mirror of https://github.com/hearot/notes
You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
174 lines
4.9 KiB
TeX
174 lines
4.9 KiB
TeX
\usepackage[top=1.5cm,bottom=1.5cm,left=1.5cm,right=1.5cm]{geometry}
|
|
\usepackage[utf8]{inputenc}
|
|
\usepackage[italian]{babel}
|
|
\usepackage{amsmath}
|
|
\usepackage{amssymb}
|
|
\usepackage{amsfonts}
|
|
\usepackage{amsthm}
|
|
\usepackage{stmaryrd}
|
|
\usepackage{mathrsfs} % per mathscr
|
|
\usepackage{graphicx} % ruota freccia per le azioni
|
|
\usepackage{marvosym} % per il \Lightning
|
|
\usepackage{array}
|
|
\usepackage{faktor} % per gli insiemi quoziente
|
|
\usepackage[colorlinks=false]{hyperref}
|
|
\usepackage{xparse} % per nuovi comandi con tanti input opzionali
|
|
\usepackage{relsize} % per \mathlarger
|
|
\usepackage{tikz-cd}
|
|
\usepackage{multicol}
|
|
\usepackage{multirow}
|
|
\usepackage{cancel}
|
|
\usepackage{enumerate}
|
|
\usepackage{soul}
|
|
\usepackage{nicefrac}
|
|
\usepackage{longtable}
|
|
\usepackage{pdflscape}
|
|
\usepackage{mathtools}
|
|
\usepackage{lmodern}
|
|
|
|
%\usepackage{tikz-3dplot}
|
|
%\usetikzlibrary{arrows.meta}
|
|
%\usetikzlibrary{intersections}
|
|
|
|
\DeclareMathOperator{\tr}{tr}
|
|
\DeclareMathOperator{\Int}{int}
|
|
|
|
\renewcommand{\vec}[1]{{\underline{#1}}}
|
|
|
|
\newcommand{\basis}{\mathcal{B}}
|
|
|
|
\newtheorem*{warn}{{\fontencoding{U}\fontfamily{futs}\selectfont\char 49\relax} \; Attenzione}
|
|
|
|
\newtheoremstyle{customth}
|
|
{\topsep}{\topsep}
|
|
{\itshape}{}{\bfseries}{.}{\newline}{}
|
|
|
|
\newtheoremstyle{customdef}
|
|
{\topsep}{\topsep}
|
|
{\normalfont}{}{\bfseries}{.}{\newline}{}
|
|
|
|
\newtheoremstyle{customrem}
|
|
{\topsep}{\topsep}
|
|
{\normalfont}{}{\itshape}{.}{\newline}{}
|
|
|
|
\theoremstyle{customth}
|
|
\newtheorem{theorem}{Teorema}[chapter]
|
|
\newtheorem{lemma}[theorem]{Lemma}
|
|
\newtheorem{corollary}[theorem]{Corollario}
|
|
\newtheorem{proposition}[theorem]{Proposizione}
|
|
\newtheorem{fact}[theorem]{Fatto}
|
|
\newtheorem{application}[theorem]{Applicazione}
|
|
\theoremstyle{customrem}
|
|
\newtheorem{remark}[theorem]{Osservazione\,}
|
|
\theoremstyle{customdef}
|
|
\newtheorem{definition}[theorem]{Definizione}
|
|
\newtheorem{notation}[theorem]{Notazione}
|
|
\newtheorem{example}[theorem]{Esempio}
|
|
|
|
\makeatletter
|
|
\renewenvironment{proof}[1][\proofname]{\par
|
|
\pushQED{\qed}%
|
|
\normalfont \topsep6\p@\@plus6\p@\relax
|
|
\trivlist
|
|
\item[\hskip\labelsep
|
|
\itshape
|
|
#1\@addpunct{.}]\mbox{}\\*
|
|
}{%
|
|
\popQED\endtrivlist\@endpefalse
|
|
}
|
|
\makeatother
|
|
|
|
%============ Simboli standard =================
|
|
\newcommand{\NN}{\mathbb{N}}
|
|
\newcommand{\ZZ}{\mathbb{Z}}
|
|
\newcommand{\RR}{\mathbb{R}}
|
|
\newcommand{\QQ}{\mathbb{Q}}
|
|
\newcommand{\CC}{\mathbb{C}}
|
|
\newcommand{\cc}{\mathcal{C}}
