302 lines
10 KiB
Plaintext
302 lines
10 KiB
Plaintext
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.5.23) 21 JUN 2026 21:25
|
|
entering extended mode
|
|
restricted \write18 enabled.
|
|
%&-line parsing enabled.
|
|
**hausaufgabe_10_loesung.tex
|
|
(./hausaufgabe_10_loesung.tex
|
|
LaTeX2e <2023-11-01> patch level 1
|
|
L3 programming layer <2024-01-22>
|
|
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
|
|
Document Class: article 2023/05/17 v1.4n Standard LaTeX document class
|
|
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo
|
|
File: size12.clo 2023/05/17 v1.4n Standard LaTeX file (size option)
|
|
)
|
|
\c@part=\count187
|
|
\c@section=\count188
|
|
\c@subsection=\count189
|
|
\c@subsubsection=\count190
|
|
\c@paragraph=\count191
|
|
\c@subparagraph=\count192
|
|
\c@figure=\count193
|
|
\c@table=\count194
|
|
\abovecaptionskip=\skip48
|
|
\belowcaptionskip=\skip49
|
|
\bibindent=\dimen140
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty
|
|
Package: inputenc 2021/02/14 v1.3d Input encoding file
|
|
\inpenc@prehook=\toks17
|
|
\inpenc@posthook=\toks18
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty
|
|
Package: fontenc 2021/04/29 v2.0v Standard LaTeX package
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/generic/babel/babel.sty
|
|
Package: babel 2024/01/07 v24.1 The Babel package
|
|
\babel@savecnt=\count195
|
|
\U@D=\dimen141
|
|
\l@unhyphenated=\language5
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/generic/babel/txtbabel.def)
|
|
\bbl@readstream=\read2
|
|
\bbl@dirlevel=\count196
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/generic/babel/locale/de/babel-ngerman.tex)
|
|
Package babel Info: Importing data for ngerman
|
|
(babel) from babel-de.ini. Reported on input line 4318.
|
|
Package babel Info: Hyphen rules for 'ngerman' set to \l@english
|
|
(babel) (\language0). Reported on input line 4318.
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
|
|
Package: amsmath 2023/05/13 v2.17o AMS math features
|
|
\@mathmargin=\skip50
|
|
|
|
For additional information on amsmath, use the `?' option.
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
|
|
Package: amstext 2021/08/26 v2.01 AMS text
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty
|
|
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
|
\@emptytoks=\toks19
|
|
\ex@=\dimen142
|
|
))
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty
|
|
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
|
\pmbraise@=\dimen143
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty
|
|
Package: amsopn 2022/04/08 v2.04 operator names
|
|
)
|
|
\inf@bad=\count197
|
|
LaTeX Info: Redefining \frac on input line 234.
|
|
\uproot@=\count198
|
|
\leftroot@=\count199
|
|
LaTeX Info: Redefining \overline on input line 399.
|
|
LaTeX Info: Redefining \colon on input line 410.
|
|
\classnum@=\count266
|
|
\DOTSCASE@=\count267
|
|
LaTeX Info: Redefining \ldots on input line 496.
|
|
LaTeX Info: Redefining \dots on input line 499.
|
|
LaTeX Info: Redefining \cdots on input line 620.
|
|
\Mathstrutbox@=\box51
|
|
\strutbox@=\box52
|
|
LaTeX Info: Redefining \big on input line 722.
|
|
LaTeX Info: Redefining \Big on input line 723.
|
|
LaTeX Info: Redefining \bigg on input line 724.
|
|
LaTeX Info: Redefining \Bigg on input line 725.
|
|
\big@size=\dimen144
|
|
LaTeX Font Info: Redeclaring font encoding OML on input line 743.
|
|
LaTeX Font Info: Redeclaring font encoding OMS on input line 744.
|
|
\macc@depth=\count268
|
|
LaTeX Info: Redefining \bmod on input line 905.
|
|
LaTeX Info: Redefining \pmod on input line 910.
|
|
LaTeX Info: Redefining \smash on input line 940.
|
|
LaTeX Info: Redefining \relbar on input line 970.
|
|
LaTeX Info: Redefining \Relbar on input line 971.
|
|
\c@MaxMatrixCols=\count269
|
|
\dotsspace@=\muskip16
|
|
\c@parentequation=\count270
|
|
\dspbrk@lvl=\count271
|
|
\tag@help=\toks20
|
|
\row@=\count272
|
|
\column@=\count273
|
|
\maxfields@=\count274
|
|
\andhelp@=\toks21
|
|
\eqnshift@=\dimen145
|
|
\alignsep@=\dimen146
|
|
\tagshift@=\dimen147
|
|
\tagwidth@=\dimen148
|
|
\totwidth@=\dimen149
|
|
\lineht@=\dimen150
|
|
\@envbody=\toks22
|
|
\multlinegap=\skip51
|
|
\multlinetaggap=\skip52
|
|
\mathdisplay@stack=\toks23
|
|
LaTeX Info: Redefining \[ on input line 2953.
|
|
LaTeX Info: Redefining \] on input line 2954.
