# How to calculate mapping in bilinear

I am trying to read a paper in cryptography. In key generation phase, paper give a definition for bilinear like G and Gt be two cyclic groups of prime order p

$e: G * G \to G_t$. be a map with the following properties:

and in one place i found a definition like

my doubt is in the last part. Specifically in m.e(g1,gn)^t suppose m is any message, g1=3,gn=13 t=6 (for more information v=5,gi=10.no problem whether all the value assumptions are true or not). then how can i compute e(g1,gn)^t part? sorry for my bad math notation

According to PBC manual, Pairing functions, map $\hat e(,)$ (without t-power) could be calculated as follows:
pairing_pp_t pp;