225 lines
7.1 KiB
TeX
225 lines
7.1 KiB
TeX
% \NeedsTeXFormat{LaTeX2e}
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% \ProvidesPackage{jerrylicious}[Jerry's Tex Mess]
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\RequirePackage{amsthm,amssymb,amsfonts,amsmath}
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\RequirePackage{enumerate}
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\RequirePackage{tikz-cd}
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% ------------- Block Environmets ---------------
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\newtheorem{theorem}[subsection]{Theorem}
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\newtheorem{proposition}[subsection]{Proposition}
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\newtheorem{lemma}[subsection]{Lemma}
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\newtheorem{definition}[subsection]{Definition}
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\newtheorem{example}[subsection]{Example}
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% \newtheorem{exercise}[subsection]{Exercise}
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% \newtheorem{situation}[subsection]{Situation}
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\newtheorem{rem}[subsection]{Remark}
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\newtheorem{remark}[subsection]{Remark}
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% \newtheorem{remarks}[subsection]{Remarks}
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% ------------- References --------------
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\newcommand{\lemmaautorefname}{Lemma}
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\newcommand{\lemautorefname}{Lemma}
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% ------------------ Shortcuts --------------------------
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% All kinds of brackets.
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\newcommand{\paren}[1]{\left(#1\right)}
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\newcommand{\parens}[1]{\left(#1\right)}
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\newcommand{\bracs}[1]{\left\{#1\right\}}
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\newcommand{\braks}[1]{\left[#1\right]}
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\newcommand{\angles}[1]{\left\langle#1\right\rangle}
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\newcommand{\abs}[1]{\left|#1\right|}
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\newcommand{\bracsn}[1]{\{{#1}\}}
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\newcommand{\anglesn}[1]{\langle {#1} \rangle}
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% Probability
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\newcommand{\ev}{\mathbb{E}}
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\newcommand{\var}[1]{\text{Var}\paren{#1}}
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\newcommand{\cov}[1]{\text{Cov}\paren{#1}}
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\newcommand{\sig}[1]{\sigma_{#1}^2}
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\newcommand{\bp}{\mathbf{P}}
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% Complex numbers
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\newcommand{\re}[1]{\text{Re}\paren{#1}}
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\newcommand{\im}[1]{\text{Im}\paren{#1}}
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\newcommand{\sgn}{\text{sgn}}
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% Bold stuff for algebra.
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\newcommand{\zero}{\mathbf{0}}
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\newcommand{\one}{\mathbf{1}}
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% Number Systems/Algebraic Structures
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\newcommand{\polyfield}[1]{\mathbb{F}[#1]}
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\newcommand{\field}{\mathbb{F}}
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\newcommand{\nat}{\mathbb{N}}
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\newcommand{\natp}{\mathbb{N}^+}
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\newcommand{\natz}{\mathbb{N}_0}
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\newcommand{\integer}{\mathbb{Z}}
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\newcommand{\complex}{\mathbb{C}}
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\newcommand{\real}{\mathbb{R}}
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\newcommand{\rd}{\real^d}
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\newcommand{\realp}{\mathbb{R}_{>0}} % Real positive
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\newcommand{\realnn}{\mathbb{R}_{\ge 0}} % Real non-negative
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\newcommand{\rational}{\mathbb{Q}}
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\newcommand{\quot}[1]{\integer/{#1}\integer}
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\newcommand{\polyfields}[1]{F[{#1}_1, \cdots, {#1}_n]}
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\newcommand{\polyfieldf}[1]{F({#1}_1, \cdots, {#1}_n)}
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\newcommand{\gal}[1]{\text{Gal}\paren{#1}}
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\newcommand{\aut}[1]{\text{Aut}\paren{#1}}
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\newcommand{\fa}{\mathfrak{a}}
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\newcommand{\fb}{\mathfrak{b}}
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\newcommand{\fv}{\mathfrak{v}}
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% Sequences and Limits
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\newcommand{\limv}[1]{\lim_{#1 \to \infty}}
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\newcommand{\seq}[1]{\bracs{#1}_{1}^{\infty}}
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\newcommand{\limsupd}[1]{\underset{#1}{\ol{\lim}}}
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\newcommand{\liminfd}[1]{\underset{#1}{\underline{\lim}}}
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\newcommand{\seqi}[1]{\bracs{{#1}_{i}}_{i \in I}}
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\newcommand{\seqj}[1]{\bracs{{#1}_{j}}_{j \in J}}
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\newcommand{\drarrow}{\searrow}
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\newcommand{\downto}{\searrow}
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\newcommand{\upto}{\nearrow}
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\newcommand{\eps}{\varepsilon}
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% Optional upper index argument.
