preamble.txt

%Start, font settings, packages
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode
\documentclass[a4paper]{report}
\usepackage{amsmath,amsfonts,amssymb,mathtools,mathdots,mathptmx,multicol,enumitem}
\usepackage{letltxmacro,nicefrac,xfrac}
\usepackage{fontspec,xltxtra,xunicode,color,textcomp,hyperref,graphicx}
\usepackage[italian]{babel}
\usepackage{marginnote,thmtools}
\usepackage[top=3cm, bottom=3.5cm, outer=4cm, inner=4cm, marginparsep=0.7cm, marginparwidth=1.5cm]{geometry}
\includeonly{27.3}
\setmathrm{Times New Roman}
\setmathsf{Times New Roman}
\setmathtt{Times New Roman}
\setboldmathrm[BoldFont={Optima ExtraBlack}]{Optima Bold}
\defaultfontfeatures{Mapping=tex-text}
\setromanfont{Times New Roman}
\setsansfont{Times New Roman}
\setmonofont{Helvetica}
\newfontfamily{\vrb}{Helvetica}
\newfontfamily{\Ak}{Akkadian}%
\newfontfamily{\mapu}{Arial Unicode MS}
\newfontfamily{\Ar}{Geeza Pro}
\newfontfamily{\Chs}{STSong}
\newfontfamily{\Cht}{PMingLiU}
\newfontfamily{\Ja}{MS Mincho}
\newfontfamily{\Ru}{Times New Roman}
\newfontfamily{\Gr}{Times New Roman}
\newfontfamily{\He}{Times New Roman}
\newfontfamily{\Ko}{Batang}
\newfontfamily{\Ind}{Devanagari MT}
\newfontfamily{\Mal}{Malayalam MN}
\newfontfamily{\Sinh}{Free Sans}
\newfontfamily{\Thai}{Free Serif}
\newcommand{\€}{\Gr{ }}
\newcommand{\mbold}{\mathbf}
\newcommand{\tbold}{\textbf}
\newcommand{\ital}{\textit}
\newcommand{\CAPS}{\textsc}
\newcommand{\slant}{\textsl}
\newcommand{\bemph}[1]{\tbold{\emph{#1}}}
%All-notes commands
\newcounter{le}
\setcounter{le}{0}
\newcommand{\lez}[1]{Lezione~\arabic{le}:~#1}
\newcommand{\Lez}[1]{\incle\chapter{\lez{#1}}}
\newcommand{\incle}[0]{\refstepcounter{le}}
\newcounter{ee}
\setcounter{ee}{0}
\newcommand{\eserc}[1]{Esercitazione~\arabic{ee}:~#1}
\newcommand{\Eserc}[1]{\incee\chapter{\eserc{#1}}}
\newcommand{\incee}[0]{\refstepcounter{ee}}
%%Greek letters
\newcommand{\bag}{\alpha}
\newcommand{\ag}{\scb{0.85}[0.85]{$\alpha$}}
\newcommand{\eag}{\expsc{\ag}}
\newcommand{\bbg}{\beta}
\newcommand{\bg}{\tallsc{\bbg}}
\newcommand{\ebg}{\expsc{\bbg}}
\newcommand{\bgg}{\gamma}
\let\oldgg\gg%
\renewcommand{\gg}{\normsc{\bgg}}
\newcommand{\tgg}{\tallsc{\bgg}}
\newcommand{\egg}{\expsc{\bgg}}
\newcommand{\bdg}{\delta}
\newcommand{\dg}{\tallsc{\bdg}}
\newcommand{\edg}{\expsc{\bdg}}
\newcommand{\beg}{\varepsilon}
\newcommand{\eg}{\normsc{\beg}}
\newcommand{\eeg}{\expsc{\beg}}
\newcommand{\bzg}{\zeta}
\newcommand{\zg}{\tallsc{\bzg}}
\newcommand{\ezg}{\expsc{\bzg}}
\newcommand{\bhg}{\eta}
\newcommand{\hg}{\normsc{\bhg}}
\newcommand{\thg}{\tallsc{\bhg}}
\newcommand{\ehg}{\expsc{\bhg}}
