This is TeX, Version 3.14159 (Web2C 7.3) (format=latex 1999.4.5) 23 AUG 1999 01:40 **luis (luis.tex LaTeX2e <1998/12/01> Babel and hyphenation patterns for american, french, german, ngerman, n ohyphenation, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 1999/01/07 v1.4a Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo File: size12.clo 1999/01/07 v1.4a 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/share/texmf/tex/latex/amsfonts/amsfonts.sty Package: amsfonts 1997/09/17 v2.2e \@emptytoks=\toks14 \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 133. ) (/usr/share/texmf/tex/latex/amsfonts/amssymb.sty Package: amssymb 1996/11/03 v2.2b ) \c@teo=\count87 \c@tea=\count88 LaTeX Warning: Unused global option(s): [thmsa]. (luis.aux) \openout1 = `luis.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 51. LaTeX Font Info: ... okay on input line 51. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 51. LaTeX Font Info: ... okay on input line 51. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 51. LaTeX Font Info: ... okay on input line 51. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 51. LaTeX Font Info: ... okay on input line 51. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 51. LaTeX Font Info: ... okay on input line 51. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 51. LaTeX Font Info: ... okay on input line 51. LaTeX Font Info: Try loading font information for U+msa on input line 53. (/usr/share/texmf/tex/latex/amsfonts/umsa.fd File: umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 53. (/usr/share/texmf/tex/latex/amsfonts/umsb.fd File: umsb.fd 1995/01/05 v2.2e AMS font definitions ) [1 ] Underfull \hbox (badness 10000) in paragraph at lines 92--106 [] [2] Underfull \hbox (badness 10000) in paragraph at lines 186--194 [] [3] Overfull \hbox (4.35623pt too wide) in paragraph at lines 230--241 \OT1/cmr/m/n/12 >From the last for-mu-la we see that: $\OML/cmm/m/it/12 m[] \OT 1/cmr/m/n/12 + \OML/cmm/m/it/12 m[] \OMS/cmsy/m/n/12 ^^Q \OT1/cmr/m/n/12 1([] \OML/cmm/m/it/12 ` \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 1)$ and $\OML/cmm/m/it/ 12 ^^O[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 p\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ^^ O[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 p\OT1/cmr/m/n/12 ) = [] Underfull \hbox (badness 10000) in paragraph at lines 262--268 [] Underfull \hbox (badness 10000) in paragraph at lines 269--272 [] [4] Package amsfonts Warning: Obsolete command \frak; \mathfrak should be used inst ead on input line 280. LaTeX Font Info: Try loading font information for U+euf on input line 280. (/usr/share/texmf/tex/latex/amsfonts/ueuf.fd File: ueuf.fd 1995/01/05 v2.2e AMS font definitions ) Underfull \hbox (badness 10000) in paragraph at lines 296--300 [] Underfull \hbox (badness 10000) in paragraph at lines 311--323 [] Underfull \hbox (badness 10000) in paragraph at lines 324--327 [] [5] Underfull \hbox (badness 10000) in paragraph at lines 372--376 [] Underfull \hbox (badness 10000) in paragraph at lines 378--379 [] Underfull \hbox (badness 10000) in paragraph at lines 382--392 [] [6] Underfull \hbox (badness 10000) in paragraph at lines 408--413 [] LaTeX Font Info: Try loading font information for OMS+cmr on input line 415. (/usr/share/texmf/tex/latex/base/omscmr.fd File: omscmr.fd 1998/03/27 v2.5g Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 415. Underfull \hbox (badness 10000) in paragraph at lines 435--438 [] Underfull \hbox (badness 10000) in paragraph at lines 439--442 [] [7] Underfull \hbox (badness 10000) in paragraph at lines 491--505 [] [8] Underfull \hbox (badness 10000) in paragraph at lines 508--512 [] [9] Overfull \hbox (58.80428pt too wide) in paragraph at lines 531--556 [][] [] Underfull \hbox (badness 10000) in paragraph at lines 531--556 [] Underfull \hbox (badness 10000) in paragraph at lines 531--556 [] Overfull \hbox (0.33752pt too wide) in paragraph at lines 