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My personal dotfiles

commit 3371aa4940d1a6bee2b8a0a85305ddae52622895
parent 560e5e339c51c49ba2cbb3f1f49429a5a213df61
Author: Pablo <pablo-escobar@riseup.net>
Date:   Mon, 22 Feb 2021 21:21:49 +0000

Updated the LaTeX packages

Diffstat:
M.config/mutt/muttrc | 1+
M.local/share/texmf/tex/latex/functional.sty | 9++++++++-
A.local/share/texmf/tex/latex/images/galois-lattice-antisomorphism.tikz | 39+++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/p-adics.eps | 834+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/projective-system-universal-property.tikz | 32++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/projective-system.tikz | 14++++++++++++++
A.local/share/texmf/tex/latex/images/sphere-quotient.tikz | 39+++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/unit-circle-covering.tikz | 16++++++++++++++++
A.local/share/texmf/tex/latex/images/unit-circle.tikz | 9+++++++++
M.local/share/texmf/tex/latex/preamble-beamer.tex | 4++++
M.local/share/texmf/tex/latex/preamble-common.tex | 4++--
M.local/share/texmf/tex/latex/xalgebra.sty | 21++++++++++++---------
M.local/share/texmf/tex/latex/xgeometry.sty | 20+++++++++++++++++++-
13 files changed, 1029 insertions(+), 13 deletions(-)
diff --git a/.config/mutt/muttrc b/.config/mutt/muttrc
@@ -45,6 +45,7 @@ color sidebar_divider white default
 
 # ============================== Composing ====================================
 
+# Don't display the timezone when replying 
 set date_format="%a, %b %d, %Y"
 
 # Format the message with Asciidoctor
diff --git a/.local/share/texmf/tex/latex/functional.sty b/.local/share/texmf/tex/latex/functional.sty
@@ -5,6 +5,7 @@
 \RequirePackage{amssymb}
 \RequirePackage{amsmath} % For the \DeclareMathOperator
 \RequirePackage{xfrac}   % For \sfrac
+\RequirePackage{relsize} % For \mathlarger
 
 % Define symbols for categories
 \newcommand{\categoryname}[1]{\ensuremath{\mathbf{#1}}}
@@ -18,7 +19,8 @@
 \DeclareMathOperator{\Aut}{Aut}     % Automorphisms
 \DeclareMathOperator{\coker}{coker} % Cokernel
 \newcommand{\normal}{\triangleleft} % A normal subobject in a pointed cathegory
-\newcommand{\mfrac}[2]{{{\Large{\sfrac{{#1}}{{#2}}}}}} % Quotient object
+\newcommand{\mfrac}[2]
+  {\mathlarger{\sfrac{#1}{#2}}}     % Quotient object
 
 % Function stuff
 \DeclareMathOperator{\dom}{dom}     % The domain of a morphism
@@ -41,11 +43,16 @@
 \newcategory{\GrpTop}{GrpTop} % The category of topological groups
 \newcategory{\Rep}{Rep}       % The category of representations of an object
 \newcategory{\Cat}{Cat}       % The category of (small) categories
+\newcategory{\LieGrp}{LieGrp} % The category of Lie groups
+\newcategory{\LieAlg}{LieAlg} % The category of Lie algebras
 % The category of vector spaces over a (parameterized) field
 \newcommand{\Vect}[1]
   {\ensuremath{#1\operatorname{-}\!\categoryname{Vect}}}
 % The category of modules over a (parameterized) ring
 \newcommand{\Mod}[1]
   {\ensuremath{#1\operatorname{-}\!\categoryname{Mod}}}
+% The category of algebras over a (parameterized) field
+\newcommand{\Alg}[1]
+  {\ensuremath{#1\operatorname{-}\!\categoryname{Alg}}}
 