\newcommand{\bqg}{\theta}
\newcommand{\qg}{\scb{0.95}[0.95]{$\bqg$}}
\newcommand{\eqg}{\scb{0.7}[0.7]{$\bqg$}}
\newcommand{\biog}{\iota}
\newcommand{\ig}{\normsc{\biog}}
\newcommand{\eig}{\expsc{\biog}}
\newcommand{\bkg}{\kappa}
\newcommand{\kg}{\normsc{\bkg}}
\newcommand{\ekg}{\expsc{\bkg}}
\let\oldlg\lg%
\newcommand{\blg}{\lambda}
\renewcommand{\lg}{\tallsc{\blg}}
\newcommand{\elg}{\expsc{\blg}}
\newcommand{\bmg}{\mu}
\newcommand{\mg}{\normsc{\bmg}}
\newcommand{\tmg}{\tallsc{\bmg}}
\newcommand{\emg}{\expsc{\bmg}}
\let\oldng\ng%
\newcommand{\bng}{\nu}
\renewcommand{\ng}{\normsc{\bng}}
\newcommand{\eng}{\expsc{\bng}}
\newcommand{\bjg}{\xi}
\newcommand{\jg}{\tallsc{\bjg}}
\newcommand{\ejg}{\expsc{\jg}}
\newcommand{\bog}{\omicron}
\newcommand{\og}{\scb{0.96}[0.96]{$\bog$}}
\newcommand{\eog}{\scb{0.72}[0.72]{$\bog$}}
\newcommand{\bpg}{\pi}
\newcommand{\pg}{\normsc{\bpg}}
\newcommand{\epg}{\expsc{\bpg}}
\newcommand{\brg}{\rho}
\newcommand{\rg}{\normsc{\brg}}
\newcommand{\trg}{\tallsc{\brg}}
\newcommand{\erg}{\expsc{\brg}}
\newcommand{\bsg}{\sigma}
\newcommand{\sg}{\normsc{\bsg}}
\newcommand{\esg}{\expsc{\bsg}}
\newcommand{\btg}{\tau}
\newcommand{\tg}{\tallsc{\btg}}
\newcommand{\etg}{\expsc{\btg}}
\newcommand{\bug}{\upsilon}
\newcommand{\ug}{\normsc{\bug}}
\newcommand{\eug}{\expsc{\bug}}
\newcommand{\bfg}{\varphi}
\newcommand{\fg}{\normsc{\bfg}}
\newcommand{\tfg}{\tallsc{\bfg}}
\newcommand{\efg}{\expsc{\bfg}}
\newcommand{\bxg}{\chi}
\newcommand{\xg}{\normsc{\bxg}}
\newcommand{\txg}{\tallsc{\bxg}}
\newcommand{\exg}{\expsc{\bxg}}
\newcommand{\byg}{\psi}
\newcommand{\yg}{\normsc{\byg}}
\newcommand{\tyg}{\tallsc{\byg}}
\newcommand{\eyg}{\expsc{\byg}}
\newcommand{\bwg}{\omega}
\newcommand{\wg}{\normsc{\bwg}}
\newcommand{\ewg}{\expsc{\bwg}}
\newcommand{\Mag}{\mathclap{\ag}}
\newcommand{\meag}{\mathclap{\eag}}
\newcommand{\mbg}{\mathclap{\bg}}
\newcommand{\mebg}{\mathclap{\ebg}}
\newcommand{\mgg}{\mathclap{\gg}}
\newcommand{\megg}{\mathclap{\egg}}
\newcommand{\mtgg}{\mathclap{\tgg}}
\newcommand{\mdg}{\mathclap{\dg}}
\newcommand{\medg}{\mathclap{\edg}}
\newcommand{\meg}{\mathclap{\eg}}
\newcommand{\meeg}{\mathclap{\eeg}}
\newcommand{\mzg}{\mathclap{\zg}}
\newcommand{\mezg}{\mathclap{\ezg}}
\newcommand{\mhg}{\mathclap{\hg}}
\newcommand{\mthg}{\mathclap{\thg}}
\newcommand{\mehg}{\mathclap{\ehg}}
\newcommand{\mqg}{\mathclap{\qg}}
\newcommand{\meqg}{\mathclap{\eqg}}
\newcommand{\mig}{\mathclap{\ig}}
\newcommand{\meig}{\mathclap{\eig}}
\newcommand{\mkg}{\mathclap{\kg}}
\newcommand{\mekg}{\mathclap{\ekg}}
\newcommand{\mlg}{\mathclap{\lg}}
\newcommand{\melg}{\mathclap{\elg}}
\newcommand{\mmg}{\mathclap{\mg}}