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
|
|
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty
|
|
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
|
|
\symAMSa=\mathgroup4
|
|
\symAMSb=\mathgroup5
|
|
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
|
|
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
|
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
|
|
))
|
|
(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty
|
|
Package: geometry 2020/01/02 v5.9 Page Geometry
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty
|
|
Package: keyval 2022/05/29 v1.15 key=value parser (DPC)
|
|
\KV@toks@=\toks24
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/generic/iftex/ifvtex.sty
|
|
Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. Use iftex instead.
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/generic/iftex/iftex.sty
|
|
Package: iftex 2022/02/03 v1.0f TeX engine tests
|
|
))
|
|
\Gm@cnth=\count275
|
|
\Gm@cntv=\count276
|
|
\c@Gm@tempcnt=\count277
|
|
\Gm@bindingoffset=\dimen151
|
|
\Gm@wd@mp=\dimen152
|
|
\Gm@odd@mp=\dimen153
|
|
\Gm@even@mp=\dimen154
|
|
\Gm@layoutwidth=\dimen155
|
|
\Gm@layoutheight=\dimen156
|
|
\Gm@layouthoffset=\dimen157
|
|
\Gm@layoutvoffset=\dimen158
|
|
\Gm@dimlist=\toks25
|
|
)
|
|
(/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
|
|
File: l3backend-pdftex.def 2024-01-04 L3 backend support: PDF output (pdfTeX)
|
|
\l__color_backend_stack_int=\count278
|
|
\l__pdf_internal_box=\box53
|
|
)
|
|
(./hausaufgabe_10_loesung.aux)
|
|
\openout1 = `hausaufgabe_10_loesung.aux'.
|
|
|
|
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 14.
|
|
LaTeX Font Info: ... okay on input line 14.
|
|
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 14.
|
|
LaTeX Font Info: ... okay on input line 14.
|
|
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 14.
|
|
LaTeX Font Info: ... okay on input line 14.
|
|
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 14.
|
|
LaTeX Font Info: ... okay on input line 14.
|
|
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 14.
|
|
LaTeX Font Info: ... okay on input line 14.
|
|
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 14.
|
|
LaTeX Font Info: ... okay on input line 14.
|
|
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 14.
|
|
LaTeX Font Info: ... okay on input line 14.
|
|
|
|
*geometry* driver: auto-detecting
|
|
*geometry* detected driver: pdftex
|
|
*geometry* verbose mode - [ preamble ] result:
|
|
* driver: pdftex
|
|
* paper: a4paper
|
|
* layout: <same size as paper>
|
|
* layoutoffset:(h,v)=(0.0pt,0.0pt)
|
|
* modes:
|
|
* h-part:(L,W,R)=(71.13188pt, 455.24411pt, 71.13188pt)
|
|
* v-part:(T,H,B)=(71.13188pt, 702.78308pt, 71.13188pt)
|
|
* \paperwidth=597.50787pt
|
|
* \paperheight=845.04684pt
|
|
* \textwidth=455.24411pt
|
|
* \textheight=702.78308pt
|
|
* \oddsidemargin=-1.1381pt
|
|
* \evensidemargin=-1.1381pt
|
|
* \topmargin=-38.1381pt
|
|
* \headheight=12.0pt
|
|
* \headsep=25.0pt
|
|
* \topskip=12.0pt
|
|
* \footskip=30.0pt
|
|
* \marginparwidth=44.0pt
|
|
* \marginparsep=10.0pt
|
|
* \columnsep=10.0pt
|
|
* \skip\footins=10.8pt plus 4.0pt minus 2.0pt
|
|
* \hoffset=0.0pt
|
|
* \voffset=0.0pt
|
|
* \mag=1000
|
|
* \@twocolumnfalse
|
|
* \@twosidefalse
|
|
* \@mparswitchfalse
|
|
* \@reversemarginfalse
|
|
* (1in=72.27pt=25.4mm, 1cm=28.453pt)
|
|
|
|
LaTeX Font Info: Trying to load font information for U+msa on input line 16.
