init

lernmaterial/loesung_probeklausur2.log

@@ -0,0 +1,709 @@
+This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.5.23)  19 JUL 2026 22:22
+entering extended mode
+ restricted \write18 enabled.
+ %&-line parsing enabled.
+**loesung_probeklausur2.tex
+(./loesung_probeklausur2.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/size11.clo
+File: size11.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/fontenc.sty
+Package: fontenc 2021/04/29 v2.0v Standard LaTeX package
+)
+(/usr/share/texmf/tex/latex/lm/lmodern.sty
+Package: lmodern 2015/05/01 v1.6.1 Latin Modern Fonts
+LaTeX Font Info:    Overwriting symbol font `operators' in version `normal'
+(Font)                  OT1/cmr/m/n --> OT1/lmr/m/n on input line 22.
+LaTeX Font Info:    Overwriting symbol font `letters' in version `normal'
+(Font)                  OML/cmm/m/it --> OML/lmm/m/it on input line 23.
+LaTeX Font Info:    Overwriting symbol font `symbols' in version `normal'
+(Font)                  OMS/cmsy/m/n --> OMS/lmsy/m/n on input line 24.
+LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `normal'
+(Font)                  OMX/cmex/m/n --> OMX/lmex/m/n on input line 25.
+LaTeX Font Info:    Overwriting symbol font `operators' in version `bold'
+(Font)                  OT1/cmr/bx/n --> OT1/lmr/bx/n on input line 26.
+LaTeX Font Info:    Overwriting symbol font `letters' in version `bold'
+(Font)                  OML/cmm/b/it --> OML/lmm/b/it on input line 27.
+LaTeX Font Info:    Overwriting symbol font `symbols' in version `bold'
+(Font)                  OMS/cmsy/b/n --> OMS/lmsy/b/n on input line 28.
+LaTeX Font Info:    Overwriting symbol font `largesymbols' in version `bold'
+(Font)                  OMX/cmex/m/n --> OMX/lmex/m/n on input line 29.
+LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `normal'
+(Font)                  OT1/cmr/bx/n --> OT1/lmr/bx/n on input line 31.
+LaTeX Font Info:    Overwriting math alphabet `\mathsf' in version `normal'
+(Font)                  OT1/cmss/m/n --> OT1/lmss/m/n on input line 32.
+LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `normal'
+(Font)                  OT1/cmr/m/it --> OT1/lmr/m/it on input line 33.
+LaTeX Font Info:    Overwriting math alphabet `\mathtt' in version `normal'
+(Font)                  OT1/cmtt/m/n --> OT1/lmtt/m/n on input line 34.
+LaTeX Font Info:    Overwriting math alphabet `\mathbf' in version `bold'
+(Font)                  OT1/cmr/bx/n --> OT1/lmr/bx/n on input line 35.
+LaTeX Font Info:    Overwriting math alphabet `\mathsf' in version `bold'
+(Font)                  OT1/cmss/bx/n --> OT1/lmss/bx/n on input line 36.
+LaTeX Font Info:    Overwriting math alphabet `\mathit' in version `bold'
+(Font)                  OT1/cmr/bx/it --> OT1/lmr/bx/it on input line 37.
+LaTeX Font Info:    Overwriting math alphabet `\mathtt' in version `bold'
+(Font)                  OT1/cmtt/m/n --> OT1/lmtt/m/n on input line 38.
+)
+(/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/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@=\toks19
+)
+(/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=\count195
+\Gm@cntv=\count196
+\c@Gm@tempcnt=\count197
+\Gm@bindingoffset=\dimen141
+\Gm@wd@mp=\dimen142
+\Gm@odd@mp=\dimen143
+\Gm@even@mp=\dimen144
+\Gm@layoutwidth=\dimen145
+\Gm@layoutheight=\dimen146
+\Gm@layouthoffset=\dimen147
+\Gm@layoutvoffset=\dimen148
+\Gm@dimlist=\toks20
+)
+(/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=\toks21
+\ex@=\dimen149
+))
+(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty
+Package: amsbsy 1999/11/29 v1.2d Bold Symbols
+\pmbraise@=\dimen150
+)
+(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty
+Package: amsopn 2022/04/08 v2.04 operator names
+)
+\inf@bad=\count198
+LaTeX Info: Redefining \frac on input line 234.