 \endinput
diff --git a/.local/share/texmf/tex/latex/images/galois-lattice-antisomorphism.tikz b/.local/share/texmf/tex/latex/images/galois-lattice-antisomorphism.tikz
@@ -0,0 +1,39 @@
+% This picture represents the lattice antisomorphism between the lattice of the 
+% subgroups of the Galois group of a Galois extension and the lattice of
+% intermediary subfields of such extension.
+% 
+% NOTE: This diagram requires the xalgebra package (for \Gal and \mfrac)
+\begin{tikzpicture}[ampersand replacement=\&]
+  % The elements of both lattices
+  \matrix(m)[matrix of math nodes,row sep=2em,column sep=2em,minimum width=2em]
+  {     \&             K \&     \&                    \{e\} \&     \\
+        \& L_1 \cdot L_2 \&     \&             H_1 \cap H_2 \&     \\
+    L_1 \&               \& H_1 \&                          \&     \\
+        \&               \& L_2 \&                          \& H_2 \\
+        \&  L_1 \cap L_2 \&     \& \langle H_1, H_2 \rangle \&     \\
+        \&             k \&     \&       \Gal(\mfrac{K}{k}) \&     \\
+    };
+
+    % The relations of both lattices
+    \draw (m-1-2) -- (m-2-2)
+                  -- (m-3-1)
+                  -- (m-5-2)
+                  -- (m-6-2)
+          (m-2-2) -- (m-4-3)
+                  -- (m-5-2);
+    \draw (m-1-4) -- (m-2-4)
+                  -- (m-3-3)
+                  -- (m-5-4)
+                  -- (m-6-4)
+          (m-2-4) -- (m-4-5)
+                  -- (m-5-4);
+
+    % The antisomorphism
+    \draw[dotted] (m-1-2) -- (m-1-4)
+                  (m-2-2) -- (m-2-4) 
+                  (m-3-1) -- (m-3-3)
+                  (m-4-3) -- (m-4-5)
+                  (m-5-2) -- (m-5-4)
+                  (m-6-2) -- (m-6-4);
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/p-adics.eps b/.local/share/texmf/tex/latex/images/p-adics.eps
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diff --git a/.local/share/texmf/tex/latex/images/projective-system-universal-property.tikz b/.local/share/texmf/tex/latex/images/projective-system-universal-property.tikz
@@ -0,0 +1,32 @@
+% This diagram represents the universal property of a projective limit
+% \varphojlim X_i, i.e. the fact the a projective limit is the limit of the
+% functor between I^op and the category of obejcts of the projective system
+% given my the projective system itself (for each index i it yields X_i and for
+% each inequality i <= j it yeilds \varphi_{i, j}
+\begin{tikzpicture}[ampersand replacement=\&]
+  % The objects
+  \matrix(m)[matrix of math nodes,row sep=3em,column sep=3em,minimum width=2em]
+  {     \&               X \&     \\
+        \& \varprojlim X_i \&     \\
+    X_i \&                 \& X_j \\};
+
+  % The morphism
+  \draw[->] (m-2-2) -- node[above right]{\(\pi_j\)} (m-3-3);
+  \draw[->] (m-2-2) -- node[above left]{\(\pi_i\)} (m-3-1);
+
+  % The projections
+  \draw[dotted, ->] (m-1-2) -- node[right]{\(\theta\)} (m-2-2);
+
+  % The arrow from the projective system
+  \draw[->] (m-3-3) -- node[below]{\(\phi_{i, j}\)} (m-3-1);
+
+  % The arrows from the compatible family of morphisms
+  \draw[->] (m-1-2) 
+            to[relative, out=-30, in=-150] 
+            node[left]{\(\theta_i\)}
+            (m-3-1);
+  \draw[->] (m-1-2) 
+            to[relative, out=30, in=150] 
+            node[right]{\(\theta_j\)}
+            (m-3-3);
+\end{tikzpicture}
diff --git a/.local/share/texmf/tex/latex/images/projective-system.tikz b/.local/share/texmf/tex/latex/images/projective-system.tikz