|
|
\newcommand{\TT}{\mathbb{T}}
|
|
|
|
\DeclareMathOperator{\ind}{ind}
|
|
\DeclareMathOperator{\mult}{mult}
|
|
|
|
\newcommand{\I}{\mathrm{I}}
|
|
\newcommand{\II}{\mathrm{II}}
|
|
|
|
\DeclareMathOperator{\SO}{SO}
|
|
\DeclareMathOperator{\rk}{rk}
|
|
|
|
\DeclareMathOperator{\vol}{vol}
|
|
\DeclareMathOperator{\crit}{crit}
|
|
|
|
\DeclareMathOperator{\Span}{span}
|
|
|
|
\newcommand{\defeq}{\overset{\mathrm{def}}{=}}
|
|
|
|
\DeclareMathOperator{\im}{im}
|
|
\DeclareMathOperator{\id}{id}
|
|
\DeclareMathOperator{\sgn}{sgn}
|
|
\DeclareMathOperator{\shape}{S}
|
|
|
|
\newcommand{\eps}{\varepsilon}
|
|
\renewcommand{\phi}{\varphi}
|
|
|
|
\newcommand{\der}[2]{\frac{\mathop{}\!\textnormal{\slshape d} #1}{\mathop{}\!\textnormal{\slshape d} #2}}
|
|
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
|
|
|
|
\newcommand{\dertime}[2]{\left. \der{}{t} #1 \right|_{#2}}
|
|
|
|
\newcommand*\dif{\mathop{}\!\textnormal{\slshape d}}
|
|
|
|
\let\oldemptyset\emptyset
|
|
\let\emptyset\varnothing
|
|
|
|
\newcommand{\dA}{\dif{A}}
|
|
\newcommand{\dx}{\dif{x}}
|
|
\newcommand{\dy}{\dif{y}}
|
|
\newcommand{\du}{\dif{u}}
|
|
\newcommand{\dv}{\dif{v}}
|
|
\newcommand{\ds}{\dif{s}}
|
|
\newcommand{\dt}{\dif{t}}
|
|
|
|
%\setcounter{secnumdepth}{1}
|
|
|
|
\newcommand{\restr}[2]{
|
|
#1\arrowvert_{#2}
|
|
}
|
|
|
|
\newcommand{\bigrestr}[2]{
|
|
#1\Big\arrowvert_{#2}
|
|
}
|
|
|
|
\newcommand{\inv}{^{-1}}
|
|
|
|
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
|
|
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
|
|
|
|
\NeedsTeXFormat{LaTeX2e}
|
|
%\ProvidesPackage{quiver}[2021/01/11 quiver]
|
|
|
|
% `tikz-cd` is necessary to draw commutative diagrams.
|
|
\RequirePackage{tikz-cd}
|
|
% `amssymb` is necessary for `\lrcorner` and `\ulcorner`.
|
|
\RequirePackage{amssymb}
|
|
% `calc` is necessary to draw curved arrows.
|
|
\usetikzlibrary{calc}
|
|
% `pathmorphing` is necessary to draw squiggly arrows.
|
|
\usetikzlibrary{decorations.pathmorphing}
|
|
|
|
% A TikZ style for curved arrows of a fixed height, due to AndréC.
|
|
\tikzset{curve/.style={settings={#1},to path={(\tikztostart)
|
|
.. controls ($(\tikztostart)!\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
|
|
and ($(\tikztostart)!1-\pv{pos}!(\tikztotarget)!\pv{height}!270:(\tikztotarget)$)
|
|
.. (\tikztotarget)\tikztonodes}},
|
|
settings/.code={\tikzset{quiver/.cd,#1}
|
|
\def\pv##1{\pgfkeysvalueof{/tikz/quiver/##1}}},
|
|
quiver/.cd,pos/.initial=0.35,height/.initial=0}
|
|
|
|
% TikZ arrowhead/tail styles.
|
|
\tikzset{tail reversed/.code={\pgfsetarrowsstart{tikzcd to}}}
|
|
\tikzset{2tail/.code={\pgfsetarrowsstart{Implies[reversed]}}}
|
|
\tikzset{2tail reversed/.code={\pgfsetarrowsstart{Implies}}}
|
|
% TikZ arrow styles.
|
|
\tikzset{no body/.style={/tikz/dash pattern=on 0 off 1mm}}
|