# How can I draw the following diagram from field theory?

How can I draw the following diagram using TikZ/PGF? I have been able to draw up to the following diagram: Using the following code:

$\begin{tikzpicture}[node distance = 2cm, auto] \node (Q) {\mathbb{Q}}; \node (E) [above of=Q, left of=Q] {\mathbb{Q}(\sqrt{2})}; \node (E1) [above of=Q] {\mathbb{Q}(\sqrt{6})}; \node (F) [above of=Q, right of=Q] {\mathbb{Q}(\sqrt{3})}; \node (K) [above of=Q, node distance = 4cm] {\mathbb{Q}(\sqrt{2}, \sqrt{3})}; \draw[-] (Q) to node {2} (E); \draw[-] (Q) to node [swap] {2} (F); \draw[-] (E) to node {2} (K); \draw[-] (F) to node [swap] {2} (K); \draw[-] (Q) to node [swap] {2} (E1); \draw[-] (E1) to node [swap] {2} (K); \end{tikzpicture}$


How can I extend this code to the above one?

• Please provide a compilable minimal working example and not only a snippet of the code you use. Jan 24 at 13:38
• It will probably be better to see it as a 4 by 4 matrix. I'd also use tikz-cd as it is made for this kind of stuff. Jan 24 at 13:43
• @daleif, thanks for the idea. But my old latex editor does not accept tikz-cd Jan 25 at 13:52
• The editor has nothing to do with the packages. If you have tikz-cd installed you can use it no matter which editor. And if doing diagrams like this you should use it. Jan 25 at 13:57
• @daleif, yes you are right that tikz-cd is very helpful for mathematical diagram. I tried in the past but failed to install it. Can you give some precise idea how to add tikz-cd with my existing latex editor ? Jan 25 at 14:01

Using the code you already have, you could simply do something like this (but since the code you provided does not exactly result in the image you posted, I don't know what you really want to achieve):

\documentclass[tikz, border=1mm]{standalone}
\usepackage{amssymb}

\begin{document}

\begin{tikzpicture}[node distance = 2cm, auto]
\node (Q) {$\mathbb{Q}$};
\node (E) [above of=Q, left of=Q] {$\mathbb{Q}(\sqrt{2})$};
\node (E1) [above of=Q] {$\mathbb{Q}(\sqrt{6})$};
\node (F) [above of=Q, right of=Q] {$\mathbb{Q}(\sqrt{3})$};
\node (K) [above of=Q, node distance = 4cm] {$\mathbb{Q}(\sqrt{2}, \sqrt{3})$};

\node (G) [right of=F] {\color{blue}$\mathbb{Q}(\sqrt{\gamma})$};

\draw[-] (Q) to node {$2$} (E);
\draw[-] (Q) to node {$2$} (F);
\draw[-] (E) to node {$2$} (K);
\draw[-] (F) to node {$2$} (K);
\draw[-] (Q) to node {$2$} (E1);
\draw[-] (E1) to node {$2$} (K);

\draw[-] (Q) to node [swap] {$3$} (G);
\draw[-] (G) to node [swap] {$2$} (K);
\end{tikzpicture}

\end{document} Edit

In case you need the vertical offset of the nodes as well, you could achieve this by using a matrix, or (as noted in the comments) using tikz-cd:

\documentclass[tikz, border=1mm]{standalone}
\usetikzlibrary{matrix}
\usepackage{amssymb}

\begin{document}

\begin{tikzpicture}

\matrix (m) [matrix of math nodes, row sep=2em, column sep=1em] {
& \color{blue}\mathbb{Q}(\zeta, \sqrt{2}) & & \\
& \mathbb{Q}(\sqrt{2}) & \mathbb{Q}(\zeta\sqrt{2}) & \mathbb{Q}(\zeta^2\sqrt{2}) \\
\color{blue}\mathbb{Q}(\zeta) & & & \\
& \color{blue}\mathbb{Q} & & \\
};

\begin{scope}[every node/.style={font=\footnotesize}]
\draw (m-1-2) to node[left] {3} (m-3-1)
to node[below left] {2} (m-4-2);
\draw (m-1-2) to node[right] {2} (m-2-2)
to node[right] {3} (m-4-2);
\draw (m-1-2) to node[below left] {2} (m-2-3)
to node[right] {3} (m-4-2);
\draw (m-1-2) to node[above right] {2} (m-2-4)
to node[below right] {3} (m-4-2);
\end{scope}

\end{tikzpicture}

\end{document} • Yes, I also get the OP's image, but it differs a lot from the result they would like to have (not only regarding the offset). Therefore, it was not clear to me, whether they also wanted this offset or not. I just made a rough guess that they wanted to include another node at the right (or left) oft the diagram. Jan 24 at 14:24
• I see. Well, in this case, daleifs comment about doing all this with a tikz-cd matrix is probably better. Jan 24 at 14:26
• Thank you very much for your both codes. I really liked the first one that extend my original code Jan 25 at 14:07

Instead of extending your code, I use plain TikZ. We even can write the one-liner code for the figure ^^ \documentclass[tikz,border=5mm]{standalone}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{tikzpicture}
\path
(0,0) node (C) {$\mathbb{Q}(\sqrt{2})$}
(2,0) node (R1) {$\mathbb{Q}(\zeta\sqrt{2})$}
(4,0) node (R2) {$\mathbb{Q}(\zeta^2\sqrt{2})$}
(0,1.5) node[blue] (A) {$\mathbb{Q}(\zeta,\sqrt{2})$}
(0,-2) node[blue] (B) {$\mathbb{Q}$}
(-2,-1)  node[blue] (L) {$\mathbb{Q}(\zeta)$}
;
\draw[nodes={scale=.8}] (A)
to node[above]{$2$} (R2)
to node[below]{$3$} (B)
to node[below]{$2$} (L)
to node[left]{$3$} (A)
to node[below]{$2$} (R1)
to node[above]{$3$} (B)
to node[right]{$3$} (C)
to node[right]{$2$} (A)
;
\end{tikzpicture}
\end{document}

• Thank you very much for your nice answer. It worked nicely Jan 25 at 14:05

For completeness, here is one made using tikz-cd

\documentclass[tikz,border=5mm]{standalone}
\usepackage{amsmath,amssymb,tikz-cd}
\usetikzlibrary{babel} % incase " is active
\begin{document}
\begin{tikzcd}
&
\mathbb{Q}(\sqrt{2})
\arrow[ddl,-,"3"']
\arrow[d,-,"2"]
\arrow[dr,-,"2"']
\arrow[drr,-,"2"]
&
&
\\
&
\mathbb{Q}(\sqrt{2})
\arrow[dd,-,"3"]
&
\mathbb{Q}(\zeta,\sqrt{2})
\arrow[ddl,-,"3"']
&
\mathbb{Q}(\zeta^2\sqrt{2})
\arrow[ddll,-,"3"]
\\
\mathbb{Q}(\zeta)
\arrow[dr,-,"2"']
&
&
&
\\
&
\mathbb{Q}
&
&
\\
\end{tikzcd}
\end{document} • Thank you for your answer. I really appreciate it Jan 25 at 14:18