+\uproot@=\count199
+\leftroot@=\count266
+LaTeX Info: Redefining \overline on input line 399.
+LaTeX Info: Redefining \colon on input line 410.
+\classnum@=\count267
+\DOTSCASE@=\count268
+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=\dimen151
+LaTeX Font Info:    Redeclaring font encoding OML on input line 743.
+LaTeX Font Info:    Redeclaring font encoding OMS on input line 744.
+\macc@depth=\count269
+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=\count270
+\dotsspace@=\muskip16
+\c@parentequation=\count271
+\dspbrk@lvl=\count272
+\tag@help=\toks22
+\row@=\count273
+\column@=\count274
+\maxfields@=\count275
+\andhelp@=\toks23
+\eqnshift@=\dimen152
+\alignsep@=\dimen153
+\tagshift@=\dimen154
+\tagwidth@=\dimen155
+\totwidth@=\dimen156
+\lineht@=\dimen157
+\@envbody=\toks24
+\multlinegap=\skip51
+\multlinetaggap=\skip52
+\mathdisplay@stack=\toks25
+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/xcolor/xcolor.sty
+Package: xcolor 2023/11/15 v3.01 LaTeX color extensions (UK)
+
+(/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg
+File: color.cfg 2016/01/02 v1.6 sample color configuration
+)
+Package xcolor Info: Driver file: pdftex.def on input line 274.
+
+(/usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def
+File: pdftex.def 2022/09/22 v1.2b Graphics/color driver for pdftex
+)
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/mathcolor.ltx)
+Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1350.
+Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1354.
+Package xcolor Info: Model `RGB' extended on input line 1366.
+Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1368.
+Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1369.
+Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1370.
+Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1371.
+Package xcolor Info: Model `Gray' substituted by `gray' on input line 1372.
+Package xcolor Info: Model `wave' substituted by `hsb' on input line 1373.
+)
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex
+\pgfutil@everybye=\toks26
+\pgfutil@tempdima=\dimen158
+\pgfutil@tempdimb=\dimen159
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def
+\pgfutil@abb=\box53
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/pgf.revision.tex)
+Package: pgfrcs 2023-01-15 v3.1.10 (3.1.10)
+))
+Package: pgf 2023-01-15 v3.1.10 (3.1.10)
+
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty
+Package: graphicx 2021/09/16 v1.2d Enhanced LaTeX Graphics (DPC,SPQR)
+
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty
+Package: graphics 2022/03/10 v1.4e Standard LaTeX Graphics (DPC,SPQR)
+
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty
+Package: trig 2021/08/11 v1.11 sin cos tan (DPC)
+)
+(/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg
+File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
+)
+Package graphics Info: Driver file: pdftex.def on input line 107.
+)
+\Gin@req@height=\dimen160
+\Gin@req@width=\dimen161
+)
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex
+Package: pgfsys 2023-01-15 v3.1.10 (3.1.10)
+
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex
+\pgfkeys@pathtoks=\toks27
+\pgfkeys@temptoks=\toks28
+
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeyslibraryfiltered
+.code.tex
+\pgfkeys@tmptoks=\toks29
+))
+\pgf@x=\dimen162
+\pgf@y=\dimen163
+\pgf@xa=\dimen164
+\pgf@ya=\dimen165
+\pgf@xb=\dimen166
+\pgf@yb=\dimen167
+\pgf@xc=\dimen168
+\pgf@yc=\dimen169
+\pgf@xd=\dimen170
+\pgf@yd=\dimen171
+\w@pgf@writea=\write3
+\r@pgf@reada=\read2
+\c@pgf@counta=\count276
+\c@pgf@countb=\count277
+\c@pgf@countc=\count278
+\c@pgf@countd=\count279
+\t@pgf@toka=\toks30
+\t@pgf@tokb=\toks31
+\t@pgf@tokc=\toks32
+\pgf@sys@id@count=\count280
+ (/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg
+File: pgf.cfg 2023-01-15 v3.1.10 (3.1.10)
+)
+Driver file for pgf: pgfsys-pdftex.def
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def
+File: pgfsys-pdftex.def 2023-01-15 v3.1.10 (3.1.10)
+
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.de
+f
+File: pgfsys-common-pdf.def 2023-01-15 v3.1.10 (3.1.10)
+)))
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.