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd
|
|
File: umsa.fd 2013/01/14 v3.01 AMS symbols A
|
|
)
|
|
LaTeX Font Info: Trying to load font information for U+msb on input line 16.
|
|
|
|
|
|
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
|
|
File: umsb.fd 2013/01/14 v3.01 AMS symbols B
|
|
)
|
|
Underfull \hbox (badness 10000) in paragraph at lines 26--28
|
|
|
|
[]
|
|
|
|
[1
|
|
|
|
{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]
|
|
Underfull \hbox (badness 10000) in paragraph at lines 61--63
|
|
|
|
[]
|
|
|
|
|
|
Overfull \hbox (82.47255pt too wide) in paragraph at lines 65--67
|
|
[]\T1/cmr/m/n/12 Da $\OML/cmm/m/it/12 FEEDBACKVERTEXSET \OMS/cmsy/m/n/12 2 \OML
|
|
/cmm/m/it/12 NP$ \T1/cmr/m/n/12 und NP-schwer ist, fol-gt dass $\OML/cmm/m/it/1
|
|
2 FEEDBACKVERTEXSET$
|
|
[]
|
|
|
|
[2]
|
|
Underfull \hbox (badness 10000) in paragraph at lines 74--75
|
|
|
|
[]
|
|
|
|
|
|
Underfull \hbox (badness 10000) in paragraph at lines 85--87
|
|
|
|
[]
|
|
|
|
|
|
Underfull \hbox (badness 10000) in paragraph at lines 94--97
|
|
|
|
[]
|
|
|
|
|
|
Underfull \hbox (badness 10000) in paragraph at lines 126--128
|
|
|
|
[]
|
|
|
|
[3]
|
|
Overfull \hbox (45.38948pt too wide) in paragraph at lines 130--132
|
|
[]\T1/cmr/m/n/12 Da $\OML/cmm/m/it/12 k[]CLIQUEUNIVERSAL \OMS/cmsy/m/n/12 2 \OM
|
|
L/cmm/m/it/12 NP$ \T1/cmr/m/n/12 und NP-schwer ist, fol-gt dass $\OML/cmm/m/it/
|
|
12 k[]CLIQUEUNIVERSAL$
|
|
[]
|
|
|
|
[4] (./hausaufgabe_10_loesung.aux)
|
|
***********
|
|
LaTeX2e <2023-11-01> patch level 1
|
|
L3 programming layer <2024-01-22>
|
|
***********
|
|
)
|
|
Here is how much of TeX's memory you used:
|
|
3692 strings out of 476182
|
|
56686 string characters out of 5795595
|
|
1933975 words of memory out of 5000000
|
|
25689 multiletter control sequences out of 15000+600000
|
|
572580 words of font info for 75 fonts, out of 8000000 for 9000
|
|
14 hyphenation exceptions out of 8191
|
|
57i,8n,65p,250b,447s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
|
</home/arbeit/.texlive2023/texmf-var/fonts/pk/ljfour/jknappen/ec/tcrm1200.60
|
|
0pk> </home/arbeit/.texlive2023/texmf-var/fonts/pk/ljfour/jknappen/ec/ecbx1200.
|
|
600pk> </home/arbeit/.texlive2023/texmf-var/fonts/pk/ljfour/jknappen/ec/ecrm120
|
|
0.600pk> </home/arbeit/.texlive2023/texmf-var/fonts/pk/ljfour/jknappen/ec/ecbx1
|
|
440.600pk> </home/arbeit/.texlive2023/texmf-var/fonts/pk/ljfour/jknappen/ec/ecb
|
|
x1728.600pk> </home/arbeit/.texlive2023/texmf-var/fonts/pk/ljfour/jknappen/ec/e
|
|
crm1440.600pk> </home/arbeit/.texlive2023/texmf-var/fonts/pk/ljfour/jknappen/ec
|
|
/ecrm2074.600pk></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/c
|
|
mmi12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.p
|
|
fb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr
|
|
/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share
|
|
/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/share/texliv
|
|
e/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb>
|
|
Output written on hausaufgabe_10_loesung.pdf (4 pages, 116624 bytes).
|
|
PDF statistics:
|
|
240 PDF objects out of 1000 (max. 8388607)
|
|
56 compressed objects within 1 object stream
|
|
0 named destinations out of 1000 (max. 500000)
|
|
1 words of extra memory for PDF output out of 10000 (max. 10000000)
|
|
|