%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % | \ % % ______ __ __ ______ _______ _______ _| ▓▓_ __ __ % % / \| \ / \| \| \ / \ ▓▓ \ | \ | \ % % | ▓▓▓▓▓▓\\▓▓\ / ▓▓ \▓▓▓▓▓▓\ ▓▓▓▓▓▓▓\ | ▓▓▓▓▓▓▓\▓▓▓▓▓▓ | ▓▓ | ▓▓ % % | ▓▓ ▓▓ \▓▓\ ▓▓ / ▓▓ ▓▓ | ▓▓ \▓▓ \ | ▓▓ __| ▓▓ | ▓▓ % % | ▓▓▓▓▓▓▓▓ \▓▓ ▓▓ | ▓▓▓▓▓▓▓ ▓▓ | ▓▓__ _\▓▓▓▓▓▓\ | ▓▓| \ ▓▓__/ ▓▓ % % \▓▓ \ \▓▓▓ \▓▓ ▓▓ ▓▓ | ▓▓ \ ▓▓ \▓▓ ▓▓\▓▓ ▓▓ % % \▓▓▓▓▓▓▓ \▓ \▓▓▓▓▓▓▓\▓▓ \▓▓\▓▓\▓▓▓▓▓▓▓ \▓▓▓▓ _\▓▓▓▓▓▓▓ % % | \__| ▓▓ % % \▓▓ ▓▓ % % \▓▓▓▓▓▓ % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Original file: % https://github.com/vEnhance/dotfiles/blob/main/texmf/tex/latex/evan/evan.sty % TL;DR of the Boost license conditions are as follows: % % 1. Any SOURCE VERSIONS must cite evan.sty and the Boost license below. % 2. For COMPILED PDF OUTPUT, attribution of evan.sty is OPTIONAL (but nice). % 3. NO OTHER REQUIREMENTS; you may modify, redistribute, sell freely. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % BOOST SOFTWARE LICENSE - VERSION 1.0 - 17 AUGUST 2003 % % Copyright (c) 2022 Evan Chen [evan at evanchen.cc] % https://web.evanchen.cc/ || github.com/vEnhance % % Available for download at: % https://github.com/vEnhance/dotfiles/blob/main/texmf/tex/latex/evan/evan.sty % % Permission is hereby granted, free of charge, to any person or organization % obtaining a copy of the software and accompanying documentation covered by % this license (the "Software") to use, reproduce, display, distribute, % execute, and transmit the Software, and to prepare derivative works of the % Software, and to permit third-parties to whom the Software is furnished to % do so, all subject to the following: % % The copyright notices in the Software and this entire statement, including % the above license grant, this restriction and the following disclaimer, % must be included in all copies of the Software, in whole or in part, and % all derivative works of the Software, unless such copies or derivative % works are solely in the form of machine-executable object code generated by % a source language processor. % % THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR % IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, % FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT % SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE % FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, % ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER % DEALINGS IN THE SOFTWARE. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ProvidesPackage{evan_notes} \ProcessOptions\relax \usepackage{amsmath,amssymb} \usepackage{iftex} \usepackage[minimal]{yhmath} \setlength\parindent{0pt} % Personal commands \newcommand{\card}[1]{\left|#1\right|} \newcommand{\nsqrt}[2]{\!\sqrt[#1]{#2}\,} \newcommand{\zeroset}{\{0\}} \newcommand{\setminuszero}{\setminus \{0\}} \newcommand{\corref}[1]{\textit{Corollario \ref{#1}}} \newcommand{\exref}[1]{\textit{Esercizio \ref{#1}}} \newcommand{\exmplref}[1]{\textit{Esempio \ref{#1}}} \newcommand{\propref}[1]{\textit{Proposizione \ref{#1}}} \newcommand{\lemref}[1]{\textit{Lemma \ref{#1}}} \newcommand{\thref}[1]{\textit{Teorema \ref{#1}}} \newcommand{\BB}{\mathcal{B}} \newcommand{\HH}{\mathbb{H}} \newcommand{\KK}{\mathbb{K}} \newcommand{\ZZp}{\mathbb{Z}_p} \newcommand{\CCx}{\mathbb{C}[x]} \newcommand{\FFpp}{\mathbb{F}_p} \newcommand{\FFpd}{\mathbb{F}_{p^d}} \newcommand{\FFpm}{\mathbb{F}_{p^m}} \newcommand{\FFpn}{\mathbb{F}_{p^n}} \newcommand{\FFp}[1]{\mathbb{F}_{p^{#1}}} \newcommand{\KKx}{\mathbb{K}[x]} \newcommand{\QQx}{\mathbb{Q}[x]} \newcommand{\RRx}{\mathbb{R}[x]} \newcommand{\ZZi}{\mathbb{Z}[i]} \newcommand{\ZZom}{\mathbb{Z}[\omega]} \newcommand{\ZZpx}{\mathbb{Z}_p[x]} \newcommand{\ZZsqrt}[1]{\mathbb{Z}[\sqrt{#1}]} \newcommand{\ZZx}{\mathbb{Z}[x]} \newcommand{\ii}{\mathbf{i}} \newcommand{\jj}{\mathbf{j}} \newcommand{\kk}{\mathbf{k}} \newcommand{\valalpha}{\varphi_\alpha} \newcommand{\Frob}{\mathcal{F}} \newcommand{\Frobexp}{\mathcal{F}{\mkern 1.5mu}} \newcommand{\dual}[1]{#1^{*}} \newcommand{\LL}[2]{\mathcal{L} \left(#1, \, #2\right)} \newcommand{\M}[1]{\mathcal{M}_{#1}\left(\KK\right)} \newcommand{\nsg}{\mathrel{\unlhd}} \renewcommand{\vec}[1]{\underline{#1}} \newcommand{\hatpi}{\hat{\pi}} \newcommand{\hatpip}{\hat{\pi}_p} % evan.sty original commands \newcommand{\cbrt}[1]{\sqrt[3]{#1}} \newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} \newcommand{\ceiling}[1]{\left\lceil #1 \right\rceil} \newcommand{\mailto}[1]{\href{mailto:#1}{\texttt{#1}}} \newcommand{\eps}{\varepsilon} \newcommand{\vocab}[1]{\textbf{\color{blue}\sffamily #1}} \providecommand{\alert}{\vocab} \newcommand{\catname}{\mathsf} \providecommand{\arc}[1]{\wideparen{#1}} % From H113 "Introduction to Abstract Algebra" at UC Berkeley \newcommand{\CC}{\mathbb C} \newcommand{\FF}{\mathbb F} \newcommand{\NN}{\mathbb N} \newcommand{\QQ}{\mathbb Q} \newcommand{\RR}{\mathbb R} \newcommand{\ZZ}{\mathbb Z} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\Inn}{Inn} \DeclareMathOperator{\Syl}{Syl} \DeclareMathOperator{\Gal}{Gal} \DeclareMathOperator{\GL}{GL} \DeclareMathOperator{\SL}{SL} %From Kiran Kedlaya's "Geometry Unbound" \newcommand{\abs}[1]{\left\lvert #1 \right\rvert} \newcommand{\norm}[1]{\left\lVert #1 \right\rVert} \newcommand{\dang}{\measuredangle} %% Directed angle \newcommand{\ray}[1]{\overrightarrow{#1}} \newcommand{\seg}[1]{\overline{#1}} % From M275 "Topology" at SJSU \newcommand{\id}{\mathrm{id}} \newcommand{\taking}[1]{\xrightarrow{#1}} \newcommand{\inv}{^{-1}} \DeclareMathOperator{\ord}{ord} \newcommand{\defeq}{\overset{\mathrm{def}}{=}} \newcommand{\defiff}{\overset{\mathrm{def}}{\iff}} % From the USAMO .tex files \newcommand{\dg}{^\circ} \newcommand{\liff}{\leftrightarrow} \newcommand{\lthen}{\rightarrow} \newcommand{\opname}{\operatorname} \newcommand{\surjto}{\twoheadrightarrow} \newcommand{\injto}{\hookrightarrow} \DeclareMathOperator{\Char}{char} \DeclareMathOperator{\Dom}{Dom} \DeclareMathOperator{\Fix}{Fix} \DeclareMathOperator{\End}{End} \DeclareMathOperator{\existsone}{\exists !} \DeclareMathOperator{\Hom}{Hom} \DeclareMathOperator{\Imm}{Im} \DeclareMathOperator{\Ker}{Ker} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\MCD}{MCD} \DeclareMathOperator{\Mor}{Mor} \DeclareMathOperator{\mcm}{mcm} \DeclareMathOperator{\Sym}{Sym} \DeclareMathOperator{\tr}{tr} \let\oldemptyset\emptyset \let\emptyset\varnothing \let\oldcirc\circ \let\circ\undefined \DeclareMathOperator{\circ}{\oldcirc} \let\oldexists\exists \let\exists\undefined \DeclareMathOperator{\exists}{\oldexists} \let\oldforall\forall \let\forall\undefined \DeclareMathOperator{\forall}{\oldforall} \let\oldnexists\nexists \let\nexists\undefined \DeclareMathOperator{\nexists}{\oldnexists} \let\oldland\land \let\land\undefined \DeclareMathOperator{\land}{\oldland} \let\oldlnot\lnot \let\lnot\undefined \DeclareMathOperator{\lnot}{\oldlnot} \let\oldlor\lor \let\lor\undefined \DeclareMathOperator{\lor}{\oldlor} \title{} \author{Gabriel Antonio