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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
%%%%%%%%% AUTHOR METADATA %%%%%%%%%% | ||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
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% Name | ||
\author{Pietro Monticone} | ||
% Affiliation | ||
\affil{Department of Mathematics, University of Trento} |
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%%%%%%%%%% THEOREM ENVIRONMENTS %%%%%%%%%% | ||
%\theoremstyle{•} | ||
% • plain: This is the default style. The header (e.g., "Theorem 1") is bolded and the body text is in italic. Both are on their own line. | ||
% • definition: The header is bolded, but the body text is not italicized. Both are on their own line. This style is typically used for definitions, examples, etc. | ||
% • remark: The header is italicized, the body text is not italicized, and both are run-in; that is, they appear on the same line. | ||
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% "Definition" style for definitions and axioms | ||
\theoremstyle{definition} | ||
\newtheorem{definition}{Definition} | ||
\newtheorem{axiom}{Axiom} | ||
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% "Plain" style for theorems, lemmas, corollaries and propositions | ||
\theoremstyle{plain} | ||
\newtheorem{theorem}{Theorem}[section] | ||
\newtheorem{lemma}[theorem]{Lemma} | ||
\newtheorem{corollary}[theorem]{Corollary} | ||
\newtheorem{proposition}[theorem]{Proposition} | ||
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% "Remark" style for examples, exercises, remarks, observations, solutions and notations | ||
\theoremstyle{remark} | ||
\newtheorem{example}[theorem]{Example} | ||
\newtheorem{non-example}[theorem]{Non Example} | ||
\newtheorem{exercise}[theorem]{Exercise} | ||
\newtheorem*{remark}{Remark} | ||
\newtheorem*{observation}{Observation} | ||
\newtheorem*{solution}{Solution} | ||
\newtheorem*{notation}{Notation} | ||
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%%%%%%%%%% BOXED ENVIRONMENTS %%%%%%%%%% | ||
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%\newtcbtheorem[number within=section, counter*=definition]{bthing}{Thing}{% | ||
% colframe=white!10!black, | ||
% colback=white!97!black, | ||
% coltitle=white, | ||
% fonttitle=\bfseries, | ||
%}{bthng} | ||
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% Notation Box | ||
\newtcbtheorem{bnotation}{Notation}{% | ||
colframe=white!10!black, | ||
colback=white!97!black, | ||
coltitle=white, | ||
fonttitle=\bfseries, | ||
}{bcpt} | ||
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% Concept Box | ||
\newtcbtheorem{bconcept}{Concept}{% | ||
colframe=white!10!black, | ||
colback=white!97!black, | ||
coltitle=white, | ||
fonttitle=\bfseries, | ||
}{bcpt} | ||
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% Axiom Box | ||
\newtcbtheorem{baxiom}{Axiom}{% | ||
colframe=white!10!black, | ||
colback=white!97!black, | ||
coltitle=white, | ||
fonttitle=\bfseries, | ||
}{bax} | ||
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% Definition Box | ||
%%%\newtcbtheorem[number within=section, use counter=definition]{bdefinition}{Definition}{% | ||
\newtcbtheorem[use counter=definition]{bdefinition}{Definition}{% | ||
colframe=white!10!black, | ||
colback=white!97!black, | ||
coltitle=white, | ||
fonttitle=\bfseries, | ||
}{bdef} | ||
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% Theorem Box | ||
\newtcbtheorem{btheorem}{Theorem}{% | ||
colframe=white!36!black, | ||
colback=white!97!black, | ||
coltitle=white, | ||
fonttitle=\bfseries, | ||
}{bthm} | ||
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% Lemma Box | ||
\newtcbtheorem{blemma}{Lemma}{% | ||
colframe=white!36!black, | ||
colback=white!97!black, | ||
coltitle=white, | ||
fonttitle=\bfseries, | ||
}{blmm} | ||
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% Proposition Box | ||
\newtcbtheorem{bproposition}{Proposition}{% | ||
colframe=white!36!black, | ||
colback=white!97!black, | ||
coltitle=white, | ||
fonttitle=\bfseries, | ||
}{bprop} | ||
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%%%%%%%%%%%% NOTATIONS %%%%%%%%%%%% | ||