\newcommand{\mtmg}{\mathclap{\tmg}}
\newcommand{\memg}{\mathclap{\emg}}
\newcommand{\mng}{\mathclap{\ng}}
\newcommand{\meng}{\mathclap{\eng}}
\newcommand{\mog}{\mathclap{\og}}
\newcommand{\meog}{\mathclap{\eog}}
\newcommand{\mpg}{\mathclap{\pg}}
\newcommand{\mepg}{\mathclap{\epg}}
\newcommand{\mrg}{\mathclap{\rg}}
\newcommand{\merg}{\mathclap{\erg}}
\newcommand{\mtrg}{\mathclap{\trg}}
\newcommand{\msg}{\mathclap{\sg}}
\newcommand{\mesg}{\mathclap{\esg}}
\newcommand{\mtg}{\mathclap{\tg}}
\newcommand{\metg}{\mathclap{\etg}}
\newcommand{\mug}{\mathclap{\ug}}
\newcommand{\meug}{\mathclap{\eug}}
\newcommand{\mfg}{\mathclap{\fg}}
\newcommand{\mtfg}{\mathclap{\tfg}}
\newcommand{\mefg}{\mathclap{\efg}}
\newcommand{\mxg}{\mathclap{\xg}}
\newcommand{\mtxg}{\mathclap{\txg}}
\newcommand{\mexg}{\mathclap{\exg}}
\newcommand{\myg}{\mathclap{\yg}}
\newcommand{\mtyg}{\mathclap{\tyg}}
\newcommand{\meyg}{\mathclap{\eyg}}
\newcommand{\mwg}{\mathclap{\wg}}
\newcommand{\mewg}{\mathclap{\ewg}}
\newcommand{\vr}{\varrho}
\newcommand{\vs}{\varsigma}
\newcommand{\vq}{\vartheta}
\newcommand{\luneps}{\epsilon}%Apparently there is no difference between varepsilon and epsilon which IS strange as I had seen it before.
%A good scaling for Greek CAPS is 0.96.
\newcommand{\Gg}{\Gamma}
\newcommand{\Dg}{\Delta}
\newcommand{\Qg}{\Theta}
\newcommand{\Lg}{\Lambda}
\newcommand{\Jg}{\Xi}
\newcommand{\Pg}{\Pi}
\newcommand{\Sg}{\Sigma}
\newcommand{\Fg}{\Phi}
\newcommand{\Yg}{\Psi}
\newcommand{\Wg}{\Omega}
\newcommand{\dig}{\digamma}
%%Mathbb letters
\newcommand{\A}{\mathbb A}
\let\stroke\B %
\renewcommand{\B}{\mathbb B}
\let\undefined\C %
\renewcommand{\C}{\mathbb C}
\newcommand{\D}{\mathbb D}
\newcommand{\E}{\mathbb E}
\newcommand{\F}{\mathbb F}
\let\dgrave\G %
\renewcommand{\G}{\mathbb G}
\let\dacute\H %
\renewcommand{\H}{\mathbb H}
\newcommand{\I}{\mathbb I}
\newcommand{\J}{\mathbb J}
\newcommand{\K}{\mathbb K}
\let\strL\L %
\renewcommand{\L}{\mathbb L}
\let\ogon\M %
\renewcommand{\M}{\mathbb M}
\newcommand{\N}{\mathbb N}
\let\barO\O %
\renewcommand{\O}{\mathbb O}
\let\lfchar\P %
\renewcommand{\P}{\mathbb P}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\let\parmark\S %
\renewcommand{\S}{\mathbb S}
\let\txtilde\~ %
\newcommand{\tildehook}[1]{\txtilde{\m{#1}}} % the old value of \T is \~{\m, where \~ was formerly a tilde (whence the \let above) and \m is a hook. Of course, \let\tildehook\T won't work as I subsequently rename \~ to be \sim, making \T invalid in both text and math mode, being \m invalid in math mode and \~ (\sim) invalid in text mode. This explains the \newcommand here instead of \let.