Videtta} \date{\today} \PassOptionsToPackage{usenames,svgnames,dvipsnames,table}{xcolor} \usepackage{xcolor} \usepackage[colorlinks=true]{hyperref} \hypersetup{urlcolor=RubineRed,linkcolor=RoyalBlue,citecolor=ForestGreen} \usepackage[nameinlink]{cleveref} \usepackage{amsthm} \usepackage{thmtools} \usepackage[framemethod=TikZ]{mdframed} \mdfdefinestyle{mdbluebox}{% roundcorner=10pt, linewidth=1pt, skipabove=12pt, innerbottommargin=9pt, skipbelow=2pt, linecolor=blue, nobreak=true, backgroundcolor=TealBlue!5, } \declaretheoremstyle[ headfont=\sffamily\bfseries\color{MidnightBlue}, mdframed={style=mdbluebox}, headpunct={\\[3pt]}, postheadspace={0pt} ]{thmbluebox} \mdfdefinestyle{mdbluebox2}{% roundcorner=10pt, linewidth=1pt, skipabove=12pt, innerbottommargin=9pt, skipbelow=2pt, linecolor=blue, nobreak=true, backgroundcolor=BlueViolet!9, } \declaretheoremstyle[ headfont=\sffamily\bfseries\color{RoyalPurple}, mdframed={style=mdbluebox2}, headpunct={\\[3pt]}, postheadspace={0pt} ]{thmbluebox2} \mdfdefinestyle{mdredbox}{% linewidth=0.5pt, skipabove=12pt, frametitleaboveskip=5pt, frametitlebelowskip=0pt, skipbelow=2pt, frametitlefont=\bfseries, innertopmargin=4pt, innerbottommargin=8pt, nobreak=true, backgroundcolor=Salmon!5, linecolor=RawSienna, } \declaretheoremstyle[ headfont=\bfseries\color{RawSienna}, mdframed={style=mdredbox}, headpunct={\\[3pt]}, postheadspace={0pt}, ]{thmredbox} \mdfdefinestyle{mdredbox2}{% roundcorner=10pt, linewidth=1pt, skipabove=12pt, innerbottommargin=9pt, skipbelow=2pt, linecolor=red, nobreak=true, backgroundcolor=WildStrawberry!5, } \declaretheoremstyle[ headfont=\sffamily\bfseries\color{Maroon}, mdframed={style=mdredbox2}, headpunct={\\[3pt]}, postheadspace={0pt} ]{thmredbox2} \mdfdefinestyle{mdgreenbox}{% skipabove=8pt, linewidth=2pt, rightline=false, leftline=true, topline=false, bottomline=false, linecolor=ForestGreen, backgroundcolor=ForestGreen!5, } \declaretheoremstyle[ headfont=\bfseries\sffamily\color{ForestGreen!70!black}, bodyfont=\normalfont, spaceabove=2pt, spacebelow=1pt, mdframed={style=mdgreenbox}, headpunct={ --- }, ]{thmgreenbox} \mdfdefinestyle{mdgreenbox2}{% roundcorner=10pt, linewidth=1pt, skipabove=12pt, innerbottommargin=9pt, skipbelow=2pt, linecolor=ForestGreen, nobreak=true, backgroundcolor=ForestGreen!5, } \declaretheoremstyle[ headfont=\sffamily\bfseries\color{ForestGreen!70!black}, mdframed={style=mdgreenbox2}, headpunct={\\[3pt]}, postheadspace={0pt} ]{thmgreenbox2} \mdfdefinestyle{mdblackbox}{% skipabove=8pt, linewidth=3pt, rightline=false, leftline=true, topline=false, bottomline=false, linecolor=black, backgroundcolor=RedViolet!5!gray!10, } \declaretheoremstyle[ headfont=\bfseries, bodyfont=\normalfont\small, spaceabove=0pt, spacebelow=0pt, mdframed={style=mdblackbox} ]{thmblackbox} \mdfdefinestyle{mdblackbox2}{% skipabove=8pt, linewidth=3pt, rightline=false, leftline=true, topline=false, bottomline=false, linecolor=gray, backgroundcolor=RedViolet!5!gray!10, } \declaretheoremstyle[ headfont=\bfseries, bodyfont=\normalfont\small, spaceabove=0pt, spacebelow=0pt, mdframed={style=mdblackbox2} ]{thmblackbox2} \newcommand{\listhack}{$\empty$\vspace{-2em}} \declaretheorem[% style=thmbluebox,name=Teorema,numberwithin=section]{theorem} \declaretheorem[style=thmgreenbox2,name=Lemma,sibling=theorem]{lemma} \declaretheorem[style=thmredbox2,name=Proposizione,sibling=theorem]{proposition} \declaretheorem[style=thmbluebox2,name=Corollario,sibling=theorem]{corollary} \declaretheorem[style=thmbluebox,name=Teorema,numbered=no]{theorem*} \declaretheorem[style=thmgreenbox2,name=Lemma,numbered=no]{lemma*} \declaretheorem[style=thmredbox2,name=Proposizione,numbered=no]{proposition*} \declaretheorem[style=thmbluebox2,name=Corollario,numbered=no]{corollary*} \declaretheorem[style=thmgreenbox,name=Claim,sibling=theorem]{claim} \declaretheorem[style=thmgreenbox,name=Claim,numbered=no]{claim*} \declaretheorem[style=thmredbox,name=Esempio,sibling=theorem]{example} \declaretheorem[style=thmredbox,name=Esempio,numbered=no]{example*} \declaretheorem[style=thmblackbox, name=Definizione,sibling=theorem]{definition} \declaretheorem[style=thmblackbox, name=Definizione,numbered=no]{definition*} \declaretheorem[style=thmblackbox2,name=Osservazione,sibling=theorem]{remark} \declaretheorem[style=thmblackbox2,name=Osservazione,numbered=no]{remark*} \declaretheorem[name=Congettura,sibling=theorem]{conjecture} \declaretheorem[name=Congettura,numbered=no]{conjecture*} \declaretheorem[name=Esercizio,sibling=theorem]{exercise} \declaretheorem[name=Esercizio,numbered=no]{exercise*} \declaretheorem[name=Asserzione,sibling=theorem]{fact} \declaretheorem[name=Asserzione,numbered=no]{fact*} \declaretheorem[name=Problema,sibling=theorem]{problem} \declaretheorem[name=Problema,numbered=no]{problem*} \declaretheorem[name=Domanda,sibling=theorem]{ques} \declaretheorem[name=Domanda,numbered=no]{ques*} \Crefname{claim}{Claim}{Claim} \Crefname{conjecture}{Congettura}{Congetture} \Crefname{exercise}{Esercizio}{Esercizi} \Crefname{fact}{Asserzione}{Asserzioni} \Crefname{problem}{Problema}{Problemi} \Crefname{ques}{Domanda}{Domande} \addtokomafont{partprefix}{} \renewcommand*{\partformat}{} \@ifundefined{chapter}{}{ \addtokomafont{partprefix}{} \renewcommand*{\partformat}{} \addtokomafont{chapterprefix}{} \RedeclareSectionCommand{chapter} \renewcommand*{\chapterformat}{} } \renewcommand*{\sectionformat}% {\color{purple}\S\thesection\enskip} \renewcommand*{\subsectionformat}% {\color{purple}\S\thesubsection\enskip} \renewcommand*{\subsubsectionformat}% {\color{purple}\S\thesubsubsection\enskip} \KOMAoptions{numbers=noenddot} \usepackage{listings} \usepackage{mathrsfs} \usepackage{textcomp} \lstset{basicstyle=\ttfamily\scriptsize, backgroundcolor=\color{green!2!white}, breakatwhitespace=true, breaklines=true, commentstyle=\color{green!70!black}, frame=shadowbox, frame=single, identifierstyle=\color{green!20!black}, keywordstyle=\bfseries, keywordstyle=\bfseries\color{blue}, numbers=left, numbersep=5pt, numberstyle=\tiny\sffamily\itshape\color{black!60}, rulecolor=\color{blue!70!black}, rulesepcolor=\color{blue!30!black}, showstringspaces=false, stringstyle=\color{orange}, tabsize=4, } \usepackage[shortlabels]{enumitem} \usepackage[obeyFinal,textsize=scriptsize,shadow]{todonotes} \usepackage{textcomp} \usepackage{multirow} \usepackage{ellipsis} \usepackage{mathtools} \usepackage{microtype} \usepackage{xstring} \usepackage{wrapfig} \addtokomafont{subtitle}{\Large} \setkomafont{author}{\Large\scshape} \setkomafont{date}{\Large\normalsize} \providecommand{\thetitle}{\@title} \providecommand{\theauthor}{\@author} \providecommand{\thedate}{\@date} \usepackage[headsepline]{scrlayer-scrpage} \renewcommand{\headfont}{} \addtolength{\textheight}{3.14cm} \setlength{\footskip}{0.5in} \setlength{\headsep}{10pt} \ihead{\footnotesize\textbf{\rightmark}} \ohead{\footnotesize Gabriel Antonio Videtta} \automark{section} \chead{} \cfoot{\pagemark} \hfuzz=\maxdimen \tolerance=10000 \hbadness=10000 \KOMAoptions{twoside=false}