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My personal dotfiles

commit 0bb931e8f57996233eee5cb7287522c7b5f015ac
parent 1a2114f3011fa271804bb8d725666c55ff38c68f
Author: Pablo Emilio Escobar Gaviria <pablo-escobar@riseup.net>
Date:   Mon,  8 Feb 2021 00:00:49 +0000

Added a Beamer-specific LaTeX preamble file and a new TeX package for differential geometry

Diffstat:
A.local/share/texmf/tex/latex/images/caleb-yau.png | 0
M.local/share/texmf/tex/latex/images/dihedral-representation.tikz | 3+++
A.local/share/texmf/tex/latex/images/euclidian-plain.tikz | 7+++++++
A.local/share/texmf/tex/latex/images/geodesic.tikz | 55+++++++++++++++++++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/hairy-doughnut.png | 0
A.local/share/texmf/tex/latex/images/hiperbolic-plain.tikz | 14++++++++++++++
D.local/share/texmf/tex/latex/images/manifold.tikz | 50--------------------------------------------------
A.local/share/texmf/tex/latex/images/n-torus.eps | 544+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/riemannian-metric.tikz | 44++++++++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/smooth-function.tikz | 36++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/smooth-manifold.tikz | 51+++++++++++++++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/sphere.tikz | 32++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/images/velocity.tikz | 48++++++++++++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/preamble-beamer.tex | 72++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
A.local/share/texmf/tex/latex/preamble-common.tex | 63+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
M.local/share/texmf/tex/latex/preamble.tex | 45++-------------------------------------------
M.local/share/texmf/tex/latex/xalgebra.sty | 4----
A.local/share/texmf/tex/latex/xgeometry.sty | 18++++++++++++++++++
18 files changed, 989 insertions(+), 97 deletions(-)
diff --git a/.local/share/texmf/tex/latex/images/caleb-yau.png b/.local/share/texmf/tex/latex/images/caleb-yau.png
Binary files differ.
diff --git a/.local/share/texmf/tex/latex/images/dihedral-representation.tikz b/.local/share/texmf/tex/latex/images/dihedral-representation.tikz
@@ -1,4 +1,6 @@
 % This picture represents the action of the dihedral group in the real plain
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
 \begin{tikzpicture}
   % The axis
   \draw[->] (-3,0)--(3,0) node[right]{\(x\)};
@@ -14,3 +16,4 @@
   % The action of tau
   \draw[<->] (-1, -1)--(1, -1) node[right]{\(\tau\)};
 \end{tikzpicture}   
+
diff --git a/.local/share/texmf/tex/latex/images/euclidian-plain.tikz b/.local/share/texmf/tex/latex/images/euclidian-plain.tikz
@@ -0,0 +1,7 @@
+% This picture represents the cartesian plain
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
+\begin{tikzpicture}
+    \draw (0, 0) node[left]{\(\RR^2\)} -- (2, 0) -- (3, 1) -- (1, 1) -- cycle;
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/geodesic.tikz b/.local/share/texmf/tex/latex/images/geodesic.tikz
@@ -0,0 +1,55 @@
+% This picture represents the fact that geodesics locally minimize distances
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
+\begin{tikzpicture}[scale=0.5]
+  % The cirference
+  \draw (0, 0) circle (3);
+
+  % The equator
+  \begin{scope}
+    \clip (-3, 0) rectangle (3, -3);
+    \draw ellipse (3 and 1);
+  \end{scope}
+
+  % Greenwhich
+  \begin{scope}
+    \clip (-3, -3) rectangle (0, 3);
+    \draw ellipse (1 and 3);
+  \end{scope}
+
+  % The curve
+  \begin{scope}
+    \clip (-3, 0) rectangle (0, -3);
+    \draw[very thick] ellipse (1 and 3);
+  \end{scope}
+  \begin{scope}
+    \clip (3, -3) rectangle (0, 3);
+    \draw[very thick, dotted] ellipse (1 and 3);
+  \end{scope}
+
+  % The ends
+  \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt);
+
+  \draw (-0.87, -1.5) circle (0.3);
+  \draw (-1.17, -1.5) -- (-4, 1);
+
+  % Zoom in ares
+  \begin{scope}[shift={(-6, 1)}]
+    \draw (0, 0) circle (2);
+
+    % The geodesic
+    \draw[very thick] (0, -2) -- (0, 2);
+    \filldraw (0, -2) circle (2pt) (0, 2) circle (2pt);
+
+    % Another curve
+    \draw[dotted] (   0,    2) to[out=180, in=90] 
+                  (-0.6,  1.4) to[out=270, in=150] 
+                  ( 0.5,  0.7) to[out=-30, in=0] 
+                  ( 0.3,  0.1) to[out=180, in=180] 
+                  ( 0.5,  0.6) to[out=0, in=120] 
+                  ( 1.3,  0.7) to[out=-60, in=60] 
+                  ( 0.4, -0.5) to[out=240, in=90] 
+                  (   0,   -2);
+  \end{scope}
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/hairy-doughnut.png b/.local/share/texmf/tex/latex/images/hairy-doughnut.png
Binary files differ.
