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My personal dotfiles

commit 841db87335ad92fb6e13fdea132900f0be224752
parent 3dd7ab8856cb58df3624e39cbfc5c47af984e1d5
Author: Pablo Emilio Escobar Gaviria <pablo-escobar@riseup.net>
Date:   Thu,  4 Feb 2021 02:01:14 +0000

Added macros for groups from differential geometry

Diffstat:
M.config/ranger/bookmarks | 2+-
A.local/share/texmf/tex/latex/images/dihedral-representation.tikz | 16++++++++++++++++
A.local/share/texmf/tex/latex/images/manifold.tikz | 50++++++++++++++++++++++++++++++++++++++++++++++++++
M.local/share/texmf/tex/latex/xalgebra.sty | 2++
4 files changed, 69 insertions(+), 1 deletion(-)
diff --git a/.config/ranger/bookmarks b/.config/ranger/bookmarks
@@ -1,4 +1,4 @@
 a:/home/pablo/Papers
 c:/home/pablo/Pictures/SP
 m:/home/pablo/Papers
-':/home/pablo/Videos/SageDays 110
+':/home/pablo/Downloads
diff --git a/.local/share/texmf/tex/latex/images/dihedral-representation.tikz b/.local/share/texmf/tex/latex/images/dihedral-representation.tikz
@@ -0,0 +1,16 @@
+% This picture represents the action of the dihedral group in the real plain
+\begin{tikzpicture}
+  % The axis
+  \draw[->] (-3,0)--(3,0) node[right]{\(x\)};
+  \draw[->] (0,-2)--(0,2) node[above]{\(y\)};
+   
+  % The triangle
+  \node[draw, regular polygon, regular polygon sides=3, minimum height=2cm]{};
+  
+  % The action of sigma
+  \draw[->] (1.5, 0.5) arc (0:90:1cm) 
+            node at (1.5, 1.4) {\(\sigma\)};
+
+  % The action of tau
+  \draw[<->] (-1, -1)--(1, -1) node[right]{\(\tau\)};
+\end{tikzpicture}   
diff --git a/.local/share/texmf/tex/latex/images/manifold.tikz b/.local/share/texmf/tex/latex/images/manifold.tikz
@@ -0,0 +1,50 @@
+% 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/xalgebra.sty b/.local/share/texmf/tex/latex/xalgebra.sty
@@ -39,6 +39,8 @@
 \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