\renewcommand{\T}{\mathbb T} %
\let\dvertabove\U %
\renewcommand{\U}{\mathbb U}
\newcommand{\V}{\mathbb V}
\newcommand{\W}{\mathbb W}
\newcommand{\X}{\mathbb X}
\newcommand{\Y}{\mathbb Y}
\newcommand{\Z}{\mathbb Z}
\DeclareSymbolFont{bbold}{U}{bbold}{m}{n}
\DeclareSymbolFontAlphabet{\bbo}{bbold}
\newcommand{\mrm}{\mathrm}
%Hebrew
\newcommand{\alef}{\aleph}
\newcommand{\bet}{\beth}
%%Set theory
\newcommand{\sps}{\!\supset\!}
\newcommand{\spse}{\!\supseteq\!}
\newcommand{\sbs}{\!\subset\!}
\newcommand{\sbse}{\!\subseteq\!}
\newcommand{\nsps}{\!\not\supset\!}
\newcommand{\nspse}{\!\not\supseteq\!}
\newcommand{\nsbs}{\!\not\subset\!}
\newcommand{\nsbse}{\!\not\subseteq\!}
\newcommand{\nin}{\!\not \in\!}
\newcommand{\nni}{\!\not \ni\!}
\newcommand{\xin}{\!\in\!}
\newcommand{\xni}{\!\ni\!}
\newcommand{\bun}{\displaystyle\bigcup}
\newcommand{\bint}{\displaystyle\bigcap}
%%Operators
\DeclareMathOperator{\spam}{span}
\newcommand{\spn}{\spam}
\DeclareMathOperator{\re}{Re}
\DeclareMathOperator{\im}{Im}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\cof}{cof}
\DeclareMathOperator{\graf}{graf}
\newcommand{\Graf}[1]{\graf\pa{#1}}
\DeclareMathOperator{\Mat}{Mat}
\DeclareMathOperator{\mis}{mis}%
\DeclareMathOperator{\diam}{diam}%
\DeclareMathOperator{\MCDo}{M.C.D.}
\newcommand{\MCD}[1]{\MCDo\pa{#1}}
\DeclareMathOperator{\mcmo}{m.c.m.}
\newcommand{\mcm}[1]{\mcmo\pa{#1}}
\DeclareMathOperator{\mcdo}{m.c.d.}
\newcommand{\mcd}[1]{\mcdo\pa{#1}}
%%General Maths
%%%[Fractions and similar
\newcommand{\fr}{\dfrac}
\newcommand{\bnm}{\binom}
\newcommand{\of}[2]{\nicefrac{^{#1}}{_{#2}}}
\newcommand{\mf}[2]{^{#1}\scb{0.5}[1]{/}_{#2}}
\newcommand{\dfr}[2]{\dsi{\fr{#1}{#2}}}
\newcommand{\dbfr}[2]{\dsib{\fr{#1}{#2}}}
\newcommand{\Der}[2][]{\fr{\dd #1}{\dd #2}}
\newcommand{\pDer}[2][]{\fr{\pd #1}{\pd #2}}
\newcommand{\xof}[2]{\raisebox{-3pt}{\scb{2}[2]{$\of{\scb{0.5}[0.5]{$#1$}\!\!}{\raisebox{-1pt}{\hsp{-2pt}\scb{0.5}[0.5]{$#2$}}}$}}}
%]
%%%[Relational Operators and other undeclared Operators
\newcommand{\grad}{\nabla}
\newcommand{\pd}{\partial}
\renewcommand{\~}{\sim}
\newcommand{\dsim}{\approx}
\newcommand{\per}{\cdot}
\newcommand{\rad}{\sqrt}
\newcommand{\cng}{\equiv}
\newcommand{\ncng}{\not\equiv}
\newcommand{\omeo}{\cong}
\newcommand{\nomeo}{\ncong}
\newcommand{\prop}{\propto}
\newcommand{\dsum}{\displaystyle\sum}
\newcommand{\dprod}{\displaystyle\prod}
\newcommand{\dlim}{\displaystyle\lim}
\newcommand{\dmin}{\displaystyle\min}
\newcommand{\dmax}{\displaystyle\max}
\newcommand{\dsup}{\displaystyle\sup}
\newcommand{\dinf}{\displaystyle\inf}
\newcommand{\xsum}[2]{\overset{\mcl{\dsi{\ssst#2}}}{\underset{\mcl{\dsi{\ssst#1}}}{\sum}}}