diff --git a/.local/share/texmf/tex/latex/images/hiperbolic-plain.tikz b/.local/share/texmf/tex/latex/images/hiperbolic-plain.tikz
@@ -0,0 +1,14 @@
+% This picture represents the hyperbolic plain
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
+\begin{tikzpicture}
+    % The axis
+    \draw[dash dot, ->] (0,  0) -- (6, 0) node[right]{\(x\)};
+    \draw[->] (1, -1) -- (1, 3) node[above]{\(y\)};
+    
+    % A strait line (in the hyperbolic plain)
+    \draw (2, 0) arc (180:0:1.5);
+    \filldraw (2, 0) circle (1pt);
+    \filldraw (5, 0) circle (1pt);
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/manifold.tikz b/.local/share/texmf/tex/latex/images/manifold.tikz
@@ -1,50 +0,0 @@
-% This picture represents the definition of a topological manifold
-\begin{tikzpicture}
-    % The surface
-    \begin{scope}[shift={(-0.5, 0)}]
-        % The fronteir of the surface
-        \draw (-4, 2) node[below]{\(M\)} to[relative, out=20, in=160] (2, 0) 
-              to[relative, out=20, in=160] (4, 3) 
-              to[relative, out=-20, in=-160] cycle;
-    
-        % The open subsets of the manifold
-        \begin{scope}[shift={(1, 2.2)}]
-            \draw (-0.5, 0) ellipse (0.7 and 0.5);
-            \draw (-1.2, 0) node[right]{\(U\)};
-            \draw (0.5, 0) ellipse (0.7 and 0.5);
-            \draw (1.2, 0) node[left]{\(V\)};
-
-            % The intersection
-            \clip (-0.5, 0) ellipse (0.7 and 0.5);
-            \draw[pattern=north west lines] (0.5, 0) ellipse (0.7 and 0.5);
-        \end{scope}
-    \end{scope}
-    
-    % The cards
-    \draw[->] (-0.7, 1.7) to[relative, out=-20, in=-160] 
-              node[left]{\(\varphi_U\)} (-2, -0.7);
-    \draw[->] (1.7, 1.7) to[relative, out=20, in=0160] 
-              node[right]{\(\varphi_V\)} (2, -0.7);
-    
-    % The corresponding open sets in the euclidian space
-    \begin{scope}[shift={(0, -1.5)}]
-        % The open sets
-        \draw (-2, 0) ellipse (1 and 0.6) (2, 0) ellipse (1 and 0.6);
-        \draw (-3, 0.5) node[above]{\(\varphi_U(U)\)};
-        \draw (3, 0.5) node[above]{\(\varphi_V(V)\)};
-        
-        % The intersections
-        \begin{scope}
-            \clip (-2, 0) ellipse (1 and 0.6);
-            \draw[pattern=north west lines] (-0.5, 0) ellipse (1 and 0.6);
-        \end{scope}
-        \begin{scope}
-            \clip (2, 0) ellipse (1 and 0.6);
-            \draw[pattern=north west lines] (0.5, 0) ellipse (1 and 0.6);
-        \end{scope}
-        
-        % The diffeomorphism between the intersections
-        \draw[->] (-0.9, 0) -- node[above]{\(\varphi_V \circ \varphi_U^{-1}\)} 
-                  (0.9, 0);
-    \end{scope}
-\end{tikzpicture}
diff --git a/.local/share/texmf/tex/latex/images/n-torus.eps b/.local/share/texmf/tex/latex/images/n-torus.eps
@@ -0,0 +1,544 @@
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+%%EOF
