latex-pictures

A collection of TikZ drawings and other images 🖌️

Commit: 6ffc5675ef371b7b251937b865d6a1b002e2e4bf
Parent: 6d8a51b7585a67ce650f8d6b723c67947ebfcbdc
Author: Pablo <pablo-escobar@riseup.net>
Date: Sat, 27 May 2023 23:40:20 +0000

Updated the drawings

Diffstat

4 files changed, 16 insertions, 74 deletions

Status	File Name	N° Changes	Insertions	Deletions
Modified	galois-lattice-antisomorphism.tikz	6	3	3
Deleted	projective-system-universal-property.tikz	33	0	33
Deleted	projective-system.tikz	15	0	15
Modified	sphere-quotient.tikz	36	13	23

diff --git a/galois-lattice-antisomorphism.tikz b/galois-lattice-antisomorphism.tikz
@@ -1,17 +1,17 @@
 % 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.
-% Copyright Pablo (C) 2021
+% Copyright Pablo (C) 2023
 \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\} \& \\
+    \& K \& \& 1 \& \\
     \& 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 \& \& \operatorname{Gal}(\mathlarger{\sfrac{K}{k}}) \& \\
+    \& k \& \& \operatorname{Gal}(K/k) \& \\
   };
 
     % The relations of both lattices

diff --git a/projective-system-universal-property.tikz b/projective-system-universal-property.tikz
@@ -1,33 +0,0 @@
-% 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}
-% Copyright Pablo (C) 2021
-\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/projective-system.tikz b/projective-system.tikz
@@ -1,15 +0,0 @@
-% This picture represents the behaviour of the morphisms of a projective system
-% (X_i, \phi_{i, j}
-% Copyright Pablo (C) 2021
-\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/sphere-quotient.tikz b/sphere-quotient.tikz
@@ -1,40 +1,30 @@
 % 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
-% Copyright Pablo (C) 2021
+% Copyright Pablo (C) 2023
 \begin{tikzpicture}[scale=0.5]
   % The sphere
-  \draw (0, 0) circle (3);
-              
+  \begin{scope}
+    \clip (-3, -3) rectangle (3, 2.625);
+    \draw (0, 0) circle (3);
+  \end{scope}
+
   % 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);
+    \clip (-3, -3) rectangle (0, 2.625);
     \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]{$T_p \mathbb{S}^n$}
-                    -- (-1.5, 3.375) 
+
+  \draw (-3, 2.625) -- ( 1.5, 2.625)
+                    -- (   3, 3.375) node[right]{$T_p \mathbb{S}^n$}
+                    -- (-1.5, 3.375)
                     -- cycle;
   \filldraw[black] (0, 3) circle (2pt) node[right]{$p$};
-  \draw (0, 3.375) node[above]{$\operatorname{SO}_n(\mathbb{R})$};
+  \draw (0, 3.375) node[above]{$\operatorname{SO}_n$};
 \end{tikzpicture}