README.md

@@ -1,2 +1,74 @@
 # Calabi-Yau-Period-Geometry
 
+This project collects code used for analysing Calabi–Yau families.
+It allows for computation of discriminant loci and topological data of manifolds defined as hypersurfaces or complete intersections in toric ambient spaces.
+
+## toric_topdata
+
+Supported initialisations are represented by the following examples.
+
+```python
+elliptic_curve_D = ToricPolytopeProjectiveSpace([1, 2, 3], model_name="elliptic_curve_D")
+
+CY3_quintic = ToricPolytopeProjectiveSpace([1, 1, 1, 1, 1], model_name="quintic")
+CY3_bicubic = ToricPolytopeCICY([[3, 3]], model_name="bi-cubic")
+CICY3_two_parameter_manual_nef = ToricPolytope([[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
+                                                [0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],
+                                                [-1,-1,0,0,0,0],[0,0,-1,-1,-1,-1]],
+                                                nef_partition=[[0,1,2,3], [4,5,6,7]])
+
+CICY5_two_parameter = ToricPolytopeCICY([[6, 1],[0, 2]])
+```
+
+The discriminant factors and topological data, e.g. for the quintic, can then be computed with the methods below.
+```python
+CY3_quintic.disc()
+
+CY3_quintic.topdata()
+```
+
+We list the output of above two lines.
+
+```term
+INFO:__main__:Discriminant factors: [[z1 + 1/3125, 0]]
+INFO:__main__:
+
+--- Polytope and GLSM table ------------------
+ 1|1|1|1|1|| 1
+
+-1|1|0|0|0|| 0
+-1|0|1|0|0|| 0
+-1|0|0|1|0|| 0
+-1|0|0|0|1|| 0
+--------------
+ 1,1,1,1,1; -5
+
+--- L-vectors (GLSM charges) -----------------
+[[1, 1, 1, 1, 1, -5]]
+
+--- Intersection numbers CY ------------------
+{(0, 0, 0): 5}
+
+--- Intersection ring ------------------------
+5*t0^3
+
+--- Intersection ring no multiplicities ------
+5*t0^3
+
+--- Chern polynomials ------------------------
+[[0], [10*t0^3], [-40*t0^3]]
+
+--- Integrated Chern classes -----------------
+[[0], [50], [-200]]
+DEBUG:__main__:
+
+--- Kähler cone generators (ambient space) ---
+['[z4]']
+
+--- Intersection numbers ambient space -------
+{(0, 0, 0, 0): 1}
+```
+
+The result is saved in the folder `data/topdata` as a JSON file — giving a model name helps keeping
+track of these outputs.
+Note that for Calabi–Yau dimensions larger than four, the additional