This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 17 NOV 2003 11:17 **alg_9.tex (alg_9.tex LaTeX2e <2001/06/01> Babel and hyphenation patterns for american, french, german, ngerman, i talian, nohyphenation, loaded. (/usr/local/share/texmf/tex/latex/base/article.cls Document Class: article 2001/04/21 v1.4e Standard LaTeX document class (/usr/local/share/texmf/tex/latex/base/size10.clo File: size10.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 ) (/usr/local/share/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. (/usr/local/share/texmf/tex/latex/amsmath/amstext.sty Package: amstext 2000/06/29 v2.01 (/usr/local/share/texmf/tex/latex/amsmath/amsgen.sty File: amsgen.sty 1999/11/30 v2.0 \@emptytoks=\toks14 \ex@=\dimen103 )) (/usr/local/share/texmf/tex/latex/amsmath/amsbsy.sty Package: amsbsy 1999/11/29 v1.2d \pmbraise@=\dimen104 ) (/usr/local/share/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. ) (/usr/local/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 2002/01/22 v2.2d (/usr/local/share/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. )) (/usr/local/share/texmf/tex/latex/jknappen/mathrsfs.sty Package: mathrsfs 1996/01/01 Math RSFS package v1.0 (jk) \symrsfs=\mathgroup6 ) No file alg_9.aux. \openout1 = `alg_9.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12. LaTeX Font Info: ... okay on input line 12. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12. 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(/usr/local/share/texmf/tex/latex/jknappen/ursfs.fd File: ursfs.fd 1998/03/24 rsfs font definition file (jk) ) [1 ] [2] Overfull \hbox (7.12335pt too wide) in paragraph at lines 81--90 \OT1/cmr/m/n/10 Then $\OML/cmm/m/it/10 deg f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x \OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 6\OT1/cmr/m/n/10 = 0\OML/cmm/m/it/10 :$ \OT1 /cmr/m/n/10 Then $\OML/cmm/m/it/10 deg f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1 /cmr/m/n/10 ) = \OML/cmm/m/it/10 m \OMS/cmsy/m/n/10 ^^U \OT1/cmr/m/n/10 1;$ let $\OML/cmm/m/it/10 f\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) = [][] \OML/cmm/m/it/10 a[]x[]:$ \OT1/cmr/m/n/10 Then $\OML/cmm/m/it/10 x \OT1/cmr/m/ n/10 = \OML/cmm/m/it/10 f[]\OT1/cmr/m/n/10 ([][] \OML/cmm/m/it/10 a[]x[]\OT1/cm r/m/n/10 ) = [] [3] [4] Overfull \hbox (9.98941pt too wide) in paragraph at lines 124--131 \OT1/cmr/m/n/10 and $\OML/cmm/m/it/10 u \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 R \ OMS/cmsy/m/n/10 ^^C \OML/cmm/m/it/10 :$ \OT1/cmr/m/n/10 Let $\OML/cmm/m/it/10 g \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/10 u[] [][ ]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 uv\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cm r/m/n/10 ))[]\OML/cmm/m/it/10 :$ \OT1/cmr/m/n/10 Then $\OML/cmm/m/it/10 f\OT1/c mr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/10 ug\OT1/cmr/m/n/10 (\OM L/cmm/m/it/10 x\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 v\OT1/cm r/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 g\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ) = [][](\OML/cmm/m/it/10 uv\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 ))[] \OMS/cmsy/m/n/10 ^^@ [] [5] [6] Overfull \hbox (18.94981pt too wide) detected at line 177 \OT1/cmr/m/n/10 (([] \OML/cmm/m/it/10 a[]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 cs[] =s\OT1/cmr/m/n/10 ([](\OML/cmm/m/it/10 a[]p[]\OT1/cmr/m/n/10 )))(\OML/cmm/m/it/ 10 r[]=s[]\OT1/cmr/m/n/10 ) = (\OML/cmm/m/it/10 cp[]s[] []\OT1/cmr/m/n/10 (\OML /cmm/m/it/10 a[]p[]\OT1/cmr/m/n/10 ))\OML/cmm/m/it/10 =\OT1/cmr/m/n/10 (\OML/cm m/m/it/10 ss[] []\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 a[]p[]\OT1/cmr/m/n/10 )) = \ OML/cmm/m/it/10 cp[]=s \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 r=s: [] [7] (alg_9.aux) ) Here is how much of TeX's memory you used: 1128 strings out of 20880 11948 string characters out of 196184 64158 words of memory out of 350001 4101 multiletter control sequences out of 10000+15000 11281 words of font info for 47 fonts, out of 400000 for 1000 14 hyphenation exceptions out of 10000 27i,8n,24p,666b,248s stack positions out of 3000i,100n,1500p,50000b,4000s Output written on alg_9.dvi (7 pages, 41536 bytes).