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Added proofs and fixed typos

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saundersp
2025-03-30 22:05:09 +02:00
parent f95eee7d29
commit 38880b1f21
8 changed files with 637 additions and 147 deletions
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15
packages/macros.sty
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@@ -20,6 +20,7 @@
\newcommand{\Cat}{\mathcal{C}} % Category
\newcommand{\Set}{\mathbf{Set}} % Set category
\newcommand{\Grp}{\mathbf{Grp}} % Group category
\newcommand{\Ring}{\mathbf{Ring}} % Ring category
\newcommand{\Ab}{\mathbf{Ab}} % Abelian category
\newcommand{\Top}{\mathbf{Top}} % Topological spaces category
\newcommand{\K}{\mathbb{K}} % Corps
@@ -43,15 +44,18 @@
\newtheorem{definition}{\lang{Définition}{Definition}}
\newtheorem{theorem}{\lang{Théorème}{Theoreme}}
\newtheorem{lemme}{Lemme}
\newtheorem{exercise}{\lang{Exercice}{Exercise}}
\newcommandx{\suite}[3][1=n,2=n]{$(#3_{#1})_{#2 \in \N}$}
\newcommand{\innerproduct}[2]{\langle #1, #2 \rangle}
\newenvironment{definition_sq}{\begin{mdframed}\begin{definition}}{\end{definition}\end{mdframed}}
\newenvironment{theorem_sq}{\begin{mdframed}\begin{theorem}}{\end{theorem}\end{mdframed}}
\newenvironment{lemme_sq}{\begin{mdframed}\begin{lemme}}{\end{lemme}\end{mdframed}}
\newenvironment{definition_sq}[1][]{\begin{mdframed}\begin{definition}[#1]}{\end{definition}\end{mdframed}}
\newenvironment{theorem_sq}[1][]{\begin{mdframed}\begin{theorem}[#1]}{\end{theorem}\end{mdframed}}
\newenvironment{lemme_sq}[1][]{\begin{mdframed}\begin{lemme}[#1]}{\end{lemme}\end{mdframed}}
\newtheorem{prop}{Proposition}
\newenvironment{prop_sq}{\begin{mdframed}\begin{prop}}{\end{prop}\end{mdframed}}
\newenvironment{prop_sq}[1][]{\begin{mdframed}\begin{prop}[#1]}{\end{prop}\end{mdframed}}
\newtheorem{corollary}{Corollaire}
\newenvironment{corollary_sq}{\begin{mdframed}\begin{corollary}}{\end{corollary}\end{mdframed}}
\newenvironment{corollary_sq}[1][]{\begin{mdframed}\begin{corollary}[#1]}{\end{corollary}\end{mdframed}}
\newenvironment{exercise_sq}[1][]{\begin{mdframed}\begin{exercise}[#1]}{\end{exercise}\end{mdframed}}
\newcommand{\inv}[1]{#1^{-1}}
\DeclarePairedDelimiter{\generator}{\langle}{\rangle}
\DeclareMathOperator{\subgroup}{\leqslant}
\DeclareMathOperator{\normalSubgroup}{\trianglelefteq}
@@ -74,6 +78,7 @@
\newcommand{\functiondef}[2]{\hspace{15pt}#1 \longmapsto #2}
\newcommand{\otherwise}{\text{\lang{Sinon}{Otherwise}}}
\DeclareMathOperator{\union}{\cup}
\DeclareMathOperator{\distinctUnion}{\sqcup}
\DeclareMathOperator{\Union}{\bigcup}
\DeclareMathOperator{\intersection}{\cap}
\DeclareMathOperator{\Intersection}{\bigcap}