Changed email address

5 files changed, 795 insertions, 0 deletions

diff --git a/src/Retake/Retake1.aux b/src/Retake/Retake1.aux
new file mode 100644
index 0000000..405f9ed
--- /dev/null
+++ b/src/Retake/Retake1.aux
@@ -0,0 +1,4 @@
+\relax 
+\newlabel{prop:fta}{{1}{1}}
+\newlabel{eq:fubini}{{2}{1}}
+\gdef \@abspage@last{4}
diff --git a/src/Retake/Retake1.log b/src/Retake/Retake1.log
new file mode 100644
index 0000000..d28cd96
--- /dev/null
+++ b/src/Retake/Retake1.log
@@ -0,0 +1,583 @@
+This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/VoidLinux) (preloaded format=pdflatex 2021.12.14)  21 DEC 2021 11:16
+entering extended mode
+ \write18 enabled.
+ %&-line parsing enabled.
+**Retake1.tex
+(./Retake1.tex
+LaTeX2e <2020-10-01> patch level 4
+L3 programming layer <2021-02-18>
+(/usr/share/texmf-dist/tex/latex/base/article.cls
+Document Class: article 2020/04/10 v1.4m Standard LaTeX document class
+(/usr/share/texmf-dist/tex/latex/base/size12.clo
+File: size12.clo 2020/04/10 v1.4m Standard LaTeX file (size option)
+)
+\c@part=\count179
+\c@section=\count180
+\c@subsection=\count181
+\c@subsubsection=\count182
+\c@paragraph=\count183
+\c@subparagraph=\count184
+\c@figure=\count185
+\c@table=\count186
+\abovecaptionskip=\skip47
+\belowcaptionskip=\skip48
+\bibindent=\dimen138
+)
+(/usr/share/texmf-dist/tex/latex/base/inputenc.sty
+Package: inputenc 2020/08/01 v1.3d Input encoding file
+\inpenc@prehook=\toks15
+\inpenc@posthook=\toks16
+)
+(/usr/share/texmf-dist/tex/latex/amsmath/amsmath.sty
+Package: amsmath 2020/09/23 v2.17i AMS math features
+\@mathmargin=\skip49
+
+For additional information on amsmath, use the `?' option.
+(/usr/share/texmf-dist/tex/latex/amsmath/amstext.sty
+Package: amstext 2000/06/29 v2.01 AMS text
+
+(/usr/share/texmf-dist/tex/latex/amsmath/amsgen.sty
+File: amsgen.sty 1999/11/30 v2.0 generic functions
+\@emptytoks=\toks17
+\ex@=\dimen139
+))
+(/usr/share/texmf-dist/tex/latex/amsmath/amsbsy.sty
+Package: amsbsy 1999/11/29 v1.2d Bold Symbols
+\pmbraise@=\dimen140
+)
+(/usr/share/texmf-dist/tex/latex/amsmath/amsopn.sty
+Package: amsopn 2016/03/08 v2.02 operator names
+)
+\inf@bad=\count187
+LaTeX Info: Redefining \frac on input line 234.
+\uproot@=\count188
+\leftroot@=\count189
+LaTeX Info: Redefining \overline on input line 399.
+\classnum@=\count190
+\DOTSCASE@=\count191
+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@=\box47
+\strutbox@=\box48
+\big@size=\dimen141
+LaTeX Font Info:    Redeclaring font encoding OML on input line 743.
+LaTeX Font Info:    Redeclaring font encoding OMS on input line 744.
+\macc@depth=\count192
+\c@MaxMatrixCols=\count193
+\dotsspace@=\muskip16
+\c@parentequation=\count194
+\dspbrk@lvl=\count195
+\tag@help=\toks18
+\row@=\count196
+\column@=\count197
+\maxfields@=\count198
+\andhelp@=\toks19
+\eqnshift@=\dimen142
+\alignsep@=\dimen143
+\tagshift@=\dimen144
+\tagwidth@=\dimen145
+\totwidth@=\dimen146
+\lineht@=\dimen147
+\@envbody=\toks20
+\multlinegap=\skip50
+\multlinetaggap=\skip51
+\mathdisplay@stack=\toks21
+LaTeX Info: Redefining \[ on input line 2923.
+LaTeX Info: Redefining \] on input line 2924.