\newcommand{\xprod}[2]{\overset{\mcl{\dsi{\ssst#2}}}{\underset{\mcl{\dsi{\ssst#1}}}{\prod}}}
\newcommand{\xlim}[1]{\underset{\mcl{\dsi{\ssst #1}}}{\lim}}
\newcommand{\xmin}[2]{\overset{\mcl{\dsi{\ssst#2}}}{\underset{\mcl{\dsi{\ssst#1}}}{\min}}}
\newcommand{\xmax}[2]{\overset{\mcl{\dsi{\ssst#2}}}{\underset{\mcl{\dsi{\ssst#1}}}{\max}}}
\newcommand{\xsup}[1]{\underset{\mcl{\dsi{\ssst #1}}}{\sup}}
\newcommand{\xinf}[1]{\underset{\mcl{\dsi{\ssst #1}}}{\inf}}
\newcommand{\x}{\times}
\newcommand{\ssm}{\smallsetminus}
\newcommand{\xint}{\di\int\limits}
\newcommand{\xints}[2]{\xint_{#1\,\,\,\,}^{\,\,\,\,#2}}
\newcommand{\xiint}{\di\iint\limits}
\newcommand{\xiints}[2]{\xiint_{#1\,\,\,\,}^{\,\,\,\,#2}}
\newcommand{\xiiint}{\di\iiint\limits}
\newcommand{\xiiints}[2]{\xiiint_{#1\,\,\,\,}^{\,\,\,\,#2}}
\newcommand{\xiiiint}{\di\iiiint\limits}
\newcommand{\xiiiints}[2]{\xiiiint_{#1\,\,\,\,}^{\,\,\,\,#2}}
\newcommand{\xidotsint}{\di\idotsint\limits}
\newcommand{\xidotsints}[2]{\xidotsint_{#1\,\,\,\,}^{\,\,\,\,#2}}
\newcommand{\eval}[2]{\scb{0.5}[1]{$\fvb$}_{#1}^{#2}}
\newcommand{\xfvb}{\eval{}{}}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\sdd}{\,\mrm{d}}
\newcommand{\dotcup}{\ensuremath{\mathaccent\cdot\cup}}
\newcommand{\dsimm}{\raisebox{1.2pt}{\scb{0.6}[0.6]{$\triangle$}}}

\LetLtxMacro{\oldsqrt}{\sqrt} % makes all sqrts closed
\renewcommand{\sqrt}[1][\ ]{%
  \def\DHLindex{#1}\mathpalette\DHLhksqrt}
\def\DHLhksqrt#1#2{%
  \setbox0=\hbox{$#1\oldsqrt[\DHLindex]{#2\,}$}\dimen0=\ht0
  \advance\dimen0-0.2\ht0
  \setbox2=\hbox{\vrule height\ht0 depth -\dimen0}%
  {\box0\lower0.71pt\box2}}
%%%[Arrows above, below and beside
\newcommand{\vct}{\overrightarrow}
\newcommand{\sv}{\underrightarrow}
\newcommand{\iv}{\overleftarrow}
\newcommand{\isv}{\underleftarrow}
\newcommand{\sse}{\Longleftrightarrow}
\newcommand{\slse}{\Longleftarrow}
\newcommand{\hla}{\hookleftarrow}
\newcommand{\hra}{\hookrightarrow}
\newcommand{\xright}{\xrightarrow}
\newcommand{\xleft}{\xleftarrow}
\newcommand{\xbright}{\xRightarrow}
\newcommand{\xbleft}{\xLeftrightarrow}
\newcommand{\xhleft}{\xhookleftarrow}
\newcommand{\xhright}{\xhookrightarrow}
\newcommand{\xmaps}{\xmapsto}
\newcommand{\xto}{\!\to\!}
%]
%%%[Logical symbols and quantifiers
\newcommand{\3}{\exists}
\newcommand{\ex}{\exists}
\newcommand{\nex}{\nexists}
\newcommand{\et}{\wedge}
\newcommand{\vel}{\vee}
\newcommand{\VA}{\forall}
%]
\newcommand{\s}{\mathcal}
\newcommand{\f}{\mathfrak}
\newcommand{\8}{\infty}
\newcommand{\0}{\varnothing}
\newcommand{\cl}[2]{[ #1 ]_#2}
%%%[Bracketing
\newcommand{\ang}[1]{\left\langle#1\right\rangle}
\newcommand{\pa}[1]{\left(#1\right)}
