FANTASY: User-Friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation. (arXiv:2010.02237v4 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Christian_P/0/1/0/all/0/1">Pierre Christian</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Chan_C/0/1/0/all/0/1">Chi-kwan Chan</a>

We present FANTASY (Finally A Numerical Trajectory Algorithm both
Straightforward and sYmplectic), a user-friendly, open-source symplectic
geodesic integrator written in Python. FANTASY is designed to work
“out-of-the-box” and does not require anything from the user aside from the
metric and the initial conditions for the geodesics. FANTASY efficiently
computes derivatives up to machine precision using automatic differentiation,
allowing the integration of geodesics in arbitrary space(times) without the
need for the user to manually input Christoffel symbols or any other metric
derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that
doubles the phase space, where two copies of the particle phase space are
evolved together. This technique allows for an integration scheme that is both
explicit and symplectic, even when the Hamiltonian is not separable. FANTASY
comes prebuilt with second and fourth order schemes, and is easily extendible
to higher order schemes. FANTASY also includes an automatic Jacobian calculator
that allows for coordinate transformations to be done automatically.

We present FANTASY (Finally A Numerical Trajectory Algorithm both
Straightforward and sYmplectic), a user-friendly, open-source symplectic
geodesic integrator written in Python. FANTASY is designed to work
“out-of-the-box” and does not require anything from the user aside from the
metric and the initial conditions for the geodesics. FANTASY efficiently
computes derivatives up to machine precision using automatic differentiation,
allowing the integration of geodesics in arbitrary space(times) without the
need for the user to manually input Christoffel symbols or any other metric
derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that
doubles the phase space, where two copies of the particle phase space are
evolved together. This technique allows for an integration scheme that is both
explicit and symplectic, even when the Hamiltonian is not separable. FANTASY
comes prebuilt with second and fourth order schemes, and is easily extendible
to higher order schemes. FANTASY also includes an automatic Jacobian calculator
that allows for coordinate transformations to be done automatically.

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