+tex
+File: pgfsyssoftpath.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgfsyssoftpath@smallbuffer@items=\count281
+\pgfsyssoftpath@bigbuffer@items=\count282
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.
+tex
+File: pgfsysprotocol.code.tex 2023-01-15 v3.1.10 (3.1.10)
+))
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex
+Package: pgfcore 2023-01-15 v3.1.10 (3.1.10)
+
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
+\pgfmath@dimen=\dimen172
+\pgfmath@count=\count283
+\pgfmath@box=\box54
+\pgfmath@toks=\toks33
+\pgfmath@stack@operand=\toks34
+\pgfmath@stack@operation=\toks35
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code
+.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonomet
+ric.code.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.cod
+e.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison
+.code.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.
+tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code
+.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.
+tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerari
+thmetics.code.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex
+\c@pgfmathroundto@lastzeros=\count284
+))
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfint.code.tex)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.te
+x
+File: pgfcorepoints.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgf@picminx=\dimen173
+\pgf@picmaxx=\dimen174
+\pgf@picminy=\dimen175
+\pgf@picmaxy=\dimen176
+\pgf@pathminx=\dimen177
+\pgf@pathmaxx=\dimen178
+\pgf@pathminy=\dimen179
+\pgf@pathmaxy=\dimen180
+\pgf@xx=\dimen181
+\pgf@xy=\dimen182
+\pgf@yx=\dimen183
+\pgf@yy=\dimen184
+\pgf@zx=\dimen185
+\pgf@zy=\dimen186
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.
+code.tex
+File: pgfcorepathconstruct.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgf@path@lastx=\dimen187
+\pgf@path@lasty=\dimen188
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code
+.tex
+File: pgfcorepathusage.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgf@shorten@end@additional=\dimen189
+\pgf@shorten@start@additional=\dimen190
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.te
+x
+File: pgfcorescopes.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgfpic=\box55
+\pgf@hbox=\box56
+\pgf@layerbox@main=\box57
+\pgf@picture@serial@count=\count285
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.c
+ode.tex
+File: pgfcoregraphicstate.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgflinewidth=\dimen191
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformation
+s.code.tex
+File: pgfcoretransformations.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgf@pt@x=\dimen192
+\pgf@pt@y=\dimen193
+\pgf@pt@temp=\dimen194
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex
+File: pgfcorequick.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.t
+ex
+File: pgfcoreobjects.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing
+.code.tex
+File: pgfcorepathprocessing.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.te
+x
+File: pgfcorearrows.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgfarrowsep=\dimen195
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex
+File: pgfcoreshade.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgf@max=\dimen196
+\pgf@sys@shading@range@num=\count286
+\pgf@shadingcount=\count287
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex
+File: pgfcoreimage.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.
+tex
+File: pgfcoreexternal.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgfexternal@startupbox=\box58
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.te
+x
+File: pgfcorelayers.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.c
+ode.tex
+File: pgfcoretransparency.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.