\newcommand{\sq}[1]{\left[#1\right]}
\newcommand{\br}[1]{\left\lbrace#1\right\rbrace}
\newcommand{\pasq}[1]{\left(#1\right]}
\newcommand{\sqpa}[1]{\left[#1\right)}
\newcommand{\pabr}[1]{\left(#1\right\rbrace}
\newcommand{\brpa}[1]{\left\lbrace#1\right)}
\newcommand{\sqbr}[1]{\left[#1\right\rbrace}
\newcommand{\brsq}[1]{\leftlbrace#1\right]}
\newcommand{\paang}[1]{\left(#1\right\rangle}
\newcommand{\angpa}[1]{\left\langle#1\right)}
\newcommand{\sqang}[1]{\left[#1\right\rangle}
\newcommand{\angsq}[1]{\left\langle#1\right]}
\newcommand{\brang}[1]{\left\rbrace#1\right\rangle}
\newcommand{\angbr}[1]{\left\langle#1\right\rbrace}
\newcommand{\lf}{\left}
\newcommand{\rt}{\right}
\newcommand{\abs}[1]{\left\vert#1\right\vert}
\newcommand{\norm}[1]{\left\|#1\right\|}
\newcommand{\mpa}[1]{\pa{\!\!\!\!#1\!\!\!\!}}
\newcommand{\msq}[1]{\sq{\!\!\!\!#1\!\!\!\!}}
\newcommand{\mbr}[1]{\br{\!\!\!\!#1\!\!\!\!}}
%]
%%%[Display modifiers
\newcommand{\us}[2]{\underset{#2}{#1}}
\newcommand{\os}[2]{\overset{#2}{#1}}
\newcommand{\ous}[3]{\os{\us{#1}{#2}}{#3}}
\newcommand{\uos}[3]{\us{\os{#1}{#3}}{#2}}
\newcommand{\di}{\displaystyle}
\newcommand{\pusher}{\scb{0}[1]{{\color{white}$\fr{}{}_\whitea$}}}
\newcommand{\push}[1][1]{\scb{#1}[#1]{$\dbfr{}{}$}}
\newcommand{\dpusher}{\scb{0}[1]{{\color{white}$\fr{}{}^\whitea$}}}
\newcommand{\mcl}{\mathclap}
\newcommand{\sstack}{\substack}
\newcommand{\ubr}{\underbrace}
\newcommand{\ubrk}{\underbracket}
%]
%%%[Accents and dots
\newcommand{\ubar}{\underline}
\newcommand{\lbar}{\overline}
\newcommand{\sdot}[1]{\underset{^{^{^{^{\scb{1.3}[1.3]{\,.}}}}}}{#1}}
\newcommand{\sddot}[1]{\underset{^{^{^{^{\scb{1.3}[1.3]{\,..}}}}}}{#1}}
\newcommand{\stdot}[1]{\underset{^{^{^{^{\scb{1.3}[1.3]{\,...}}}}}}{#1}}
\newcommand{\tdot}[1]{\overset{_{\scb{1.1}[1.1]{...}}}{#1}}
\newcommand{\tupdot}[1]{$\dot{\hbox{#1}}$}
\newcommand{\tddot}[1]{$\ddot{\hbox{#1}}$}
\newcommand{\ttdot}[1]{$\tdot{\hbox{#1}}$}
\newcommand{\tsdot}[1]{$\sdot{\hbox{#1}}$}
\newcommand{\tsddot}[1]{$\sddot{\hbox{#1}}$}
\newcommand{\tstdot}[1]{$\stdot{\hbox{#1}}$}
\newcommand{\pint}[1]{\mathaccent23{#1}}
\newcommand{\dvect}[1]{\dot{\vct{#1}}}
\newcommand{\dlbar}[1]{\lbar{\lbar{#1}}}
\newcommand{\dubar}[1]{\ubar{\ubar{#1}}}
\newcommand{\mdot}[1]{\dot{#1\,\,}\!\!}
\newcommand{\mddot}[1]{\ddot{#1\,\,}\!\!}
\newcommand{\mtdot}[1]{\tdot{#1\,\,}\!\!}
\newcommand{\msdot}[1]{\sdot{#1\,\,}\!\!}
\newcommand{\msddot}[1]{\sddot{#1\,\,}\!\!}
\newcommand{\mstdot}[1]{\stdot{#1\,\,}\!\!}
\newcommand{\mtupdot}[1]{\tupdot{#1\,\,}\!\!}
\newcommand{\mtddot}[1]{\tddot{#1\,\,}\!\!}
\newcommand{\mttdot}[1]{\ttdot{#1\,\,}\!\!}
\newcommand{\mtsdot}[1]{\tsdot{#1\,\,}\!\!}
