Visualize relations among Sarkisov links
Visualize relations among Sarkisov links over a perfect field
[here] and [here] on the hompage of Stéphane Lamy.
Decompose birational maps of the plane
This is program created by Thibault Chailleux in his [master thesis]. It decomposes any birational map of the complex projective plane into quadratic maps.
Due to long computation time I limited the degree to < 31.
Let me know if you need me to increase the limit.
Here is how it works:
- Crate the map and decompose :
- Give it a name (f,g,...).
- Pick a letter used for the base-points (choose p if you want to name your points p0, p1, p2,...).
- Choose the degree of your transformation. Due to long computation time I limited the degree to < 31.
- Press "Compute transformation". It lists all possible characteristics for your chosen degree. Pick one and press "Compute transformation" again.
- Choose which base-points you want to be infinitely near whom. The points are automatically ordered so that p_i can only be infinitely near p_j, j< i.
- Press "Add transformation". It safes it on the right-hand side, where you also get its decomposition into quadratic transformations. You have now finished creating the transformation.
- If you have created more than one transformation, you can choose under "Transformation" which map you want to see a decomposition of.
- Compose transformations from the right-hand side:
- Choose a name of your decomposition (f,g,...) that you have not used yet.
- Under "Sub transformation" you can choose any of the transformations you have created.
- The list below contains your chosen map and the quadratic transformations from the given decomposition.
- Choose the maps in this list you want to compose. You may change the "sub-transformation" any time to add other maps to the composition.
- Press "compute". You now find the decomposition in the list "Transformation".