559--584 [][] [] Underfull \hbox (badness 10000) in paragraph at lines 559--584 [] Underfull \hbox (badness 10000) in paragraph at lines 559--584 [] [10] Underfull \hbox (badness 10000) in paragraph at lines 617--638 [] Underfull \hbox (badness 10000) in paragraph at lines 640--658 [] [11] Underfull \hbox (badness 10000) in paragraph at lines 689--692 [] Underfull \hbox (badness 10000) in paragraph at lines 693--699 [] [12] Overfull \hbox (20.40399pt too wide) in paragraph at lines 732--732 []\OT1/cmr/bx/n/17.28 Three ex-am-ples de-signed to re-al-ize $\OML/cmm/m/it/17 .28 PGL\OT1/cmr/m/n/17.28 (2\OML/cmm/m/it/17.28 ; \U/msb/m/n/17.28 F[]\OT1/cmr/ m/n/17.28 )$ [] Underfull \hbox (badness 10000) in paragraph at lines 752--759 [] Underfull \hbox (badness 10000) in paragraph at lines 761--767 [] [13] Underfull \hbox (badness 10000) in paragraph at lines 775--781 [] Underfull \hbox (badness 10000) in paragraph at lines 789--796 [] Overfull \hbox (15.71977pt too wide) detected at line 804 \OML/cmm/m/it/12 A[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ) = \OML /cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 9\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \ OT1/cmr/m/n/12 222\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 459 \OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 2133\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 7362\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 9045\OML/cmm/m /it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 55485\OML/cmm/m/it/12 x[] [] Underfull \hbox (badness 10000) in paragraph at lines 808--810 [] [14] Overfull \hbox (27.27509pt too wide) detected at line 814 \OML/cmm/m/it/12 A[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ) = \OML /cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 18\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 81\ OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 399\OML/cmm/m/it/12 x[ ] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 4347\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/1 2 ^^@ \OT1/cmr/m/n/12 4077\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 72270\OML/cmm/ m/it/12 x[] \OT1/cmr/m/n/12 + 216621\OML/cmm/m/it/12 x[] [] Overfull \hbox (35.79608pt too wide) detected at line 815 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 480411\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 2883570\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/ m/n/12 56565\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 19123614\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 20821662\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m /n/12 67078422\OML/cmm/m/it/12 x[] [] Overfull \hbox (12.21588pt too wide) detected at line 816 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 137250288\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/ 12 + 98869950\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 423746154\OML/cmm/m/it/12 x [] \OT1/cmr/m/n/12 + 82935981\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr /m/n/12 662094576\OML/cmm/m/it/12 x[] [] Overfull \hbox (1.09058pt too wide) detected at line 817 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 503302086\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/ 12 + 423203940\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 625539429\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 37164501\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cm r/m/n/12 254848680\OML/cmm/m/it/12 x[] [] Underfull \hbox (badness 10000) in paragraph at lines 817--819 [] Underfull \hbox (badness 10000) in paragraph at lines 820--827 [] Underfull \hbox (badness 10000) in paragraph at lines 828--831 [] Overfull \hbox (74.0937pt too wide) in paragraph at lines 832--840 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 3839798343339\OML/cmm/m/it/12 x[] \OMS/cmsy /m/n/12 ^^@ \OT1/cmr/m/n/12 72574129126800\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 