\newcommand{\mtsddot}[1]{\tsddot{#1\,\,}\!\!}
\newcommand{\mtstdot}[1]{\tstdot{#1\,\,}\!\!}
\newcommand{\mtilde}[1]{\tilde{#1\,\,}\!\!}

%%%[Miscellanea
\newcommand{\olvb}{\,\,\scalebox{1}[1.2]{$\left|\scalebox{0.1}[1]{{\color{white}$^a_b$}}\right.$}}
\newcommand{\fvb}{\,\,\left|\scalebox{0.1}[1]{{\color{white}$\fr{^a}{_b}$}}\right.}
\newcommand{\1}{\prime}
\newcommand{\case}[1]{\left\lbrace\mat{@{\,}cl@{}}#1\emat\right.}
\newcommand{\mat}{\begin{array}}
\newcommand{\emat}{\end{array}}
\newcommand{\blockmatLineVColVLetter}[8]{\scb{0.1}[1]{$\mat{c}%
\scb{10}[1]{$\mat{cccc}#1&#2&#3&#4\\\emat$}  \\%
\mat{ll}%
\scb{10}[1]{$\mat{l}#5\\#6\\#7\\\emat$}\scb{10}[1]{\hsp{0.3cm}}  &  \scb{0.625}[0.0625]{$\mat{l}\\\scalebox{48}[48]{$^{#8}$\hsp{0.2cm}}\\\emat$}\\%
\emat%
\emat$}} %Makes a block matrix much like the A at the beginning of page 62, with parameters #1 through #4 in the line vector which is the first line of the matrix, parameters #5 through #7 in the column vector which contains the three v^i in that A, and parameter #8 in the place of the maxi R of that A. It is advisable to use parameters similar to that of the A matrix above mentioned, because using parameters wider that those of that matrix may cause decentering and an ugly resulting output of the matrix.
%]
\newcommand{\block}[9][-5]{\!\!\mat{c|ccc}#2&#3&#4&#5\\\hline#6&\multicolumn{3}{c}{\multirow{3}{*}{\raisebox{#1pt}{\Huge{$#9$}}}}\\#7&\\#8&\emat\!\!}
\DeclareMathOperator{\diag}{diag}
\newcommand{\blocks}[9][-10]{\!\!\mat{cccc}#2&#3\hsp{-0.2cm}&\multicolumn{2}{r}{\multirow{2}{*}{\raisebox{-14pt}{\scb{1}[1.3]{\Huge{|}}}\hsp{0.2cm}\raisebox{#1pt}{\Huge{$#6$}}}}\\#4&#5\hsp{-0.2cm}\\[0.2em]\hline\multicolumn{2}{r}{\multirow{2}{*}{\raisebox{#9pt}{\Huge{$#7$}\hsp{-0.2cm}}}}&\multicolumn{2}{r}{\multirow{2}{*}{\raisebox{-5pt}{\scb{1}[1]{\Huge{|}}}\hsp{0.2cm}\raisebox{#9pt}{\Huge{$#8$}}}}\\\\\emat\!\!}

%%Footnotes and associated
\newcommand{\fn}{\footnote}
\newcommand{\fnt}{\footnotetext}
\newcommand{\fnm}{\footnotemark}
\newcommand{\ic}{\addtocounter}
\newcommand{\ifnc}{\ic{footnote}}
\makeatletter
\def\blfn{\xdef\@thefnmark{}\@footnotetext}
\makeatother
\newcommand{\rmfn}{\renewcommand{\thefootnote}{\roman{footnote}}}
\newcommand{\Rmfn}{\renewcommand{\thefootnote}{\Roman{footnote}}}
\newcommand{\afn}{\renewcommand{\thefootnote}{\alph{footnote}}}
\newcommand{\Afn}{\renewcommand{\thefootnote}{\Alph{footnote}}}
\newcommand{\symbfn}{\renewcommand{\thefootnote}{\fnsymbol{footnote}}}
\newcommand{\setfnm}{\renewcommand{\thefootnote}}
\newcommand{\fnmreset}{\renewcommand{\thefootnote}{\arabic{footnote}}}

%%Text sectioning, lists
\newcommand{\sect}{\section}
\newcommand{\ssect}{\subsection}