+tex
+File: pgfcorepatterns.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex
+File: pgfcorerdf.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)))
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex
+File: pgfmoduleshapes.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgfnodeparttextbox=\box59
+) (/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex
+File: pgfmoduleplot.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65
+.sty
+Package: pgfcomp-version-0-65 2023-01-15 v3.1.10 (3.1.10)
+\pgf@nodesepstart=\dimen197
+\pgf@nodesepend=\dimen198
+)
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18
+.sty
+Package: pgfcomp-version-1-18 2023-01-15 v3.1.10 (3.1.10)
+)) (/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgffor.sty
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex))
+(/usr/share/texlive/texmf-dist/tex/latex/pgf/math/pgfmath.sty
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex))
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex
+Package: pgffor 2023-01-15 v3.1.10 (3.1.10)
+\pgffor@iter=\dimen199
+\pgffor@skip=\dimen256
+\pgffor@stack=\toks36
+\pgffor@toks=\toks37
+))
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex
+Package: tikz 2023-01-15 v3.1.10 (3.1.10)
+
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers
+.code.tex
+File: pgflibraryplothandlers.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgf@plot@mark@count=\count288
+\pgfplotmarksize=\dimen257
+)
+\tikz@lastx=\dimen258
+\tikz@lasty=\dimen259
+\tikz@lastxsaved=\dimen260
+\tikz@lastysaved=\dimen261
+\tikz@lastmovetox=\dimen262
+\tikz@lastmovetoy=\dimen263
+\tikzleveldistance=\dimen264
+\tikzsiblingdistance=\dimen265
+\tikz@figbox=\box60
+\tikz@figbox@bg=\box61
+\tikz@tempbox=\box62
+\tikz@tempbox@bg=\box63
+\tikztreelevel=\count289
+\tikznumberofchildren=\count290
+\tikznumberofcurrentchild=\count291
+\tikz@fig@count=\count292
+
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex
+File: pgfmodulematrix.code.tex 2023-01-15 v3.1.10 (3.1.10)
+\pgfmatrixcurrentrow=\count293
+\pgfmatrixcurrentcolumn=\count294
+\pgf@matrix@numberofcolumns=\count295
+)
+\tikz@expandcount=\count296
+
+(/usr/share/texlive/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tik
+zlibrarytopaths.code.tex
+File: tikzlibrarytopaths.code.tex 2023-01-15 v3.1.10 (3.1.10)
+)))
+\shadedbox=\box64
+LaTeX Font Info:    Trying to load font information for T1+lmr on input line 44
+.
+ (/usr/share/texmf/tex/latex/lm/t1lmr.fd
+File: t1lmr.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
+)
+(/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=\count297
+\l__pdf_internal_box=\box65
+)
+(./loesung_probeklausur2.aux)
+\openout1 = `loesung_probeklausur2.aux'.
+
+LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 44.
+LaTeX Font Info:    ... okay on input line 44.
+LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 44.
+LaTeX Font Info:    ... okay on input line 44.
+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 44.
+LaTeX Font Info:    ... okay on input line 44.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 44.
+LaTeX Font Info:    ... okay on input line 44.
+LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 44.
+LaTeX Font Info:    ... okay on input line 44.
+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 44.
+LaTeX Font Info:    ... okay on input line 44.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 44.
+LaTeX Font Info:    ... okay on input line 44.
+
+*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=11.0pt
+* \footskip=30.0pt
+* \marginparwidth=50.0pt
+* \marginparsep=10.0pt
+* \columnsep=10.0pt
+* \skip\footins=10.0pt 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)
+
+(/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
+[Loading MPS to PDF converter (version 2006.09.02).]
+\scratchcounter=\count298
+\scratchdimen=\dimen266
+\scratchbox=\box66
+\nofMPsegments=\count299
+\nofMParguments=\count300
+\everyMPshowfont=\toks38
+\MPscratchCnt=\count301
+\MPscratchDim=\dimen267
+\MPnumerator=\count302
+\makeMPintoPDFobject=\count303
+\everyMPtoPDFconversion=\toks39
+) (/usr/share/texlive/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty
+Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
+Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
+85.