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\newcommand{\seqf}[2][n]{\bracs{#2}_{1}^{#1}}
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\newcommand{\seqfz}[2][n]{\bracs{#2}_{0}^{#1}}
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% Isomorphisms
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\newcommand{\isoto}{\tilde{\rightarrow}}
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\newcommand{\iso}{\cong}
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\newcommand{\modulo}{\text{mod }}
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% Algebra properties
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\newcommand{\ord}{\text{Ord }}
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\newcommand{\orb}[1]{\text{Orb}\paren{#1}}
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\newcommand{\stab}[1]{\text{Stab}\paren{#1}}
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\newcommand{\rank}{\text{rank }}
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\newcommand{\inp}{\angles{\cdot, \cdot}}
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\newcommand{\eig}{\text{Eig}}
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\newcommand{\proj}{\text{proj}}
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\newcommand{\tr}{\text{tr}}
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\newcommand{\spec}[1]{\text{Spec}\paren{#1}}
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\newcommand{\ba}{\mathbf{A}}
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% Dual Pairings & Inner Products
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\newcommand{\dpb}[2]{\angles{#1}_{#2}} % Dual Pairing with a specific space. B because it's apparently already defined in tex.
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\newcommand{\dpn}[2]{\langle {#1} \rangle_{#2}} % Dual Pairing, without scaling the braces.
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\newcommand{\dprd}[1]{\dpb{#1}{\rd}} % R^d dual pairing.
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\newcommand{\dprdn}[1]{\dpn{#1}{\rd}} % R^d dual pairing.
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\newcommand{\dpd}[1]{\dpb{#1}{\mathcal{D}}} % Distribution dual pairing
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\newcommand{\dpdn}[1]{\dpn{#1}{\mathcal{D}}}
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\newcommand{\dpe}[1]{\dpb{#1}{E}} % E for Banach.
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\newcommand{\dpen}[1]{\dpn{#1}{E}} % E for Banach.
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\newcommand{\dph}[1]{\dpb{#1}{H}} % H for Hilbert.
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\newcommand{\dphn}[1]{\dpn{#1}{H}} % H for Hilbert.
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% Floor and ceiling
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\newcommand{\fl}[1]{\left\lfloor #1 \right\rfloor}
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\newcommand{\cl}[1]{\left\lceil #1 \right\rceil}
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% Topology
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\newcommand{\topo}{\mathcal{T}}
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\newcommand{\inte}{\text{int}}
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\newcommand{\exte}{\text{ext}}
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\newcommand{\diam}{\text{diam}}
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\newcommand{\net}[1]{\angles{{#1}_{\alpha}}_{\alpha \in A}}
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\newcommand{\netb}[1]{\angles{{#1}_{\beta}}_{\beta \in B}}
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\newcommand{\supp}[1]{\text{supp}\paren{#1}}
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\newcommand{\fF}{\mathfrak{F}}
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\newcommand{\fS}{\mathfrak{S}}
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\newcommand{\fB}{\mathfrak{B}}
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\newcommand{\fU}{\mathfrak{U}}
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\newcommand{\fV}{\mathfrak{V}}
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\newcommand{\fG}{\mathfrak{G}}
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\newcommand{\bs}{\mathbf{S}}
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% Curly Letters
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\newcommand{\alg}{\mathcal{A}}
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\newcommand{\agb}[1]{\mathcal{M}\paren{#1}}
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\newcommand{\cm}{\mathcal{M}}
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\newcommand{\cf}{\mathcal{F}}
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\newcommand{\ce}{\mathcal{E}}
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\newcommand{\ci}{\mathcal{I}}
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\newcommand{\pow}[1]{\mathcal{P}\paren{#1}}
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\newcommand{\cb}{\mathcal{B}}
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\newcommand{\cn}{\mathcal{N}}
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\newcommand{\lms}{\mathcal{L}}