+)
+(/usr/share/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/texmf-dist/tex/latex/amsfonts/amssymb.sty
+Package: amssymb 2013/01/14 v3.01 AMS font symbols
+)
+(/usr/share/texmf-dist/tex/latex/amscls/amsthm.sty
+Package: amsthm 2020/05/29 v2.20.6
+\thm@style=\toks22
+\thm@bodyfont=\toks23
+\thm@headfont=\toks24
+\thm@notefont=\toks25
+\thm@headpunct=\toks26
+\thm@preskip=\skip52
+\thm@postskip=\skip53
+\thm@headsep=\skip54
+\dth@everypar=\toks27
+)
+(/usr/share/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty
+(/usr/share/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty
+(/usr/share/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex
+\pgfutil@everybye=\toks28
+\pgfutil@tempdima=\dimen148
+\pgfutil@tempdimb=\dimen149
+
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfutil-common-lists.tex))
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfutil-latex.def
+\pgfutil@abb=\box49
+)
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfrcs.code.tex
+(/usr/share/texmf-dist/tex/generic/pgf/pgf.revision.tex)
+Package: pgfrcs 2020/12/27 v3.1.8b (3.1.8b)
+))
+Package: pgf 2020/12/27 v3.1.8b (3.1.8b)
+
+(/usr/share/texmf-dist/tex/latex/pgf/basiclayer/pgfcore.sty
+(/usr/share/texmf-dist/tex/latex/graphics/graphicx.sty
+Package: graphicx 2020/09/09 v1.2b Enhanced LaTeX Graphics (DPC,SPQR)
+
+(/usr/share/texmf-dist/tex/latex/graphics/keyval.sty
+Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
+\KV@toks@=\toks29
+)
+(/usr/share/texmf-dist/tex/latex/graphics/graphics.sty
+Package: graphics 2020/08/30 v1.4c Standard LaTeX Graphics (DPC,SPQR)
+
+(/usr/share/texmf-dist/tex/latex/graphics/trig.sty
+Package: trig 2016/01/03 v1.10 sin cos tan (DPC)
+)
+(/usr/share/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 105.
+
+(/usr/share/texmf-dist/tex/latex/graphics-def/pdftex.def
+File: pdftex.def 2020/10/05 v1.2a Graphics/color driver for pdftex
+))
+\Gin@req@height=\dimen150
+\Gin@req@width=\dimen151
+)
+(/usr/share/texmf-dist/tex/latex/pgf/systemlayer/pgfsys.sty
+(/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsys.code.tex
+Package: pgfsys 2020/12/27 v3.1.8b (3.1.8b)
+
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex
+\pgfkeys@pathtoks=\toks30
+\pgfkeys@temptoks=\toks31
+
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex
+\pgfkeys@tmptoks=\toks32
+))
+\pgf@x=\dimen152
+\pgf@y=\dimen153
+\pgf@xa=\dimen154
+\pgf@ya=\dimen155
+\pgf@xb=\dimen156
+\pgf@yb=\dimen157
+\pgf@xc=\dimen158
+\pgf@yc=\dimen159
+\pgf@xd=\dimen160
+\pgf@yd=\dimen161
+\w@pgf@writea=\write3
+\r@pgf@reada=\read2
+\c@pgf@counta=\count199
+\c@pgf@countb=\count266
+\c@pgf@countc=\count267
+\c@pgf@countd=\count268
+\t@pgf@toka=\toks33
+\t@pgf@tokb=\toks34
+\t@pgf@tokc=\toks35
+\pgf@sys@id@count=\count269
+
+(/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgf.cfg
+File: pgf.cfg 2020/12/27 v3.1.8b (3.1.8b)
+)
+Driver file for pgf: pgfsys-pdftex.def
+
+(/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-pdftex.def
+File: pgfsys-pdftex.def 2020/12/27 v3.1.8b (3.1.8b)
+
+(/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsys-common-pdf.def
+File: pgfsys-common-pdf.def 2020/12/27 v3.1.8b (3.1.8b)
+)))
+(/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex
+File: pgfsyssoftpath.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgfsyssoftpath@smallbuffer@items=\count270
+\pgfsyssoftpath@bigbuffer@items=\count271
+)
+(/usr/share/texmf-dist/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex
+File: pgfsysprotocol.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+))
+(/usr/share/texmf-dist/tex/latex/xcolor/xcolor.sty
+Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK)
+
+(/usr/share/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 225.
+Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348.
+Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352.