@@ -0,0 +1,14 @@
+% This picture represents the behaviour of the morphisms of a projective system
+% (X_i, \phi_{i, j}
+\begin{tikzpicture}[ampersand replacement=\&]
+  % The objects
+  \matrix(m)[matrix of math nodes,row sep=2em,column sep=2em,minimum width=2em]
+  {     \& X_j \& \\
+    X_i \&     \& X_k \\};
+
+  % The arrows
+  \draw[->] (m-2-3) -- node[below]{\(\phi_{i, k}\)} (m-2-1);
+  \draw[->] (m-1-2) -- node[above left]{\(\phi_{i, j}\)} (m-2-1);
+  \draw[->] (m-2-3) -- node[above right]{\(\phi_{j, k}\)} (m-1-2);
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/sphere-quotient.tikz b/.local/share/texmf/tex/latex/images/sphere-quotient.tikz
@@ -0,0 +1,39 @@
+% This picture represents the isomorphism between the n-dimensional sphere and
+% the quotient of the (n + 1)-dimensional simple orthogonal group by the
+% n-dimensional simple orthogonal group
+\begin{tikzpicture}[scale=0.5]
+    % The sphere
+    \draw (0, 0) circle (3);
+                
+    % The equator
+    \begin{scope}
+        \clip (-3, 0) rectangle (3, -3);
+        \draw ellipse (3 and 1);
+    \end{scope}
+            
+    % The equator (on the other side of the sphere)
+    \begin{scope}
+        \clip (-3, 0) rectangle (3, 3);
+        \draw[dotted] ellipse (3 and 1);
+    \end{scope}
+            
+    % Greenwhich
+    \begin{scope}
+        \clip (-3, -3) rectangle (0, 3);
+        \draw ellipse (1 and 3);
+    \end{scope}
+            
+    % Greenwhich (on the other side of the sphere)
+    \begin{scope}
+        \clip (3, -3) rectangle (0, 3);
+        \draw[dotted] ellipse (1 and 3);
+    \end{scope}
+    
+    \draw (-3, 2.625) -- (1.5, 2.625) 
+                      -- (3, 3.375) 
+                      node[right]{\(T_p S^n\)}
+                      -- (-1.5, 3.375) 
+                      -- cycle;
+    \filldraw[black] (0, 3) circle (2pt) node[right]{\(p\)};
+    \draw (0, 3.375) node[above]{\(\SO_n(\RR)\)};
+\end{tikzpicture}
diff --git a/.local/share/texmf/tex/latex/images/unit-circle-covering.tikz b/.local/share/texmf/tex/latex/images/unit-circle-covering.tikz
@@ -0,0 +1,16 @@
+% This picture represents the universal convering of the unit circle
+\begin{tikzpicture}[scale=0.75]
+\begin{scope}[shift={(-3.5, -1)}]
+    \begin{axis}[view={0}{60}, axis lines=none, ymin=-2, ymax=5, xmin=-2, xmax=2]
+    
+        \addplot3 [very thick, domain=-1.25*pi:6.25*pi, samples = 200, samples y=0] ({0.5 * sin(deg(-x))}, {0.5 * cos(deg(-x))}, {-x});
+    
+        \addplot3 [very thick, dotted, domain=-1.5*pi:-1.25*pi, samples = 200, samples y=0] ({0.5 * sin(deg(-x))}, {0.5 * cos(deg(-x))}, {-x});
+    
+        \addplot3 [very thick, dotted, domain=6.25*pi:6.5*pi, samples = 200, samples y=0] ({0.5 * sin(deg(-x))}, {0.5 * cos(deg(-x))}, {-x});
+    \end{axis}
+\end{scope}
+
+\draw[thick, ->] (0, 0) -- node[right]{\(p\)} (0, -1);
+\draw[thick] (0, -1.5) ellipse (0.9 and 0.25);
+\end{tikzpicture}
diff --git a/.local/share/texmf/tex/latex/images/unit-circle.tikz b/.local/share/texmf/tex/latex/images/unit-circle.tikz
@@ -0,0 +1,9 @@
+% This picture represents the unit complex circle
+\begin{tikzpicture}[scale=1.2]
+  \node[above] (O) at (0,1) {\(i\)};
+  \node[right] (O) at (1,0) {\(1\)};
+  \filldraw[black] (0, 1) circle (1pt);
+  \filldraw[black] (1, 0) circle (1pt);
+  \draw (0, 0) circle (1);
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/preamble-beamer.tex b/.local/share/texmf/tex/latex/preamble-beamer.tex
@@ -30,6 +30,7 @@
 \pgfplotsset{compat=1.16}
 