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\newcommand{\ch}{\mathcal{H}}
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\newcommand{\cg}{\mathcal{H}}
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\renewcommand{\cl}{\mathcal{L}}
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\newcommand{\cc}{\mathcal{C}}
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\newcommand{\ct}{\mathcal{T}}
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\newcommand{\cx}{\mathcal{X}}
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\newcommand{\cy}{\mathcal{Y}}
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\newcommand{\cs}{\mathcal{S}}
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\newcommand{\cd}{\mathcal{D}}
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\newcommand{\calr}{\mathcal{R}}
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\newcommand{\scp}{\mathscr{P}}
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% Jokes
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\newcommand{\lol}{\boxed{\text{LOL.}}}
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\newcommand{\ez}{\boxed{\mathbb{EZ}}}
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% Colours
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\newcommand{\pblue}[1]{\textcolor[rgb]{0, 0.44, 0.75}{#1}}
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\newcommand{\poran}[1]{\textcolor{orange}{#1}}
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\newcommand{\pb}[1]{\pblue{#1}}
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\newcommand{\po}[1]{\poran{#1}}
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\newcommand{\pg}[1]{\textcolor[rgb]{0, 0.69, 0.31}{#1}}
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\newcommand{\pp}[1]{\textcolor[rgb]{0.35, 0.25, 0.64}{#1}}
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\newcommand{\ps}[1]{\textcolor[rgb]{0.58, 0.25, 0.45}{#1}}
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% Formatting
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\newcommand{\ol}[1]{\overline{#1}}
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\newcommand{\ul}[1]{\underline{#1}}
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\newcommand{\wh}[1]{\widehat{#1}}
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\newcommand{\td}[1]{\widetilde{#1}}
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\newcommand{\norm}[1]{\abs{\abs{#1}}}
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\newcommand{\norms}[2]{\abs{\abs{#1}}_{#2}}
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\newcommand{\normn}[1]{||{#1}||}
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\newcommand{\normns}[2]{||{#1}||_{#1}}
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\newcommand{\normrd}[1]{\norms{#1}{\real^d}}
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\newcommand{\normrdn}[1]{\normns{#1}{\real^d}}
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% Category Shenanigans
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\newcommand{\mf}[1]{\mathfrak{#1}}
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\newcommand{\catc}{\mathfrak{C}}
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\newcommand{\cata}{\mathfrak{A}}
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\newcommand{\obj}[1]{\text{Ob}\paren{#1}}
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\newcommand{\mor}[1]{\text{Mor}\paren{#1}}
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% Tangent Space Shenanigans
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\newcommand{\ppi}{\frac{\partial}{\partial x^i}}
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\newcommand{\ppj}{\frac{\partial}{\partial y^j}}
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\newcommand{\ppip}{\ppi\bigg\vert_p}
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\newcommand{\vf}{\mathfrak{X}}
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\newcommand{\grad}[1]{\text{grad}\paren{#1}}
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\newcommand{\Grad}[1]{\text{Grad}\paren{#1}}
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\renewcommand{\div}[1]{\text{div}\paren{#1}}
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% Random spaces
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\newcommand{\laut}[1]{\text{Laut}({#1})}
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\newcommand{\loci}{L^1_{\text{loc}}}
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\newcommand{\symbi}{L^2_{\text{sym}}}
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\newcommand{\met}{\text{Met}}
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\newcommand{\ri}{\text{Ri}}
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\newcommand{\ind}[1]{\text{ind}\paren{#1}}
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\newcommand{\scl}{\mathscr{L}}
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\newcommand{\sch}{\mathscr{H}}
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\newcommand{\frl}{\mathfrak{L}}
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% Real or Complex Numbers
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\newcommand{\RC}{\bracs{\real, \complex}}
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