322522524201888\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 5072 75006736879\OML/cmm/m/it/12 x[]$ [] Overfull \hbox (13.44443pt too wide) in paragraph at lines 832--840 \OT1/cmr/m/n/12 +11881100841555393\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 508801 36840412436\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 32267290657623723\OML/cmm/m/i t/12 x[]$ [] Overfull \hbox (30.65263pt too wide) in paragraph at lines 832--840 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 583118269440460587\OML/cmm/m/it/12 x[] \OMS /cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 2803147835818522302\OML/cmm/m/it/12 x[] \OMS/c msy/m/n/12 ^^@ \OT1/cmr/m/n/12 6056528831138196135\OML/cmm/m/it/12 x[]$ [] Overfull \hbox (42.01338pt too wide) in paragraph at lines 832--840 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 5328052040331553149\OML/cmm/m/it/12 x[] \OT 1/cmr/m/n/12 + 4040855350703314974\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 143648 03283290718444\OML/cmm/m/it/12 x[]$ [] Overfull \hbox (31.38838pt too wide) in paragraph at lines 832--840 \OT1/cmr/m/n/12 +11649146213084963013\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 205 986024736020486\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 386323 2567933946101\OML/cmm/m/it/12 x$ [] Underfull \hbox (badness 10000) in paragraph at lines 832--840 [] Underfull \hbox (badness 10000) in paragraph at lines 841--842 [] Overfull \hbox (21.02469pt too wide) in paragraph at lines 843--851 \OT1/cmr/m/n/12 +21785693796\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/ m/n/12 42415128438\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 214 9133334543\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 3249157564620\OML/cmm/m/it/12 x[]$ [] Overfull \hbox (13.44443pt too wide) in paragraph at lines 843--851 \OT1/cmr/m/n/12 +286365050094708\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 17414664 7974621273\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 137088225897636096\OML/cmm/m/i t/12 x[]$ [] Overfull \hbox (42.20795pt too wide) in paragraph at lines 843--851 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 3067205587844711523\OML/cmm/m/it/12 x[] \OM S/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 4979500588408020255\OML/cmm/m/it/12 x[] \OT1/ cmr/m/n/12 + 29948677258338999450\OML/cmm/m/it/12 x[]$ [] Overfull \hbox (65.7077pt too wide) in paragraph at lines 843--851 \OT1/cmr/m/n/12 +76790301210845625861\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 119349417294626396391\OML/cmm/m/it/12 x[] \OMS/cmsy/m/n/12 ^^@ \OT1/cmr/m/n/12 535760443536103781838\OML/cmm/m/it/12 x[]$ [] Overfull \hbox (78.3879pt too wide) in paragraph at lines 843--851 \OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 167198875027467682545\OML/cmm/m/it/12 x[] \ OT1/cmr/m/n/12 + 1273594079757375456489\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + 1 827054356350586351796\OML/cmm/m/it/12 x$ [] Underfull \hbox (badness 10000) in paragraph at lines 843--851 [] [15] Underfull \hbox (badness 10000) in paragraph at lines 852--857 [] Overfull \hbox (0.46875pt too wide) in paragraph at lines 892--907 \OT1/cmr/m/n/12 We com-put-ed the primes $\OML/cmm/m/it/12 ` \OMS/cmsy/m/n/12 ^ ^U \OT1/cmr/m/n/12 5$ up to $500000$ such that the group-s $\OML/cmm/m/it/12 PG L\OT1/cmr/m/n/12 (2\OML/cmm/m/it/12 ; \U/msb/m/n/12 F[]\OT1/cmr/m/n/12 )$ [] Underfull \hbox (badness 10000) in paragraph at lines 892--907 [] [16] Underfull \hbox (badness 10000) in paragraph at lines 908--916 [] [17] [18] (luis.aux) ) Here is how much of TeX's memory you used: 671 strings out of 10898 6833 string characters out of 72048 53463 words of memory out of 263001 3630 multiletter control sequences out of 10000+0 18789 words of font info for 73 fonts, out of 200000 for 1000 15 hyphenation exceptions out of 1000 30i,11n,22p,175b,325s stack positions out of 300i,100n,500p,30000b,4000s Output written on luis.dvi (18 pages, 52852 bytes).