 % Blockquotes
+\let\blockquote\relax
 \NewDocumentEnvironment{blockquote}{m O{Citação}}
     {\begin{block}{#2}}
     {\newline {\normalfont \rightline{\rm --- #1}}\end{block}}
@@ -42,6 +43,9 @@
 \theoremstyle{definition}
 \newtheorem*{definition}{Definição}
 \newtheorem*{example}{Exemplo}
+\theoremstyle{remark}
+\let\note\relax
+\newtheorem*{note}{Nota}
 
 % Beamer settings
 \usetheme{Rochester}
diff --git a/.local/share/texmf/tex/latex/preamble-common.tex b/.local/share/texmf/tex/latex/preamble-common.tex
@@ -14,7 +14,7 @@
 
 \usepackage{amsmath, amssymb, amsthm, stmaryrd, mathrsfs, gensymb, dsfont}
 \usepackage{enumitem, xfrac, xcolor, cancel, multicol, tabularx, relsize}
-\usepackage{hyperref, cleveref, lipsum}
+\usepackage{hyperref, csquotes}
 \usepackage{xalgebra, xgeometry, functional, capitalgreekall}
 \usepackage{ytableau}
 \usepackage[backend=biber]{biblatex}
@@ -75,6 +75,6 @@
 
 % Display long arrows instead of short ones
 \renewcommand{\to}{\longrightarrow}
-\renewcommand{\mapsto}{\longrightarrow}
+\renewcommand{\mapsto}{\longmapsto}
 \renewcommand{\To}{\Longrightarrow}
 
diff --git a/.local/share/texmf/tex/latex/xalgebra.sty b/.local/share/texmf/tex/latex/xalgebra.sty
@@ -18,25 +18,23 @@
 \newcommand{\FF}{\mathbb{F}}   % Generic (finite) field
 \newcommand{\HH}{\mathbb{H}}   % Quaternions
 \newcommand{\OO}{\mathbb{O}}   % Octonions
-\renewcommand{\SS}{\mathbb{S}} % Sedenions
 
 % Linear Algebra stuff
 \newenvironment{system}
   {\left \{ \begin{aligned}}
-  {\end{aligned} \right.}          % Linear system of equations
-\DeclareMathOperator{\Tr}{Tr}      % Operator trace
-\DeclareMathOperator{\Id}{Id}      % Identity operator
-\DeclareMathOperator{\Bil}{Bil}    % The space of bilinear maps
-\DeclareMathOperator{\Mat}{Mat}    % Matrix algebra
-\DeclareMathOperator{\Sym}{Sym}    % Symetric product of vector-spaces
-\newcommand{\base}{\mathscr B}     % Vectorspace base
+  {\end{aligned} \right.}       % Linear system of equations
+\DeclareMathOperator{\Tr}{Tr}   % Operator trace
+\DeclareMathOperator{\Id}{Id}   % Identity operator
+\DeclareMathOperator{\Bil}{Bil} % The space of bilinear maps
+\DeclareMathOperator{\Mat}{Mat} % Matrix algebra
+\DeclareMathOperator{\Sym}{Sym} % Symetric product of vector-spaces
+\newcommand{\base}{\mathscr B}  % Vectorspace base
 \newcommand{\norm}[1]{\left\lVert\nobreak#1\nobreak\right\rVert} % Vector norm
 