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% Links | ||
\newcommand{\defref}[2]{\hyperref[def:#1]{\textbf{#2}}} | ||
\newcommand{\axref}[2]{\hyperref[ax:#1]{\textbf{#2}}} | ||
\newcommand{\thmref}[2]{\hyperref[thm:#1]{\textbf{#2}}} | ||
\newcommand{\lmmref}[2]{\hyperref[lmm:#1]{\textbf{#2}}} | ||
\newcommand{\bdefref}[2]{\hyperref[bdef:#1]{\textbf{#2}}} | ||
\newcommand{\baxref}[2]{\hyperref[bax:#1]{\textbf{#2}}} | ||
\newcommand{\bthmref}[2]{\hyperref[bthm:#1]{\textbf{#2}}} | ||
\newcommand{\blmmref}[2]{\hyperref[blmm:#1]{\textbf{#2}}} | ||
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% Basics | ||
\newcommand{\bb}[1]{\mathbb{#1}} % Blackboard bold font | ||
\newcommand{\cc}[1]{\mathcal{#1}} % Calligraphic font | ||
\newcommand{\dd}[1]{\mathrm{d}#1} % Differential operator | ||
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% Set | ||
\newcommand{\set}[1]{\ensuremath{\left\{#1\right\}}} | ||
\newcommand{\setb}[2]{\ensuremath{\left\{#1\mid#2\right\}}} | ||
%\newcommand{\set}[2]{\ensuremath{\left\{#1:#2\right\}}} | ||
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% Functions | ||
\newcommand{\fun}[3]{\ensuremath{#1:#2\to#3}} | ||
\newcommand{\id}{\ensuremath{\mathrm{id}}} | ||
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% Number sets | ||
\newcommand{\N}{\ensuremath{\mathbb{N}}} % Natural | ||
\newcommand{\Z}{\ensuremath{\mathbb{Z}}} % Integer | ||
\newcommand{\Q}{\ensuremath{\mathbb{Q}}} % Rational | ||
\newcommand{\R}{\ensuremath{\mathbb{R}}} % Real | ||
\newcommand{\C}{\ensuremath{\mathbb{C}}} % Complex | ||
\newcommand{\K}{\ensuremath{\mathbb{K}}} % Generic Field | ||
\newcommand{\F}{\ensuremath{\mathbb{F}}} % Generic Field | ||
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% Mathematical logic | ||
\newcommand{\imp}{\rightarrow} % Implication | ||
\newcommand{\biimp}{\leftrightarrow} % Biconditional | ||
\newcommand{\all}{\forall} % Universal quantifier | ||
\newcommand{\ex}{\exists} % Existential quantifier | ||
\newcommand{\sat}{\models} % Satisfies | ||
\newcommand{\ent}{\vdash} % Entails | ||
\newcommand{\nent}{\nvdash} % Does not entail | ||
\newcommand{\proves}{\vdash} % Proves | ||
\newcommand{\nproves}{\nvdash} % Does not prove | ||
\newcommand{\true}{\top} % Tautology | ||
\newcommand{\false}{\bot} % Contradiction | ||
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% Others | ||
\newcommand{\abs}[1]{\left|#1\right|} % Absolute value | ||
\newcommand{\avg}[1]{\left\langle#1\right\rangle} % Average value | ||
\newcommand{\norm}[1]{\left\|#1\right\|} % Norm | ||
\newcommand{\bra}[1]{\left\langle#1\right|} % Bra notation | ||
\newcommand{\ket}[1]{\left|#1\right\rangle} % Ket notation | ||
\newcommand{\braket}[2]{\left\langle#1\mid|#2\right\rangle} % Bra-ket notation | ||
\newcommand{\expect}[1]{\left\langle#1\right\rangle} % Expectation value | ||
\newcommand{\op}[1]{\hat{#1}} % Operator notation | ||
\newcommand{\comm}[2]{\left[#1,#2\right]} % Commutator | ||
\newcommand{\acomm}[2]{\left\{#1,#2\right\}} % Anticommutator | ||
\newcommand{\tr}[1]{\mathrm{Tr}\left[#1\right]} % Trace | ||
\newcommand{\diag}[1]{\mathrm{diag}\left(#1\right)} % Diagonal matrix | ||
\newcommand{\rank}[1]{\mathrm{rank}\left(#1\right)} % Rank of a matrix | ||
\newcommand{\erf}[1]{\mathrm{erf}\left(#1\right)} % Error function | ||
\newcommand{\erfc}[1]{\mathrm{erfc}\left(#1\right)} % Complementary error function | ||
\newcommand{\sinc}[1]{\mathrm{sinc}\left(#1\right)} % Sinc function | ||
\newcommand{\sign}[1]{\mathrm{sign}\left(#1\right)} % Sign function | ||
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor} % Floor function | ||
\newcommand{\ceil}[1]{\left\lceil#1\right\rceil} % Ceiling function | ||
\newcommand{\round}[1]{\left\lfloor#1\right\rceil} % Rounding function | ||
\newcommand{\argmin}[1]{\mathrm{argmin}\left\{#1\right\}} % Argmin | ||
\newcommand{\argmax}[1]{\mathrm{argmax}\left\{#1\right\}} % Argmax |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
%%%%%%%%%%%%% PACKAGES %%%%%%%%%%%%%%% | ||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
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%%%%%%%%%%%% AUTHORSHIP %%%%%%%%%%%%%% | ||