\newcommand{\sssect}{\subsubsection}
\newcommand{\secta}{\section*}
\newcommand{\ssecta}{\subsection*}
\newcommand{\sssecta}{\subsubsection*}
\newcommand{\ben}{\begin{enumerate}}
\newcommand{\een}{\end{enumerate}}
\newcommand{\bde}{\begin{description}}
\newcommand{\ede}{\end{description}}
\newcommand{\bi}{\begin{itemize}}
\newcommand{\ei}{\end{itemize}}
\newcommand{\spar}{\hsp{0.55cm}}
\newcommand{\whitea}{{\color{white}a}}
\newcommand{\xwhitea}{\scb{0}[1]{\whitea}}
\newcommand{\lfeed}{\hsp{0cm}\\}

%%Environments
\newenvironment{sistema}%
{\left \lbrace \begin{array}{@{}l@{}}}%l
{\end{array}\right.}
\newtheorem{defi}{Definizione}[section]
\newtheorem{teor}{Teorema}[section]
\newtheorem{es}{Esempio}[section]
\newtheorem{ese}{Esercizio}[section]
\newtheorem{pt}{Punto}
\newtheorem{riass}{Riassunto}
\newtheorem{propo}{Proposizione}[section]
\newtheorem{oss}{Osservazione}[section]
\newtheorem{cor}{Corollario}[section]
\newtheorem{esecasa}{Esercizio svolto da me}[chapter]
\newtheorem{esecasab}{Esercizio svolto da me}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{fatto}{Fatto}[section]
\newtheorem{eseese}{Esercizio Masieriano}[section]% to be adapted to the notes' subject,  naturally

%%Graphic scalings
\newcommand{\scb}{\scalebox}
\newcommand{\scbtt}{\scb{0.1}[1]}
\newcommand{\scbt}{\scb{10}[1]}
\newcommand{\ta}[2]{\scbtt{$\left.\begin{array}{c} \scbt{$#1$} \\ \scbt{$#2$} \\ \end{array}\right.$}}
\newcommand{\dsi}[1]{\scalebox{0.7}[0.7]{$#1$}}
\newcommand{\dsib}[1]{\scb{0.5}[0.5]{$#1$}}
\newcommand{\scaleOpointnine}[1]{\scalebox{0.9}[0.9]{$#1$}}
\newcommand{\expsc}[1]{\scb{0.65}[0.65]{$#1$}}
\newcommand{\normsc}[1]{\scb{0.85}[0.85]{$#1$}}
\newcommand{\tallsc}[1]{\scb{0.88}[0.88]{$#1$}}

%%Text positioning
\newcommand{\tsup}[1]{$^{\hbox{#1}}$}
\newcommand{\tsub}[1]{$_{\hbox{#1}}$}
\newcommand{\tus}[2]{$\us{\hbox{#1}}{\hbox{#2}}$}
\newcommand{\tos}[2]{$\os{\hbox{#1}}{\hbox{#2}}$}
\newcommand{\tous}[3]{$\ous{\hbox{#1}}{\hbox{#2}}{\hbox{3}}$}
\newcommand{\tuos}[3]{$\uos{\hbox{#1}}{\hbox{#2}}{\hbox{#3}}$}
\newcommand{\centre}[1]{$$\hbox{\ital{#1}}$$}
\newcommand{\hsp}{\hspace}
\newcommand{\vsp}{\vspace}

%%Other
\newcommand{\tick}{\checkmark}
\newcommand{\crux}{\dagger}
\newcommand{\dcrux}{\ddagger}
\newcommand{\hs}{\heartsuit}
\newcommand{\ds}{\diamondsuit}
\newcommand{\cs}{\clubsuit}
\let\sz\ss
\renewcommand{\ss}{\spadesuit}
\newcommand{\tcrux}{$\dagger$}
\newcommand{\tdcrux}{$\ddagger$}
\newcommand{\ths}{$\heartsuit$}
\newcommand{\tds}{$\diamondsuit$}
\newcommand{\tcs}{$\clubsuit$}
\newcommand{\tss}{$\spadesuit$}
\newcommand{\bs}{\backslash}
\newcommand{\tbs}{$\bs$}
\newcommand{\bk}{\Gr{ }}