diff --git a/.local/share/texmf/tex/latex/images/riemannian-metric.tikz b/.local/share/texmf/tex/latex/images/riemannian-metric.tikz
@@ -0,0 +1,44 @@
+% This picture is a comparison between the euclian distance and the Riemannian 
+% distance in a three-dimensional sphere
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
+\begin{tikzpicture}
+  % The cirference
+  \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}
+
+  % The dots
+  \filldraw (0, 3) circle (2pt) (-1, 0) circle (2pt);
+
+  \draw[thick, dotted] (0, 3) -- (-1, 0);
+
+  % 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}
+
+  % Greenwhich (on the other side of the sphere)
+  \begin{scope}
+    \clip (-3, 0) rectangle (0, 3);
+    \draw[very thick] ellipse (1 and 3);
+  \end{scope}
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/smooth-function.tikz b/.local/share/texmf/tex/latex/images/smooth-function.tikz
@@ -0,0 +1,36 @@
+% This picture represents the definition of a smooth maps between smooth
+% manifolds
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
+\begin{tikzpicture}
+  \def\manifold{
+    \draw  (-1.5, -0.5) to[relative, out=20, in=160] 
+          +(   2,    0) to[relative, out=20, in=160] 
+          +(   1,    1) to[relative, out=-20, in=-160] 
+          +(  -2,    0) to[relative, out=-20, in=-160] cycle;
+  }
+
+  % The manifolds
+  \begin{scope}[shift={(-2, 0)}]
+    \manifold
+    \draw (0.5, -0.5) node[right]{\(M\)};
+  \end{scope}
+  \begin{scope}[shift={(2, 0)}]
+    \manifold
+    \draw (0.5, -0.5) node[right]{\(N\)};
+  \end{scope}
+
+  % The functions
+  \draw[->] (-1,  0.9) to[out=30, in=150] node[above]{\(f\)} (1, 0.9);
+  \draw[->] (-1, -1.7) to[out=30, in=150] 
+            node[above]{\(\psi \circ f \circ \varphi^{-1}\)} (1, -1.7);
+  \draw[->] (-2, -0.7) -- node[left]{\(\varphi\)} +(0, -1);
+  \draw[->] ( 2, -0.7) -- node[left]{\(\psi\)} +(0, -1);
+
+  % The open sets in euclidian space
+  \draw[dash dot] (-2, -3) node{\(\varphi(U)\)} ellipse (1 and 0.5);
+  \draw[dash dot] ( 2, -3) node{\(\psi(V)\)} ellipse (1 and 0.5);
+  \draw (-3.5, -4) node[left]{\(\RR^m\)} rectangle +(3, 2);
+  \draw ( 0.5, -4) node[left]{\(\RR^n\)} rectangle +(3, 2);
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/smooth-manifold.tikz b/.local/share/texmf/tex/latex/images/smooth-manifold.tikz
@@ -0,0 +1,51 @@
+% This picture represents the definition of a smooth manifold
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
+\begin{tikzpicture}
+  % The manifold
+  \begin{scope}[shift={(-0.5, 0)}]
+    % The contour
+    \draw (-4, 2) node[below]{\(M\)} to[relative, out=20, in=160] 
+          (2, 0) to[relative, out=20, in=160] 
+          (4, 3) to[relative, out=-20, in=-160] cycle;
+
+    % The open sets of the manifold
+    \begin{scope}[shift={(1, 2.2)}]
+      \draw (-0.5, 0) ellipse (0.7 and 0.5);
+      \draw (-1.2, 0) node[right]{\(U\)};