+
+(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
+File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
+e
+))
+[1
+
+{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}{/usr/share/texmf/fonts/enc/
+dvips/lm/lm-ec.enc}]
+LaTeX Font Info:    Trying to load font information for OT1+lmr on input line 6
+0.
+ (/usr/share/texmf/tex/latex/lm/ot1lmr.fd
+File: ot1lmr.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
+)
+LaTeX Font Info:    Trying to load font information for OML+lmm on input line 6
+0.
+
+(/usr/share/texmf/tex/latex/lm/omllmm.fd
+File: omllmm.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
+)
+LaTeX Font Info:    Trying to load font information for OMS+lmsy on input line 
+60.
+
+(/usr/share/texmf/tex/latex/lm/omslmsy.fd
+File: omslmsy.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
+)
+LaTeX Font Info:    Trying to load font information for OMX+lmex on input line 
+60.
+
+(/usr/share/texmf/tex/latex/lm/omxlmex.fd
+File: omxlmex.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
+)
+LaTeX Font Info:    External font `lmex10' loaded for size
+(Font)              <10.95> on input line 60.
+LaTeX Font Info:    External font `lmex10' loaded for size
+(Font)              <8> on input line 60.
+LaTeX Font Info:    External font `lmex10' loaded for size
+(Font)              <6> on input line 60.
+LaTeX Font Info:    Trying to load font information for U+msa on input line 60.
+
+
+(/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 60.
+
+
+(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
+File: umsb.fd 2013/01/14 v3.01 AMS symbols B
+)
+LaTeX Font Info:    Trying to load font information for TS1+lmr on input line 6
+3.
+
+(/usr/share/texmf/tex/latex/lm/ts1lmr.fd
+File: ts1lmr.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
+)
+LaTeX Font Info:    External font `lmex10' loaded for size
+(Font)              <5> on input line 76.
+LaTeX Font Info:    External font `lmex10' loaded for size
+(Font)              <10> on input line 89.
+LaTeX Font Info:    External font `lmex10' loaded for size
+(Font)              <7> on input line 89.
+ [2
+
+{/usr/share/texmf/fonts/enc/dvips/lm/lm-rm.enc}{/usr/share/texmf/fonts/enc/dvip
+s/lm/lm-mathit.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-ts1.enc}{/usr/share/
+texmf/fonts/enc/dvips/lm/lm-mathsy.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-
+mathex.enc}] [3
+
+]
+LaTeX Font Info:    Trying to load font information for T1+lmss on input line 1
+70.
+
+(/usr/share/texmf/tex/latex/lm/t1lmss.fd
+File: t1lmss.fd 2015/05/01 v1.6.1 Font defs for Latin Modern
+)
+Overfull \hbox (100.09642pt too wide) in paragraph at lines 207--210
+[]\T1/lmr/m/n/10.95 Da \T1/lmr/m/sc/10.95 Sub-set-Sum \T1/lmr/m/n/10.95 NP-voll
+ständig ist, $[] \OMS/lmsy/m/n/10.95 ^^T[] \OML/lmm/m/it/10.95 L$ \T1/lmr/m/n/1
+0.95 gilt und $\OML/lmm/m/it/10.95 L \OMS/lmsy/m/n/10.95 2 []$\T1/lmr/m/n/10.95
+ , ist $\OML/lmm/m/it/10.95 L \OT1/lmr/m/n/10.95 = []$
+ []
+
+[4
+
+]
+
+LaTeX Font Warning: Font shape `T1/lmr/bx/sc' undefined
+(Font)              using `T1/lmr/bx/n' instead on input line 214.