+Package xcolor Info: Model `RGB' extended on input line 1364.
+Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366.
+Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367.
+Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368.
+Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369.
+Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370.
+Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371.
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcore.code.tex
+Package: pgfcore 2020/12/27 v3.1.8b (3.1.8b)
+
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathutil.code.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathparser.code.tex
+\pgfmath@dimen=\dimen162
+\pgfmath@count=\count272
+\pgfmath@box=\box50
+\pgfmath@toks=\toks36
+\pgfmath@stack@operand=\toks37
+\pgfmath@stack@operation=\toks38
+)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.code.tex
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code
+.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.random.code.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.comparison.code.te
+x) (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.base.code.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.round.code.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics
+.code.tex))) (/usr/share/texmf-dist/tex/generic/pgf/math/pgfmathfloat.code.tex
+\c@pgfmathroundto@lastzeros=\count273
+)) (/usr/share/texmf-dist/tex/generic/pgf/math/pgfint.code.tex)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex
+File: pgfcorepoints.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgf@picminx=\dimen163
+\pgf@picmaxx=\dimen164
+\pgf@picminy=\dimen165
+\pgf@picmaxy=\dimen166
+\pgf@pathminx=\dimen167
+\pgf@pathmaxx=\dimen168
+\pgf@pathminy=\dimen169
+\pgf@pathmaxy=\dimen170
+\pgf@xx=\dimen171
+\pgf@xy=\dimen172
+\pgf@yx=\dimen173
+\pgf@yy=\dimen174
+\pgf@zx=\dimen175
+\pgf@zy=\dimen176
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex
+File: pgfcorepathconstruct.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgf@path@lastx=\dimen177
+\pgf@path@lasty=\dimen178
+) (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
+File: pgfcorepathusage.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgf@shorten@end@additional=\dimen179
+\pgf@shorten@start@additional=\dimen180
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex
+File: pgfcorescopes.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgfpic=\box51
+\pgf@hbox=\box52
+\pgf@layerbox@main=\box53
+\pgf@picture@serial@count=\count274
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex
+File: pgfcoregraphicstate.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgflinewidth=\dimen181
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransformations.code.t
+ex
+File: pgfcoretransformations.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgf@pt@x=\dimen182
+\pgf@pt@y=\dimen183
+\pgf@pt@temp=\dimen184
+) (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorequick.code.tex
+File: pgfcorequick.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex
+File: pgfcoreobjects.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.te
+x
+File: pgfcorepathprocessing.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+) (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorearrows.code.tex
+File: pgfcorearrows.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgfarrowsep=\dimen185
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex
+File: pgfcoreshade.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgf@max=\dimen186
+\pgf@sys@shading@range@num=\count275
+\pgf@shadingcount=\count276
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex
+File: pgfcoreimage.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex
+File: pgfcoreexternal.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgfexternal@startupbox=\box54
+))
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex
+File: pgfcorelayers.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex
+File: pgfcoretransparency.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+) (/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex
+File: pgfcorepatterns.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)
+(/usr/share/texmf-dist/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex
+File: pgfcorerdf.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)))
+(/usr/share/texmf-dist/tex/generic/pgf/modules/pgfmoduleshapes.code.tex
+File: pgfmoduleshapes.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgfnodeparttextbox=\box55