+      \draw (0.5, 0) ellipse (0.7 and 0.5);
+      \draw (1.2, 0) node[left]{\(V\)};
+      \clip (-0.5, 0) ellipse (0.7 and 0.5);
+      \draw[pattern=north west lines] (0.5, 0) ellipse (0.7 and 0.5);
+    \end{scope}
+  \end{scope}
+
+  % The cards
+  \draw[->] (-0.7, 1.7) to[relative, out=-20, in=-160] 
+            node[left]{\(\varphi_U\)} (-2, -0.7);
+  \draw[->] (1.7, 1.7) to[relative, out=20, in=160] 
+            node[right]{\(\varphi_V\)} (2, -0.7);
+
+  % The corresponding open sets in euclidian space
+  \begin{scope}[shift={(0, -1.5)}]
+    % The open sets
+    \draw (-2, 0) ellipse (1 and 0.6) (2, 0) ellipse (1 and 0.6);
+    \draw (-3, 0.5) node[above]{\(\varphi_U(U)\)};
+    \draw (3, 0.5) node[above]{\(\varphi_V(V)\)};
+
+    % The intersections
+    \begin{scope}
+      \clip (-2, 0) ellipse (1 and 0.6);
+      \draw[pattern=north west lines] (-0.5, 0) ellipse (1 and 0.6);
+    \end{scope}
+    \begin{scope}
+      \clip (2, 0) ellipse (1 and 0.6);
+      \draw[pattern=north west lines] (0.5, 0) ellipse (1 and 0.6);
+    \end{scope}
+
+    % The diffeomorphism
+    \draw[->] (-0.9, 0) -- 
+              node[above]{\(\varphi_V \circ \varphi_U^{-1}\)} (0.9, 0);
+  \end{scope}
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/sphere.tikz b/.local/share/texmf/tex/latex/images/sphere.tikz
@@ -0,0 +1,32 @@
+% This picture represents a three-dimentional sphere
+% 
+% Pablo Emilio Escobar Gaviria (C) 2020
+\begin{tikzpicture}[scale=0.4]
+    % The cirference
+    \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}
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/images/velocity.tikz b/.local/share/texmf/tex/latex/images/velocity.tikz
@@ -0,0 +1,48 @@
+\begin{tikzpicture}[scale=0.7]
+  % The manifold
+  \draw[] (-4, 2) node[below]{\(M\)} to[relative, out=20, in=160] 
+          ( 2, 0) to[relative, out=20, in=160] 
+          ( 4, 3) to[relative, out=-20, in=-160] cycle;
+
+  % The curve
+  \begin{scope}[scale=0.4, shift={(-3, 1.6)}]
+    \draw (7.55860157,0.01017668) to[in=-20, out=160]
+          (6.14948031,3.96764439) to[out=160, in=-40]
+          (4.56234331,3.40876565) to[out=140, in=-40]
+          (5.59037480,5.96236565) to[out=140, in=-10]
+          (2.18838425,2.93330109) to[out=170, in=-30]
+          (1.43769449,5.74579872) to[out=150, in=0]
+          (0.47111811,3.99633101) to[out=180, in=0]
+          (0.00283465,5.29618613);
+
+    \filldraw (7.55860157,0.01017668) circle (2.5pt) 
+              (0.00283465,5.29618613) circle (2.5pt);
+
+    % The tanget vectors
+    \begin{scope}[shift={(7.55860157,0.01017668)}]
+      \draw[->, rotate=160] (0, 0) -- +(1, 0);
+    \end{scope}
+    \begin{scope}[shift={(6.14948031,3.96764439)}]
+      \draw[->, rotate=160] (0, 0) -- +(1, 0);
+    \end{scope}
+    \begin{scope}[shift={(4.56234331,3.40876565)}]
+      \draw[->, rotate=140] (0, 0) -- +(1, 0);
