# latex-pictures

A collection of TikZ drawings and other images 🖌️

## galois-lattice-antisomorphism.tikz (1281B)

 1 % This picture represents the lattice antisomorphism between the lattice of the
2 % subgroups of the Galois group of a Galois extension and the lattice of
3 % intermediary subfields of such extension.
4 % Copyright Pablo (C) 2023
5 \begin{tikzpicture}[ampersand replacement=\&]
6   % The elements of both lattices
7   \matrix(m)[matrix of math nodes,row sep=2em,column sep=2em,minimum width=2em]
8   {
9     \& K \& \& 1 \& \\
10     \& L_1 \cdot L_2 \& \& H_1 \cap H_2 \& \\
11     L_1 \& \& H_1 \& \& \\
12     \& \& L_2 \& \& H_2 \\
13     \& L_1 \cap L_2 \& \& \langle H_1, H_2 \rangle \& \\
14     \& k \& \& \operatorname{Gal}(K/k) \& \\
15   };
16
17     % The relations of both lattices
18     \draw (m-1-2) -- (m-2-2)
19                   -- (m-3-1)
20                   -- (m-5-2)
21                   -- (m-6-2)
22           (m-2-2) -- (m-4-3)
23                   -- (m-5-2);
24     \draw (m-1-4) -- (m-2-4)
25                   -- (m-3-3)
26                   -- (m-5-4)
27                   -- (m-6-4)
28           (m-2-4) -- (m-4-5)
29                   -- (m-5-4);
30
31     % The antisomorphism
32     \draw[dotted] (m-1-2) -- (m-1-4)
33                   (m-2-2) -- (m-2-4)
34                   (m-3-1) -- (m-3-3)
35                   (m-4-3) -- (m-4-5)
36                   (m-5-2) -- (m-5-4)
37                   (m-6-2) -- (m-6-4);
38 \end{tikzpicture}
39