Example usage of “Zedhat” package

“Zedhat” is a simple Mathematica package created by Nikita A. Sopenko back in 2019. 
In this short notebook, we demonstrate how to use it to compute (OverHat[Z]) invariants for some negative-definite plumbed 3-manifolds.

Loading the package

FindFile["Zedhat`"]

<< Zedhat`

(OverHat[Z]) computation

?Zhat

G = {{-1,-2,-3,-7},{1\[UndirectedEdge]2, 1\[UndirectedEdge]3, 1\[UndirectedEdge]4}}; (* a plumbing graph *)
Graph[G[[2]],VertexLabels-> Table[i-> StringForm["``",G[[1,i]]],{i,Length[G[[1]]]}]]

b={1,1,1,1}; (* a choice of spin-c structure *)

With[{qmax=100,kmax=3},Zhat[q,G,b,kmax,qmax]] (* Here, qmax is a cutoff of the degree of q, and kmax is a cutoff in calculation of Zhat; increase kmax to improve accuracy *)