+    \end{scope}
+    \begin{scope}[shift={(5.59037480,5.96236565)}]
+      \draw[->, rotate=140] (0, 0) -- +(1, 0);
+    \end{scope}
+    \begin{scope}[shift={(2.18838425,2.93330109)}]
+      \draw[->, rotate=170] (0, 0) -- +(1, 0);
+    \end{scope}
+    \begin{scope}[shift={(1.43769449,5.74579872)}]
+      \draw[->, rotate=150] (0, 0) -- +(1, 0);
+    \end{scope}
+    \begin{scope}[shift={(0.47111811,3.99633101)}]
+      \draw[->, rotate=180] (0, 0) -- +(1, 0);
+    \end{scope}
+    \begin{scope}[shift={(0.00283465,5.29618613)}]
+      \draw[->, rotate=180] (0, 0) -- +(1, 0);
+    \end{scope}
+  \end{scope}
+\end{tikzpicture}
+
diff --git a/.local/share/texmf/tex/latex/preamble-beamer.tex b/.local/share/texmf/tex/latex/preamble-beamer.tex
@@ -0,0 +1,72 @@
+%                                 _     _            _                          
+%  _ __  _ __ ___  __ _ _ __ ___ | |__ | | ___      | |__   ___  __ _ _ __ ___  
+% | '_ \| '__/ _ \/ _` | '_ ` _ \| '_ \| |/ _ \_____| '_ \ / _ \/ _` | '_ ` _ \ 
+% | |_) | | |  __/ (_| | | | | | | |_) | |  __/_____| |_) |  __/ (_| | | | | | |
+% | .__/|_|  \___|\__,_|_| |_| |_|_.__/|_|\___|     |_.__/ \___|\__,_|_| |_| |_|
+% |_|                                                                           
+%            _            
+%   ___ _ __| |_ _____  __
+%  / _ \ '__| __/ _ \ \/ /
+% |  __/ | _| ||  __/>  < 
+%  \___|_|(_)\__\___/_/\_\
+%                         
+% Pablo Emilio Escobar Gaviria (C) 2020
+
+\documentclass[notheorems, 9pt]{beamer}
+\usepackage{amsmath, amssymb, amsthm, stmaryrd, mathrsfs, gensymb, dsfont}
+\usepackage{enumitem, xfrac, xcolor, cancel, multicol, tabularx, relsize}
+\usepackage{hyperref, cleveref, lipsum}
+\usepackage{xalgebra, xgeometry, functional, capitalgreekall}
+\usepackage[backend=biber]{biblatex}
+\usepackage{pgfplots, tikz, tikz-cd}
+\usepackage{graphicx, wrapfig}
+\usepackage{xparse}
+\usepackage[normalem]{ulem}
+\usepackage[brazil]{babel}
+
+% TODO: Get the color from the beamer template
+\definecolor{marineblue}{RGB}{4, 6, 76}
+
+% Configure how link look
+\hypersetup{
+	colorlinks=true,
+	citecolor=marineblue,
+	linkcolor=marineblue, 
+}
+
+% Configure graphics
+\usetikzlibrary{calc, shadows.blur, shapes.geometric, patterns}
+\pgfplotsset{compat=1.16}
+
+\input{preamble-common}
+
+% Blockquotes
+\NewDocumentEnvironment{blockquote}{m O{Citação}}
+    {\begin{block}{#2}}
+    {\newline {\normalfont \rightline{\rm --- #1}}\end{block}}
+
+% Useful theorem definitions
+\newtheorem*{theorem}{Teorema}
+\newtheorem*{lemma}{Lema}
+\newtheorem*{corollary}{Corolário}
+\newtheorem*{proposition}{Proposição}
+\theoremstyle{definition}
+\newtheorem*{definition}{Definição}
+\newtheorem*{example}{Exemplo}
+
+% Beamer settings
+\usetheme{Rochester}
+\usecolortheme{crane}
+\usefonttheme{serif}
+\setbeamertemplate{itemize items}{\textbullet}
+\setbeamertemplate{bibliography item}{\textbullet}
