Combinatorial Patchworking Tool

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Developed by Boulos El-Hilany, Johannes Rau, Arthur Reneaudineau
This tool is heavily based on Christopher O'Neill's Viro Triangulation Picker. Thanks a lot!!
For more advanced computations of Viro patchworkings, check out the more powerful Sage tool Viro Patchworking.

Quick Introduction

With this tool you can create the shapes of real algebraic curves with only a few clicks. The construction method is called Viro's combinatorial patchworking.

• On the left hand side you can pick a triangulation and swap the color (called "sign") of the vertices.
• On the right hand side you can see the result: It is a graph in the plane which stands for the "topological type" of a corresponding real algebraic curves (sorry, no details here). Actually, what you see is the topology of an affine curve. The projective type is obtained by gluing/identifying the ends of the graph which lie on opposite points of the boundary of the tilted square.
• We added a few buttons for quick selection of a some typical triangulations and sign distributions. But you can also create your own patchworks by hand:
• Remove triangle: Click on it.
• Add triangle: Select three vertices with single clicks.
• Swap color of vertex: Double click on vertex.
• The constructed graph on the right is typically not connected. The software computes the number of connected components for you.
• Affine components: Counts the number of connected components of the graph the way it is depicted.
• Projective components: Counts the number of connected components after gluing the opposite ends, as explained above.
• WARNING: The displayed graph as well as the computation of the numbers of connected components is only "correct" if certain criteria are met (in particular, if you use the convex triangulation of a standard triangle). The software does not check these criteria.
• The program, in particular the extended settings, are still very much beta. Be kind to your browser, you might need it later to watch cat pictures.