+)
+(/usr/share/texmf-dist/tex/generic/pgf/modules/pgfmoduleplot.code.tex
+File: pgfmoduleplot.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)
+(/usr/share/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-0-65.sty
+Package: pgfcomp-version-0-65 2020/12/27 v3.1.8b (3.1.8b)
+\pgf@nodesepstart=\dimen187
+\pgf@nodesepend=\dimen188
+)
+(/usr/share/texmf-dist/tex/latex/pgf/compatibility/pgfcomp-version-1-18.sty
+Package: pgfcomp-version-1-18 2020/12/27 v3.1.8b (3.1.8b)
+))
+(/usr/share/texmf-dist/tex/latex/pgf/utilities/pgffor.sty
+(/usr/share/texmf-dist/tex/latex/pgf/utilities/pgfkeys.sty
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgfkeys.code.tex))
+(/usr/share/texmf-dist/tex/latex/pgf/math/pgfmath.sty
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex))
+(/usr/share/texmf-dist/tex/generic/pgf/utilities/pgffor.code.tex
+Package: pgffor 2020/12/27 v3.1.8b (3.1.8b)
+
+(/usr/share/texmf-dist/tex/generic/pgf/math/pgfmath.code.tex)
+\pgffor@iter=\dimen189
+\pgffor@skip=\dimen190
+\pgffor@stack=\toks39
+\pgffor@toks=\toks40
+))
+(/usr/share/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex
+Package: tikz 2020/12/27 v3.1.8b (3.1.8b)
+
+(/usr/share/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers.code.te
+x
+File: pgflibraryplothandlers.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgf@plot@mark@count=\count277
+\pgfplotmarksize=\dimen191
+)
+\tikz@lastx=\dimen192
+\tikz@lasty=\dimen193
+\tikz@lastxsaved=\dimen194
+\tikz@lastysaved=\dimen195
+\tikz@lastmovetox=\dimen196
+\tikz@lastmovetoy=\dimen197
+\tikzleveldistance=\dimen198
+\tikzsiblingdistance=\dimen199
+\tikz@figbox=\box56
+\tikz@figbox@bg=\box57
+\tikz@tempbox=\box58
+\tikz@tempbox@bg=\box59
+\tikztreelevel=\count278
+\tikznumberofchildren=\count279
+\tikznumberofcurrentchild=\count280
+\tikz@fig@count=\count281
+ (/usr/share/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex
+File: pgfmodulematrix.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgfmatrixcurrentrow=\count282
+\pgfmatrixcurrentcolumn=\count283
+\pgf@matrix@numberofcolumns=\count284
+)
+\tikz@expandcount=\count285
+
+(/usr/share/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrary
+topaths.code.tex
+File: tikzlibrarytopaths.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+))) (/usr/share/texmf-dist/tex/latex/tikz-cd/tikz-cd.sty
+Package: tikz-cd 2018/11/19 v0.9f Commutative diagrams with TikZ
+
+(/usr/share/texmf-dist/tex/generic/tikz-cd/tikzlibrarycd.code.tex
+(/usr/share/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrary
+matrix.code.tex
+File: tikzlibrarymatrix.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)
+(/usr/share/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrary
+quotes.code.tex
+File: tikzlibraryquotes.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+)
+(/usr/share/texmf-dist/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex
+File: pgflibraryarrows.meta.code.tex 2020/12/27 v3.1.8b (3.1.8b)
+\pgfarrowinset=\dimen256
+\pgfarrowlength=\dimen257
+\pgfarrowwidth=\dimen258
+\pgfarrowlinewidth=\dimen259
+))) (/usr/share/texmf-dist/tex/latex/enumitem/enumitem.sty
+Package: enumitem 2019/06/20 v3.9 Customized lists
+\labelindent=\skip55
+\enit@outerparindent=\dimen260
+\enit@toks=\toks41
+\enit@inbox=\box60
+\enit@count@id=\count286
+\enitdp@description=\count287
+)
+(/usr/share/texmf-dist/tex/latex/geometry/geometry.sty
+Package: geometry 2020/01/02 v5.9 Page Geometry
+
+(/usr/share/texmf-dist/tex/generic/iftex/ifvtex.sty
+Package: ifvtex 2019/10/25 v1.7 ifvtex legacy package. Use iftex instead.
+
+(/usr/share/texmf-dist/tex/generic/iftex/iftex.sty
+Package: iftex 2020/03/06 v1.0d TeX engine tests
+))
+\Gm@cnth=\count288
+\Gm@cntv=\count289
+\c@Gm@tempcnt=\count290
+\Gm@bindingoffset=\dimen261
+\Gm@wd@mp=\dimen262
+\Gm@odd@mp=\dimen263
+\Gm@even@mp=\dimen264
+\Gm@layoutwidth=\dimen265
+\Gm@layoutheight=\dimen266
+\Gm@layouthoffset=\dimen267
+\Gm@layoutvoffset=\dimen268
+\Gm@dimlist=\toks42
+)
+\c@prop=\count291
+\c@ex=\count292
+\c@remark=\count293
+
+(/usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdftex.def
+File: l3backend-pdftex.def 2021-03-18 L3 backend support: PDF output (pdfTeX)
+\l__color_backend_stack_int=\count294
+\l__pdf_internal_box=\box61
+) (./Retake1.aux)
+\openout1 = `Retake1.aux'.
+
+LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 23.
+LaTeX Font Info:    ... okay on input line 23.
+LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 23.