+
+% Configure how items look
+\setenumerate[0]{label={\color{marineblue}\normalfont(\roman*)}}
+\setitemize{label=\usebeamerfont*{itemize item}%
+    \usebeamercolor[fg]{itemize item}
+    \usebeamertemplate{itemize item}}
+   
+% Configure the spacing of columns in tables
+\setlength{\tabcolsep}{5pt}
+
diff --git a/.local/share/texmf/tex/latex/preamble-common.tex b/.local/share/texmf/tex/latex/preamble-common.tex
@@ -0,0 +1,63 @@
+%                                 _     _                                
+%  _ __  _ __ ___  __ _ _ __ ___ | |__ | | ___        ___ ___  _ __ ___  
+% | '_ \| '__/ _ \/ _` | '_ ` _ \| '_ \| |/ _ \_____ / __/ _ \| '_ ` _ \ 
+% | |_) | | |  __/ (_| | | | | | | |_) | |  __/_____| (_| (_) | | | | | |
+% | .__/|_|  \___|\__,_|_| |_| |_|_.__/|_|\___|      \___\___/|_| |_| |_|
+% |_|                                                                    
+%                         _            
+%  _ __ ___   ___  _ __  | |_ _____  __
+% | '_ ` _ \ / _ \| '_ \ | __/ _ \ \/ /
+% | | | | | | (_) | | | || ||  __/>  < 
+% |_| |_| |_|\___/|_| |_(_)__\___/_/\_\
+%                                      
+% Pablo Emilio Escobar Gaviria (C) 2020
+
+% Use \blacksquare for \qed
+\renewcommand{\qedsymbol}{\ensuremath{\blacksquare}}
+
+% Only use \smallsetminus
+\renewcommand{\setminus}{\smallsetminus}
+
+% Make the \mid symbol taller (this is useful for Group Theory)
+\renewcommand{\mid}{\,\mathlarger{\mathlarger{\mathchar"326A}}\,}
+\renewcommand{\nmid}{\,\mathlarger{\mathlarger{\mathchar"352D}}\,}
+
+% Get propper inequality symbols
+\renewcommand{\leq}{\leqslant}
+\renewcommand{\le}{\leqslant}
+\renewcommand{\geq}{\geqslant}
+\renewcommand{\ge}{\geqslant}
+\renewcommand{\preceq}{\preccurlyeq}
+\renewcommand{\succeq}{\succcurlyeq}
+
+% Add missing arrows
+\newcommand{\longhookrightarrow}{\lhook\joinrel\longrightarrow}
+\newcommand{\longhookleftarrow}{\longleftarrow\joinrel\rhook}
+\DeclareRobustCommand\longtwoheadrightarrow
+     {\relbar\joinrel\twoheadrightarrow}
+
+% Translate \gcd and \lcm to portuguese
+\let\gcd\relax
+\DeclareMathOperator{\gcd}{mdc}
+\let\lcm\relax
+\DeclareMathOperator{\lcm}{mmc}
+
+% Redefine \bar
+\renewcommand{\bar}{\overline}
+
+% A semantic alternative to \textbf
+\newcommand{\strong}[1]{\textbf{#1}}
+
+% Differentials and derivatives
+\newcommand{\dd}{\mathrm{d}}
+\newcommand{\dx}{\dd x}
+\newcommand{\dy}{\dd y}
+\newcommand{\dz}{\dd z}
+\newcommand{\dt}{\dd t}
+
+% Set cardinal
+\newcommand{\card}[1]{\left|\nobreak#1\nobreak\right|}
+
+% Empty macro (it's usefull for typesetting Young diagrams)
+\newcommand{\void}{ }
+
diff --git a/.local/share/texmf/tex/latex/preamble.tex b/.local/share/texmf/tex/latex/preamble.tex
@@ -21,27 +21,11 @@
 \usepackage[normalem]{ulem}
 \usepackage[brazil]{babel}
 
-% Use \blacksquare for \qed
-\renewcommand{\qedsymbol}{\ensuremath{\blacksquare}}
-
