notes/tex/latex/style/personal_commands.sty

\ProvidesPackage{personal_commands}

\usepackage{amsmath,amssymb}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{amsopn}
\usepackage{mathtools}
\usepackage{stmaryrd}
\usepackage{marvosym}
\usepackage{float}

\hfuzz=\maxdimen
\tolerance=10000
\hbadness=10000

\newcommand{\system}[1]{\begin{cases} #1 \end{cases}}

% Modalità matematica/fisica
\renewcommand{\vec}[1]{\underline{#1}}

\newcommand{\lemmaref}[1]{\textit{Lemma \ref{#1}}}
\newcommand{\thref}[1]{\textit{Teorema \ref{#1}}}

\newcommand{\li}[0]{$\blacktriangleright\;\;$}

\newcommand{\tendsto}[1]{\xrightarrow[\text{$x \to #1$}]{}}
\newcommand{\tendston}[0]{\xrightarrow[\text{$n \to \infty$}]{}}

\setlength\parindent{0pt}

% Principio di induzione e setup dimostrativi.
\newcommand{\basestep}{(\textit{passo base})\;}
\newcommand{\inductivestep}{(\textit{passo induttivo})\;}

\newcommand{\rightproof}{($\,\implies$)\;}
\newcommand{\leftproof}{($\impliedby$)\;}

% Spesso utilizzati al corso di Fisica 1.
\newcommand{\dx}{\dot{x}}
\newcommand{\ddx}{\ddot{x}}
\newcommand{\dv}{\dot{v}}

\newcommand{\tendstot}[0]{\xrightarrow[\text{$t \to \infty$}]{}}

% Spesso utilizzati al corso di Analisi 1.
%\newcommand{\liminf}{\lim_{x \to \infty}}
\newcommand{\liminfty}{\lim_{x \to \infty}}
\newcommand{\liminftym}{\lim_{x \to -\infty}}
\newcommand{\liminftyn}{\lim_{n \to \infty}}
\newcommand{\limzero}{\lim_{x \to 0}}
\newcommand{\limzerop}{\lim_{x \to 0^+}}
\newcommand{\limzerom}{\lim_{x \to 0^-}}

\newcommand{\xbar}{\overline{x}}
\newcommand{\RRbar}{\overline{\RR}}

% Spesso utilizzati al corso di Geometria 1.
\DeclareMathOperator{\val}{val}
\DeclareMathOperator{\Span}{Span}
\newcommand{\charpoly}[1]{p_{#1}}
\newcommand{\minpoly}[1]{\varphi_{#1}}
\newcommand{\valf}{\val_f}
\newcommand{\valfv}{\val_{f,\V}}
\newcommand{\e}[1]{\vec{e_{#1}}}
\newcommand{\V}{\vec{v}}
\newcommand{\VV}[1]{\vec{v_{#1}}}
\newcommand{\Matrix}[1]{\begin{pmatrix} #1 \end{pmatrix}}
\newcommand{\Vector}[1]{\begin{pmatrix} #1 \end{pmatrix}}

\let\v\undefined
\newcommand{\v}{\vec{v}}
\newcommand{\vv}[1]{\vec{v_{#1}}}

\newcommand{\mapstoby}[1]{\xmapsto{#1}}

% Comandi personali.

\newcommand{\card}[1]{\left|#1\right|}
\newcommand{\nsqrt}[2]{\!\sqrt[#1]{#2}\,}
\newcommand{\zeroset}{\{0\}}
\newcommand{\setminuszero}{\setminus \{0\}}

\theoremstyle{definition}

\let\abstract\undefined
\let\endabstract\undefined

\newtheorem*{abstract}{Abstract}
\newtheorem{corollary}{Corollario}
\newtheorem*{definition}{Definizione}
\newtheorem*{example}{Esempio}
\newtheorem{exercise}{Esercizio}
\newtheorem{lemma}{Lemma}
\newtheorem*{note}{Nota}
\newtheorem*{remark}{Osservazione}
\newtheorem*{proposition}{Proposizione}
\newtheorem*{summary}{Sommario}
\newtheorem*{theorem}{Teorema}

\newcommand{\basis}{\mathcal{B}}
\newcommand{\BB}{\mathcal{B}}

\newcommand{\HH}{\mathbb{H}}

\newcommand{\FFp}[1]{\mathbb{F}_p}
\newcommand{\FFpx}[1]{\mathbb{F}_p[x]}

\newcommand{\CCx}{\mathbb{C}[x]}

\newcommand{\KK}{\mathbb{K}}
\newcommand{\KKx}{\mathbb{K}[x]}

\newcommand{\QQx}{\mathbb{Q}[x]}
\newcommand{\RRx}{\mathbb{R}[x]}

\newcommand{\ZZi}{\mathbb{Z}[i]}
\newcommand{\ZZp}{\mathbb{Z}_p}
\newcommand{\ZZpx}{\mathbb{Z}_p[x]}
\newcommand{\ZZx}{\mathbb{Z}[x]}

\newcommand{\ii}{\mathbf{i}}
\newcommand{\jj}{\mathbf{j}}
\newcommand{\kk}{\mathbf{k}}

\newcommand{\bidual}[1]{#1^{**}}
\newcommand{\dual}[1]{#1^{*}}
\newcommand{\LL}[2]{\mathcal{L} \left(#1, \, #2\right)} % L(V, W)

\newcommand{\nsg}{\mathrel{\unlhd}} % sottogruppo normale

% 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{\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}

% Alcuni degli operatori più comunemente utilizzati.

\DeclareMathOperator{\Char}{char}
\DeclareMathOperator{\Dom}{Dom}
\DeclareMathOperator{\Fix}{\textit{Fix}\,}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\existsone}{\exists !}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Imm}{Imm}
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\MCD}{MCD}
\DeclareMathOperator{\Mor}{Mor}
\DeclareMathOperator{\mcm}{mcm}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\tr}{tr}

% Reimposta alcuni simboli presenti di default in LaTeX con degli analoghi
% più comuni.

\let\oldemptyset\emptyset
\let\emptyset\varnothing

% Trasforma alcuni simboli in operatori matematici.

\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}