 % Group Theory stuff
 \DeclareMathOperator{\Inn}{Inn}  % Inner automorphism group
 \DeclareMathOperator{\Out}{Out}  % Outer automorphism group
 \DeclareMathOperator{\sgn}{sgn}  % Permutation sign (parity)
-\DeclareMathOperator{\Gal}{Gal}  % Galois group
 
 % Ring Theory stuff
 \DeclareMathOperator{\Frac}{Frac}  % Field of fractions
@@ -46,5 +44,10 @@
 \DeclareMathOperator{\Rad}{Rad} % Jacobson radical
 \DeclareMathOperator{\Ind}{Ind} % Induced representation
 
+% Galois Theory
+\DeclareMathOperator{\Gal}{Gal}             % Galois group
+\newcommand{\sepcloj}[1]{{#1}^\textsc{sep}} % Separable clojure of a Galois 
+                                            % extension
+
 \endinput
 
diff --git a/.local/share/texmf/tex/latex/xgeometry.sty b/.local/share/texmf/tex/latex/xgeometry.sty
@@ -6,6 +6,9 @@ geometry and Lie groups/algebras]
 \RequirePackage{amsmath}  % For \DeclareMathOperator
 \RequirePackage{tikz}     % For \tikzset
 
+% Smooth manifolds
+\DeclareMathOperator{\Diff}{Diff} % Group of diffeomorphisms of a given manifold
+
 % Riemannian geometry
 \newcommand{\g}{\mathrm{g}}     % Reimannian metric
 \DeclareMathOperator{\Iso}{Iso} % Isometry group
@@ -16,15 +19,30 @@ geometry and Lie groups/algebras]
 \DeclareMathOperator{\SL}{SL}     % Simple linear group
 \DeclareMathOperator{\SO}{SO}     % Simple orthogonal group
 \DeclareMathOperator{\Sp}{Sp}     % Sympletic group
+\let\O\relax
+\DeclareMathOperator{\O}{O}       % Orthogonal group
+\newcommand{\PR}{\mathbb{PR}}     % Projective real group
+\newcommand{\RP}{\mathbb{RP}}     % Projective real group
+\newcommand{\PC}{\mathbb{PC}}     % Projective complex group
+\newcommand{\CP}{\mathbb{CP}}     % Projective complex group
 \DeclareMathOperator{\PGL}{PGL}   % Projective general linear group
 \DeclareMathOperator{\PSL}{PSL}   % Projective general linear group
+\DeclareMathOperator{\Der}{Der}   % The Lie algebra of derivations over a field
 \newcommand{\gl}{\mathfrak{gl}}   % Lie algebra of \GL
 \renewcommand{\sl}{\mathfrak{sl}} % Lie algebra of \SL
-\newcommand{\so}{\mathfrak{sl}}   % Lie algebra of \SO
+\newcommand{\so}{\mathfrak{so}}   % Lie algebra of \SO
 \renewcommand{\sp}{\mathfrak{sp}} % Lie algebra of \Sp
+\newcommand{\pr}{\mathfrak{pr}}   % Lie algebra of \PR
+\newcommand{\rp}{\mathfrak{rp}}   % Lie algebra of \RP
+\newcommand{\pc}{\mathfrak{pC}}   % Lie algebra of \PC
+\newcommand{\cp}{\mathfrak{cp}}   % Lie algebra of \CP
 \newcommand{\pgl}{\mathfrak{pgl}} % Lie algebra of \PGL
 \newcommand{\psl}{\mathfrak{psl}} % Lie algebra of \PSL
 
+% Representation theory of Lie groups
+\DeclareMathOperator{\Ad}{Ad}
+\DeclareMathOperator{\ad}{ad}
+
 % Tikz pictures
 \tikzset{
   manifold/.pic = {