+
+[5
+
+]
+Overfull \hbox (79.29286pt too wide) in paragraph at lines 324--332
+\T1/lmr/m/it/10.95 Schlechteste Kan-ten-rei-hen-folge: \T1/lmr/m/n/10.95 Man or
+d-net die $\OML/lmm/m/it/10.95 n=\OT1/lmr/m/n/10.95 2$ \T1/lmr/m/n/10.95 paar-w
+eise dis-junk-ten Kan-ten $\OMS/lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 v[]; v[]\OM
+S/lmsy/m/n/10.95 g\OML/lmm/m/it/10.95 ; \OMS/lmsy/m/n/10.95 f\OML/lmm/m/it/10.9
+5 v[]; v[]\OMS/lmsy/m/n/10.95 g\OML/lmm/m/it/10.95 ; [] ; \OMS/lmsy/m/n/10.95 f
+\OML/lmm/m/it/10.95 v[]; v[]\OMS/lmsy/m/n/10.95 g$
+ []
+
+[6
+
+]
+Overfull \hbox (42.7213pt too wide) in paragraph at lines 344--351
+[]\T1/lmr/m/it/10.95 Ungünstige Rei-hen-folge: \T1/lmr/m/n/10.95 Ordne die $\OM
+L/lmm/m/it/10.95 k$ \T1/lmr/m/n/10.95 paar-weise dis-junk-ten Kan-ten $\OMS/lms
+y/m/n/10.95 f\OML/lmm/m/it/10.95 v[]; v[]\OMS/lmsy/m/n/10.95 g\OML/lmm/m/it/10.
+95 ; \OMS/lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 v[]; v[]\OMS/lmsy/m/n/10.95 g\OML
+/lmm/m/it/10.95 ; [] ; \OMS/lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 v[]; v[]\OMS/lm
+sy/m/n/10.95 g$
+ []
+
+[7] (./loesung_probeklausur2.aux)
+ ***********
+LaTeX2e <2023-11-01> patch level 1
+L3 programming layer <2024-01-22>
+ ***********
+
+
+LaTeX Font Warning: Some font shapes were not available, defaults substituted.
+
+ ) 
+Here is how much of TeX's memory you used:
+ 14094 strings out of 476182
+ 278764 string characters out of 5795595
+ 1939975 words of memory out of 5000000
+ 35819 multiletter control sequences out of 15000+600000
+ 625702 words of font info for 84 fonts, out of 8000000 for 9000
+ 14 hyphenation exceptions out of 8191
+ 102i,11n,107p,402b,643s stack positions out of 10000i,1000n,20000p,200000b,200000s
+</usr/share/texmf/fonts/type1/public/lm/lmbx10.pfb></usr/share/texmf/fonts/ty
+pe1/public/lm/lmbx12.pfb></usr/share/texmf/fonts/type1/public/lm/lmcsc10.pfb></
+usr/share/texmf/fonts/type1/public/lm/lmex10.pfb></usr/share/texmf/fonts/type1/
+public/lm/lmmi10.pfb></usr/share/texmf/fonts/type1/public/lm/lmmi8.pfb></usr/sh
+are/texmf/fonts/type1/public/lm/lmr10.pfb></usr/share/texmf/fonts/type1/public/
+lm/lmr6.pfb></usr/share/texmf/fonts/type1/public/lm/lmr7.pfb></usr/share/texmf/
+fonts/type1/public/lm/lmr8.pfb></usr/share/texmf/fonts/type1/public/lm/lmri10.p
+fb></usr/share/texmf/fonts/type1/public/lm/lmss10.pfb></usr/share/texmf/fonts/t
+ype1/public/lm/lmsy10.pfb></usr/share/texmf/fonts/type1/public/lm/lmsy6.pfb></u
+sr/share/texmf/fonts/type1/public/lm/lmsy8.pfb></usr/share/texlive/texmf-dist/f
+onts/type1/public/amsfonts/symbols/msam10.pfb></usr/share/texlive/texmf-dist/fo
+nts/type1/public/amsfonts/symbols/msbm10.pfb>
+Output written on loesung_probeklausur2.pdf (7 pages, 286555 bytes).
+PDF statistics:
+ 128 PDF objects out of 1000 (max. 8388607)
+ 82 compressed objects within 1 object stream
+ 0 named destinations out of 1000 (max. 500000)
+ 13 words of extra memory for PDF output out of 10000 (max. 10000000)
+