-% Only use \smallsetminus
-\renewcommand{\setminus}{\smallsetminus}
-
-% Make the \mid symbol taller (this is useful for Group Theory)
-\renewcommand{\mid}{\,\mathlarger{\mathlarger{\mathchar"326A}}\,}
-\renewcommand{\nmid}{\,\mathlarger{\mathlarger{\mathchar"352D}}\,}
-
-% Get propper inequality symbols
-\renewcommand{\leq}{\leqslant}
-\renewcommand{\le}{\leqslant}
-\renewcommand{\geq}{\geqslant}
-\renewcommand{\ge}{\geqslant}
-\renewcommand{\preceq}{\preccurlyeq}
-\renewcommand{\succeq}{\succcurlyeq}
-
 % Configure the enumerate environment to use bold roman numerals
 \setenumerate[0]{label={\bfseries(\roman*)}}
 
+\input{preamble-common}
+
 % Useful theorem definitions
 \newtheorem{theorem}{Teorema}
 \newtheorem*{theorem*}{Teorema}
@@ -59,28 +43,3 @@
 \newtheorem{example}{Exemplo}
 \newtheorem*{example*}{Exemplo}
 
-% Translate \gcd and \lcm to portuguese
-\let\gcd\relax
-\DeclareMathOperator{\gcd}{mdc}
-\let\lcm\relax
-\DeclareMathOperator{\lcm}{mmc}
-
-% Redefine \bar
-\renewcommand{\bar}{\overline}
-
-% A semantic alternative to \textbf
-\newcommand{\strong}[1]{\textbf{#1}}
-
-% Differentials and derivatives
-\newcommand{\dd}{\mathrm{d}}
-\newcommand{\dx}{\dd x}
-\newcommand{\dy}{\dd y}
-\newcommand{\dz}{\dd z}
-\newcommand{\dt}{\dd t}
-
-% Set cardinal
-\newcommand{\card}[1]{\left|\nobreak#1\nobreak\right|}
-
-% Empty macro (it's usefull for typesetting Young diagrams)
-\newcommand{\void}{ }
-
diff --git a/.local/share/texmf/tex/latex/xalgebra.sty b/.local/share/texmf/tex/latex/xalgebra.sty
@@ -36,11 +36,7 @@
 \DeclareMathOperator{\Inn}{Inn}  % Inner automorphism group
 \DeclareMathOperator{\Out}{Out}  % Outer automorphism group
 \DeclareMathOperator{\sgn}{sgn}  % Permutation sign (parity)
-\DeclareMathOperator{\GL}{GL}    % General linear group
-\DeclareMathOperator{\SL}{SL}    % Simple linear group
 \DeclareMathOperator{\Gal}{Gal}  % Galois group
-\DeclareMathOperator{\Hol}{Hol}  % Holonomy group
-\DeclareMathOperator{\Iso}{Iso}  % Isometry group
 
 % Ring Theory stuff
 \DeclareMathOperator{\Frac}{Frac}  % Field of fractions
diff --git a/.local/share/texmf/tex/latex/xgeometry.sty b/.local/share/texmf/tex/latex/xgeometry.sty
@@ -0,0 +1,18 @@
+\NeedsTeXFormat{LaTeX2e}[1994/06/01]
+\ProvidesPackage{xgeometry}[2020/09/10 1.0.0 Usefull definitions for differential geometry]
+
+\RequirePackage{amssymb}  % For the standard sets
+\RequirePackage{amsmath}  % For the \DeclareMathOperator
+%\RequirePackage{mathrsfs} % For \mathscr
+%\RequirePackage{xfrac}    % For \sfrac
+
+% Reimannian metric
+\newcommand{\g}{\mathrm{g}}
+
+\DeclareMathOperator{\Hol}{Hol} % Holonomy group
+\DeclareMathOperator{\Iso}{Iso} % Isometry group
+\DeclareMathOperator{\GL}{GL}   % General linear group
+\DeclareMathOperator{\SL}{SL}   % Simple linear group
+\newcommand{\Gl}{\mathfrak{gl}} % General linear group
+\newcommand{\Sl}{\mathfrak{sl}} % Simple linear group
+