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imagen en el ejemplo

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Alba Larraya Sancho 2026-04-09 12:32:04 +02:00
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generaldegree.tex
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@ -320,5 +320,30 @@ The $2$-faces of the simplicial complex $\Delta^d$ will then be identified to th
Finally, we will have $8$ $2$-faces. For three edges to form a face on the simplex, we need the corresponding vertices of the edges to coincide, that is, the edges with non-zero first coordinate must both take the same sign on said coordinate, and equivalently for the rest of coordinates. Then, the faces are defined by taking the square root of the coordinates of the points in $S_1$ with sign equal to those in the edges. Finally, we will have $8$ $2$-faces. For three edges to form a face on the simplex, we need the corresponding vertices of the edges to coincide, that is, the edges with non-zero first coordinate must both take the same sign on said coordinate, and equivalently for the rest of coordinates. Then, the faces are defined by taking the square root of the coordinates of the points in $S_1$ with sign equal to those in the edges.
\begin{figure}[h]
\begin{center}
\begin{tikzpicture}[scale=0.7]
\draw[gray, thin] (-5,0) to (5,0);
\draw[gray, thin] (0,-5) to (0,5);
\draw[gray, thin] (-4,-4) to (4,4);
\draw[fill, red] (4,0) circle (2pt);
\draw[fill, red] (-4,0) circle (2pt);
\draw[fill, green] (0,4) circle (2pt);
\draw[fill, green] (0,-4) circle (2pt);
\draw[fill, blue] (1.41,1.41) circle (2pt);
\draw[fill, blue] (-1.41,-1.41) circle (2pt);
\draw (0,0) circle (4cm);
\draw (-4,0) arc (180:360:4 and 1.5);
\draw[dashed] (4,0) arc (0:180:4 and 1.5);
\draw[dashed] (0,4) arc (90:270:-1.5 and 4);
\draw (0,-4) arc (270:90:1.5 and 4);
\end{tikzpicture}
\end{center}
\caption{Division in simplices of $S_2$}
\label{S2}
\end{figure}
\end{example} \end{example}
\end{document} \end{document}