+LaTeX Font Info:    ... okay on input line 23.
+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 23.
+LaTeX Font Info:    ... okay on input line 23.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 23.
+LaTeX Font Info:    ... okay on input line 23.
+LaTeX Font Info:    Checking defaults for TS1/cmr/m/n on input line 23.
+LaTeX Font Info:    ... okay on input line 23.
+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 23.
+LaTeX Font Info:    ... okay on input line 23.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 23.
+LaTeX Font Info:    ... okay on input line 23.
+ (/usr/share/texmf-dist/tex/context/base/mkii/supp-pdf.mkii
+[Loading MPS to PDF converter (version 2006.09.02).]
+\scratchcounter=\count295
+\scratchdimen=\dimen269
+\scratchbox=\box62
+\nofMPsegments=\count296
+\nofMParguments=\count297
+\everyMPshowfont=\toks43
+\MPscratchCnt=\count298
+\MPscratchDim=\dimen270
+\MPnumerator=\count299
+\makeMPintoPDFobject=\count300
+\everyMPtoPDFconversion=\toks44
+) (/usr/share/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/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
+))
+*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)=(56.9055pt, 483.69687pt, 56.9055pt)
+* v-part:(T,H,B)=(56.9055pt, 731.23584pt, 56.9055pt)
+* \paperwidth=597.50787pt
+* \paperheight=845.04684pt
+* \textwidth=483.69687pt
+* \textheight=731.23584pt
+* \oddsidemargin=-15.36449pt
+* \evensidemargin=-15.36449pt
+* \topmargin=-52.36449pt
+* \headheight=12.0pt
+* \headsep=25.0pt
+* \topskip=12.0pt
+* \footskip=30.0pt
+* \marginparwidth=35.0pt
+* \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 33.
+
+(/usr/share/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 33.
+
+
+(/usr/share/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 OMS+cmtt on input line 
+51.
+LaTeX Font Info:    No file OMScmtt.fd. on input line 51.
+
+
+LaTeX Font Warning: Font shape `OMS/cmtt/m/n' undefined
+(Font)              using `OMS/cmsy/m/n' instead
+(Font)              for symbol `textbackslash' on input line 51.
+
+[1
+
+{/usr/share/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2]
+<bc.png, id=23, 453.1329pt x 338.2236pt>
+File: bc.png Graphic file (type png)
+<use bc.png>
+Package pdftex.def Info: bc.png  used on input line 171.
+(pdftex.def)             Requested size: 226.56589pt x 169.11139pt.
+ [3 <./bc.png>] [4] (./Retake1.aux)
+
+LaTeX Font Warning: Some font shapes were not available, defaults substituted.
+
+ ) 
+Here is how much of TeX's memory you used:
+ 14663 strings out of 478994
+ 296548 string characters out of 5864718
+ 572498 words of memory out of 5000000
+ 31890 multiletter control sequences out of 15000+600000
+ 411415 words of font info for 56 fonts, out of 8000000 for 9000
+ 1141 hyphenation exceptions out of 8191
+ 113i,14n,116p,409b,1111s stack positions out of 5000i,500n,10000p,200000b,80000s
+{/usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc}</usr/share/
+texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texmf-dist/fon
+ts/type1/public/amsfonts/cm/cmex10.pfb></usr/share/texmf-dist/fonts/type1/publi
+c/amsfonts/cm/cmmi12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/
+cmmi8.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr12.pfb></usr
+/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/share/texmf-dis
+t/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texmf-dist/fonts/type1/
+public/amsfonts/cm/cmsy8.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts
+/cm/cmti12.pfb></usr/share/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt12.pfb
+></usr/share/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb></usr/sh
+are/texmf-dist/fonts/type1/public/cm-super/sfrm1200.pfb>
+Output written on Retake1.pdf (4 pages, 134096 bytes).
