Documentation¶

CYTools provides six main Python classes containing various functions specific to the objects they describe. These classes are the following:

• Polytope: Handles all computations relating to lattice polytopes, such as the computation of lattice points and faces. When using reflexive polytopes, it also allows the computation of topological properties of the arising Calabi-Yau hypersurfaces that only depend on the polytope.
• PolytopeFace: Handles all computations relating to faces of lattice polytopes.
• Triangulation: Handles triangulations of lattice polytopes. It can compute various properties of the triangulation, as well as construct a ToricVariety or CalabiYau object if the triangulation is suitable.
• ToricVariety: Handles various computations relating to toric varieties. It can be used to compute intersection numbers and the Kähler cone, among other things.
• CalabiYau: Handles various computations relating to the Calabi-Yau manifold itself. It can be used to compute intersection numbers and the toric Mori and Kähler cones, among other things.
• Cone: Handles all computations relating to rational polyhedral cones, such as cone duality and extremal ray computations. It is mainly used for the study of Kähler and Mori cones.

There are also a few more specialized classes and modules:

• HPolytope: Polytopes specified by a list of inequalities (their H-representation) instead of a list of points.
• VectorConfiguration and Fan: Vector configurations and the (simplicial) fans obtained from their triangulations.
• NTFE enumeration: Enumeration of triangulations that are not two-face equivalent.
• F-theory and orientifolds: Datasets of orientifolds and F-theory uplifts.

Apart from the above, there are other miscellaneous functions that are documented in the misc functions page. There are also a few configuration options that can be found in the configuration page, and some experimental features documented in the experimental features page.

CYTools is open-source software distributed under the GNU GPLv3 license. See the license page for more details.