\usepackage{authblk} % Helps format author and affiliation information | ||
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%%%%%%%%%%%%%%% TEXT %%%%%%%%%%%%%%%%% | ||
\usepackage[T1]{fontenc} % Output font encoding for international characters. | ||
\usepackage[utf8]{inputenc} % Allows the use of UTF-8 characters in the LaTeX source code. | ||
%\usepackage[italian]{babel} % Loads the babel package with Italian localization settings | ||
\usepackage{lmodern} % Modern font family for improved readability. | ||
\usepackage{comment} % Enable comment environment | ||
\usepackage{microtype} % Improve typography by enhancing character protrusion, adjusts kerning, and allowing for font expansion | ||
\usepackage{lipsum} % Generate "filler" text in documents for testing or demo | ||
\usepackage{fancyvrb} % Enables advanced verbatim text features | ||
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%%%%%%%%%%%%%%% CODE %%%%%%%%%%%%%%%%% | ||
\usepackage{listings} | ||
%\usepackage{minted} | ||
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%%%%%%%%%%%%%% LAYOUT %%%%%%%%%%%%%%%% | ||
\usepackage{parskip} % Sets space between paragraphs and setting \parindent to 0pt | ||
\usepackage[a4paper]{geometry} % Enables customization of page layout and margins | ||
\usepackage{fancyhdr} % Allows customization of page headers and footers | ||
\usepackage{setspace} % Controls line spacing | ||
\usepackage{titlesec} % Package for customizing section and chapter headings | ||
\usepackage{booktabs} % Enables better spacing and horizontal rules | ||
\usepackage{array} % Enhance column formatting | ||
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%%%%%%%%%%%% MATHEMATICS %%%%%%%%%%%%% | ||
\usepackage{amsmath} % Provides enhanced math environments and features | ||
\usepackage{amsfonts} % Gives access to a variety of mathematical fonts | ||
\usepackage{amssymb} % Provides additional mathematical symbols | ||
\usepackage{amsthm} % Allows for the definition of theorems, lemmas, and proofs | ||
\usepackage{mathdots} % Provides various dot symbols for mathematics. | ||
\usepackage{mathtools} % Extends the functionality of amsmath package for more math tools. | ||
\usepackage{expl3} | ||
\usepackage[unicode,colorlinks=true,linkcolor=blue,urlcolor=magenta, citecolor=blue]{hyperref} | ||
\usepackage[warnings-off={mathtools-colon,mathtools-overbracket}]{unicode-math} | ||
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%%%%%%%%%%%%%%% LISTS %%%%%%%%%%%%%%%% | ||
\usepackage{enumerate} % Allows customization of enumeration and itemize lists | ||
\usepackage{enumitem} % Offers control over the formatting of itemized lists. | ||
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%%%%%%%%%%% VISUALISATION %%%%%%%%%%%% | ||
\usepackage[dvipsnames]{xcolor} % Allows the definition and use of colors | ||
\usepackage{tikz} % A powerful tool for creating graphics and diagrams | ||
\usepackage[most]{tcolorbox} % Enables colored text boxes | ||
\usepackage{graphicx} % Supports the inclusion of external images | ||
\usepackage{caption} % Customizes captions for figures and tables | ||
\usepackage{float} % Improved interface for floating objects like figures and tables | ||
\definecolor{keywordcolor}{rgb}{0.7, 0.1, 0.1} % red | ||
\definecolor{tacticcolor}{rgb}{0.0, 0.1, 0.6} % blue | ||
\definecolor{commentcolor}{rgb}{0.4, 0.4, 0.4} % grey | ||
\definecolor{symbolcolor}{rgb}{0.0, 0.1, 0.6} % blue | ||
\definecolor{sortcolor}{rgb}{0.1, 0.5, 0.1} % green | ||
\definecolor{attributecolor}{rgb}{0.7, 0.1, 0.1} % red | ||
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%%%%%%%%%%%%%% TABLES %%%%%%%%%%%%%%%% | ||
\usepackage{tabularx} % Extends the tabular environment for better table control | ||
\usepackage{multirow} % Allows cells in tables to span multiple rows | ||
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%%%%%%%%%%%% REFERENCES %%%%%%%%%%%%%% | ||
\usepackage{hyperref} % Enables internal & external hyperlinks | ||
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%%%%%%%%%%% BIBLIOGRAPHY %%%%%%%%%%%%% | ||
\usepackage[backend=biber]{biblatex} |
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