+PDF statistics:
+ 72 PDF objects out of 1000 (max. 8388607)
+ 51 compressed objects within 1 object stream
+ 0 named destinations out of 1000 (max. 500000)
+ 18 words of extra memory for PDF output out of 10000 (max. 10000000)
+
diff --git a/src/Retake/Retake1.pdf b/src/Retake/Retake1.pdf
new file mode 100644
index 0000000..4f70e80
--- /dev/null
+++ b/src/Retake/Retake1.pdf
diff --git a/src/Retake/Retake1.tex b/src/Retake/Retake1.tex
new file mode 100644
index 0000000..bbff371
--- /dev/null
+++ b/src/Retake/Retake1.tex
@@ -0,0 +1,208 @@
+\documentclass[12pt,a4paper]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{amsthm}
+\usepackage{tikz,tikz-cd}
+\usepackage{enumitem}
+\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
+
+\title{Mathematical software - homework 1}
+\author{Sebastiano Tronto}
+
+\newtheorem*{thm}{Theorem}
+\newtheorem{prop}{Proposition}
+
+\theoremstyle{definition}
+\newtheorem{ex}{Exercise}
+
+\theoremstyle{definition}
+\newtheorem{remark}{Remark}
+
+\begin{document}
+
+\noindent\hrulefill
+
+\begin{center}
+\Huge{\textbf{Mathematical Software - Retake}}
+\end{center}
+
+\noindent\hrulefill
+\begin{center}
+\begin{tabular}{lcr}
+\texttt{sebastiano.tronto@uni.lu} & \qquad \qquad \qquad \qquad &
+\textbf{Deadline: Wednesday, February 9th}
+\end{tabular}
+\end{center}
+
+\vspace{0.3cm}
+
+\begin{center}
+  \emph{\large For exercises 1 and 2 submit a .tex and a .pdf file.
+    For exercises 3 and 4 submit your Sage code either in text format (.txt or
+    .sage) or as a Jupyter Notebook file (.ipynb).
+  }
+\end{center}
+
+
+\section*{Exercise 1}
+  Write a short Latex document that contains the following theorem-like
+  environments using the \texttt{\textbackslash newtheorem} command of the
+  \texttt{amsthm} package (the box around the text is not needed):
+  \begin{center}
+    \fbox{\parbox{0.95\textwidth}{
+      \begin{prop}[Fundamental Theorem of Algebra]
+        \label{prop:fta}
+        Let \(p(x)\) be a non-constant polynomial with coefficients in
+        $\mathbb C$. Then there is \(z\in\mathbb C\) such that $p(z)=0$.
+      \end{prop}
+
+      \begin{remark}
+        Proposition \ref{prop:fta} is not true for polynomials with
+        coefficients in $\mathbb R$. For example
+        \begin{align}
+          p(x) = x^2+1
+        \end{align}
+        does not have real roots.
+      \end{remark}
+
+      \begin{thm}
+        If $X$ and $Y$ are $\sigma$-finite measure spaces and $f:X\times Y\to
+        \mathbb R$ is measurable and such that
+        \begin{align*}
+          \int_{X\times Y}|f(x,y)|\mathrm d(x,y) < \infty
+        \end{align*}
+        then
+        \begin{align}
+          \label{eq:fubini}
+          \int_X\left(\int_Yf(x,y)\mathrm d y\right)\mathrm d x =
+          \int_Y\left(\int_Xf(x,y)\mathrm d x\right)\mathrm d y =
+          \int_{X\times Y} f(x,y)\mathrm d(x,y)\,.
+        \end{align}
+      \end{thm}
+
+      \begin{remark}
+        In practice, equation \eqref{eq:fubini} means that we can switch the
+        order of integration in a double integral.
+      \end{remark}
+    }}
+  \end{center}
+  Notice that Propositions, Remarks and some of the equations are numbered,
+  and some of them are referred to in the Remarks. This numbering should change
+  accordingly if more numbered Theorems and equations are added before this
+  part of the text.
+
+\newpage
+
+\section*{Exercise 2}
+Create a Latex document containing the following pictures:
+\begin{enumerate}
+\item[(a)] The following commutative diagram:
+        \begin{center}
+                \begin{tikzcd}
+                        M \ar[r, "f"] \ar[d,swap,"i",hook] & A \\
+                        N \ar[ur, swap, "\tilde f", dashed]
+                \end{tikzcd}
+        \end{center}
+\item[(b)] A triangle with verteces on a grid, as below.
+           Moreover, the position of the vertex $C$ below must be easy to
+           change at will: you should use the
+           \texttt{\textbackslash pgfmathsetmacro} command to set a value
+           for its coordinates at the beginning, so that changing only 
+           those numbers makes the whole picture change accordingly (sides,
+           dots, labels).
