Gravitational waves (GW) from eccentric binaries have intricate signals
encoding important features about the location, creation and evolution of the
sources. Eccentricity shortens the merger time, making the emitted GW
statistically predominant in the observed data once detectors will reach the
required sensitivity. We present a novel implementation of fully analytical GW
templates from eccentric binary black hole (BBH) mergers within the
\texttt{Wolfram Mathematica} software. We increase the accuracy by identifying
and minimizing the possible source of errors. We start with an overview of the
physics involved in eccentric mergers, then assemble the strain for the
inspiral by employing up to six post-Newtonian (PN) corrections. We complete
the eccentric inspiral with the quasi-circular Backwards one Body (BoB) merger
model in frequency, amplitude and phase, then we build the hybrid GW strain for
the whole evolution of the binary. For low eccentricity we reach coincidence in
the overlap, with no ambiguity in the time interval, a remarkable improvement
from the usual matching techniques. For high-eccentricity we compensate for the
implicit quasi-circular assumption of the BOB approach, by introducing a small
rescaling in amplitude. Our streamlined implementation is relevant for the new
field of GW astronomy and is straightforward to understand, use and extend,
offering researchers in the field a valuable open resource tool.
