Tope fields were introduced in the study of tropical oriented matroids and have been used generalise and study matching fields. In this package we follow the conventions of tope fields given by Smith and Loho, i.e., the type of a tope field contains positive entries.
The combinatorial data of a tope field is given by a matching field for $Gr(k,n)$ together with a type: $(t_1, \dots, t_s)$ where $t_1 + \dots + t_s = k$ and each $t_i$ is a positive integer. The bipartite graphs of the tope field are encoded in the tuples of the matching field as follows. Let $(i_{1,1}, i_{1,2}, \dots i_{1,t_1}, i_{2,1}, \dots, i_{s, t_s})$ be a tuple of the matching field, the bipartite graph on vertices $L := [n]$ and $R := [s]$ has edges $\{i_{j, t}, j\}$ where $j \in [s]$ and $t \in [t_j]$.
For example, if $(1,3,2)$ is a tuple of a matching field for $Gr(3,4)$ of a tope field of type $(2,1)$, then corresponding bipartite graph on vertices $L = [4]$ and $R = [2]$ has edges: $E = \{11, 31, 22 \}$.
The TopeField type in this package is a HashTable that stores the matching field and type. A tope field can be defined from a matching field using the constructor topeField. New tope fields can be constructed from old using the function amalgamation. Note that amalgamation is only defined for linkage tope field, see isLinkage.