+      \begin{center}
+        \begin{tikzpicture}[scale=1]
+                \pgfmathsetmacro{\ax}{2}
+                \pgfmathsetmacro{\ay}{1}
+                \pgfmathsetmacro{\bx}{8}
+                \pgfmathsetmacro{\by}{1}
+                \pgfmathsetmacro{\cx}{9}
+                \pgfmathsetmacro{\cy}{7}
+
+                \draw[lightgray!30,thin] (0,0) grid (10,10);
+                \draw[-] (\ax, \ay) -- (\bx, \by) -- (\cx, \cy) -- cycle;
+                \filldraw[blue] (\ax, \ay) circle[radius=0.1] node[below left] {$A$};
+                \filldraw[blue] (\bx, \by) circle[radius=0.1] node[below right] {$B$};
+                \filldraw[red] (\cx, \cy) circle[radius=0.1] node[above] {$C$};
+
+        \end{tikzpicture}
+      \end{center}
+ 
+\end{enumerate}
+
+\newpage
+\section*{Exercise 3}
+Use SageMath to solve the following problems:
+\begin{enumerate}[label=(\arabic*)]
+        \item Find the roots of the following polynomial over $\mathbb Q$,
+                over $\mathbb R$ and over $\mathbb C$:
+                \[ p(x) = x^6+x^5-2x^4-3x^3-x^2+2x+2 \]
+        \item Find the determinant, the trace and the characteristic polynomial
+                   of the following matrix:
+                \[A=
+                \left(\begin{array}{rrrrr}
+                2 & 3 & 0 & 1 & 2 \\
+                1 & 0 & \frac{1}{2} & 1 & -1 \\
+                0 & 0 & -1 & 0 & 0 \\
+                0 & -1 & -1 & 0 & -1 \\
+                -1 & -1 & -1 & -1 & 0
+                \end{array}\right)
+                \]
+        \item Find the solutions of the linear system $A\mathbf x=\mathbf 0$, where
+                $A$ is the matrix above and $\mathbf 0$ is the zero vector.
+        \item Find the points of intersection of the circle of equation $x^2+y^2=4$
+                   ad the ellipse of equation $\left(\frac{x}{2}\right)^2+(2y)^2=4$
+        \item Plot the graph of the function $f(x)=\sqrt{1-x^6}$.
+        \item Find the area between the $x$-axis and the grap of the function of
+                   the previous point.
+        \item Find the derivative, a primitive (integral) and the Taylor series
+              expansion up to order 4 of the function $h(x)=\log(1+x+x^2)$.
+        \item Use Sage to get the Latex code for the objects you computed in
+                the previous point.
+        \item Find a solution for the differential equation with initial conditions
+                   \[
+                        \begin{cases}g'(x)&=\frac{1}{3}g(x) - 7\\g(1)&=30\end{cases}
+                   \]
+        \item Draw a bar chart of the data set $[0,1,3,7,5,7,2,8,9,3]$, like the foll
+              following:
+                \begin{center}
+              \includegraphics[scale=0.5]{bc.png}
+              \end{center}
+\end{enumerate}
+
+\newpage
+\section*{Grading}
+
+\vspace{0.3cm}
+\textbf{Exercise 1 (5 points).}
+\begin{itemize}
+  \item A correct use of the \texttt{\textbackslash newtheorem} command is
+        worth 2 out of 5 points.
+  \item A correct use of the labelling and reference system is worth 2 points.
+  \item Reproducing correctly the mathematical formulas is worth 1 point.
+\end{itemize}
+
+\vspace{0.3cm}
+\textbf{Exercise 2 (5 points).}
+\begin{itemize}
+        \item Part (a) is worth 2 points: 1 point for having the letters
+              $M$, $N$ and $A$ in the correct position and the arrows
+              pointing between them and 1 point for the style of the arrows
+              and the labels $f$, $i$ and $\tilde f$ in the correct position.
+        \item Part (b) is worth 3 points: 1 point for drawing a triangle, 1
+              point for the other decorative elements (colored dots, grid lines
+              and labels) and 1 point for having the point $C$ correctly set
+              as a macro so that it can be changed easily.
+\end{itemize}
+
+\vspace{0.3cm}
+\textbf{Exercise 3 (10 points).}
+\begin{itemize}
+        \item Each of the 10 parts is worth 1 point.
+\end{itemize}
+
+
+
+\end{document}
diff --git a/src/Retake/bc.png b/src/Retake/bc.png
new file mode 100644
index 0000000..72e73cd
--- /dev/null
+++ b/src/Retake/bc.png