Software implementation of symmetric and asymmetric bilinear pairings I have recently read a paper about pairings, which only implemented asymmetric bilinear pairings and it mentiond that $\eta_{T}$ pairing is the most efficient algorithm for symmetric pairings. I wonder is there any software implementation on elliptic curves could achieve both asymmetric and symmetrci pairings e.g. $e(g,g), e(g,h), g\in G_{1}, h\in G_{2}$
Take a look to MAGMA. To evaluate MAGMA scripts, in their website go to the tab Calculator. Craige Costello has a free tutorial titled Pairings for Beginners with examples of the Weil and Tate pairings in MAGMA.