 2001/04/21 v1.4e Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (C:\CTeX\texmf\tex\latex\amsmath\amsmath.sty Package: amsmath 2000/07/18 v2.13 AMS math features \@mathmargin=\skip43 For additional information on amsmath, use the `?' option. (C:\CTeX\texmf\tex\latex\amsmath\amstext.sty Package: amstext 2000/06/29 v2.01 (C:\CTeX\texmf\tex\latex\amsmath\amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks14 \ex@=\dimen103 )) (C:\CTeX\texmf\tex\latex\amsmath\amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen104 ) (C:\CTeX\texmf\tex\latex\amsmath\amsopn.sty Package: amsopn 1999/12/14 v2.01 operator names ) \inf@bad=\count87 LaTeX Info: Redefining \frac on input line 211. \uproot@=\count88 \leftroot@=\count89 LaTeX Info: Redefining \overline on input line 307. \classnum@=\count90 \DOTSCASE@=\count91 LaTeX Info: Redefining \ldots on input line 379. LaTeX Info: Redefining \dots on input line 382. LaTeX Info: Redefining \cdots on input line 467. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen105 LaTeX Font Info: Redeclaring font encoding OML on input line 567. LaTeX Font Info: Redeclaring font encoding OMS on input line 568. \macc@depth=\count92 \c@MaxMatrixCols=\count93 \dotsspace@=\muskip10 \c@parentequation=\count94 \dspbrk@lvl=\count95 \tag@help=\toks15 \row@=\count96 \column@=\count97 \maxfields@=\count98 \andhelp@=\toks16 \eqnshift@=\dimen106 \alignsep@=\dimen107 \tagshift@=\dimen108 \tagwidth@=\dimen109 \totwidth@=\dimen110 \lineht@=\dimen111 \@envbody=\toks17 \multlinegap=\skip44 \multlinetaggap=\skip45 \mathdisplay@stack=\toks18 LaTeX Info: Redefining \[ on input line 2666. LaTeX Info: Redefining \] on input line 2667. ) (C:\CTeX\texmf\tex\latex\amsfonts\amsfonts.sty Package: amsfonts 2001/10/25 v2.2f \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 132. ) (C:\CTeX\texmf\tex\latex\amsfonts\amssymb.sty Package: amssymb 2002/01/22 v2.2d ) \c@thm=\count99 (srank.aux) LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 21. LaTeX Font Info: ... okay on input line 21. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 21. LaTeX Font Info: ... okay on input line 21. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 21. LaTeX Font Info: ... okay on input line 21. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 21. LaTeX Font Info: ... okay on input line 21. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 21. LaTeX Font Info: ... okay on input line 21. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 21. LaTeX Font Info: ... okay on input line 21. LaTeX Font Info: Try loading font information for U+msa on input line 24. (C:\CTeX\texmf\tex\latex\amsfonts\umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 24. (C:\CTeX\texmf\tex\latex\amsfonts\umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) [1 ] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] Overfull \hbox (3.31374pt too wide) in paragraph at lines 1042--1044 [][]\OT1/cmr/m/it/12 if $\OML/cmm/m/it/12 m \OT1/cmr/m/n/12 + \OML/cmm/m/it/12 n$ \OT1/cmr/m/it/12 is odd, we have $\OML/cmm/m/it/12 Q[] \OT1/cmr/m/n/12 = []( \OML/cmm/m/it/12 M\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 ; []\OT1/cmr/m/n/12 ))$\O T1/cmr/m/it/12 , where $\OML/cmm/m/it/12 [] \OT1/cmr/m/n/12 = (\OML/cmm/m/it/1 2 []; [] ; []; \OT1/cmr/m/n/12 0)$\OT1/cmr/m/it/12 . [] [15] LaTeX Font Warning: Command \tiny invalid in math mode on input line 1126. Package amsmath Warning: Foreign command \atop; (amsmath) \frac or \genfrac should be used instead (amsmath) on input line 1126. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1127. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1138. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1139. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1140. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1141. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1149. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1151. [16] LaTeX Font Warning: Command \tiny invalid in math mode on input line 1202. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1204. [17] LaTeX Font Warning: Command \tiny invalid in math mode on input line 1255. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1257. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1274. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1276. [18] LaTeX Font Warning: Command \tiny invalid in math mode on input line 1326. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1328. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1380. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1382. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1384. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1385. [19] LaTeX Font Warning: Command \tiny invalid in math mode on input line 1406. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1407. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1409. LaTeX Font Warning: Command \tiny invalid in math mode on input line 1410. 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[20] [21] [22] [23] [24] Underfull \hbox (badness 10000) in paragraph at lines 1779--1780 [][]\OT1/cmr/m/n/12 J. R. Stem-bridge, The SF Pack-age for Maple, [] [25] (srank.aux) ) Here is how much of TeX's memory you used: 1261 strings out of 96052 12671 string characters out of 1197040 65324 words of memory out of 1061334 4189 multiletter control sequences out of 35000 14225 words of font info for 55 fonts, out of 500000 for 1000 14 hyphenation exceptions out of 607 27i,10n,22p,201b,293s stack positions out of 1500i,500n,5000p,200000b,32768s Output written on srank.dvi (25 pages, 105372 bytes).