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Active galactic nuclei (AGNs) and quasars are important astrophysical objectsto understand. Recently, microlensing observations have constrained the size ofthe quasar X-ray emission region to be of the order of 10 gravitational radiiof the central supermassive black hole. For distances within a fewgravitational radii, light paths are strongly bent by the strong gravity fieldof the central black hole. If the central black hole has nonzero angularmomentum (spin), a photon's polarization plane will be rotated by thegravitational Faraday effect. The observed X-ray flux and polarization willthen be influenced significantly by the strong gravity field near the source.Consequently, linear gravitational lensing theory is inadequate for suchextreme circumstances. We present simple algorithms computing strong lensingeffects of Kerr black holes, including effects on polarization. Our algorithmsare realized in a program "KERTAP" in two versions: MATLAB and Python. The keyingredients of KERTAP are: a graphic user interface, a {\it backward}ray-tracing algorithm, a polarization propagator dealing with gravitationalFaraday rotation, and algorithms computing observables such as fluxmagnification and polarization angles. Our algorithms can be easily realized inother programming languages such as FORTRAN, C, and C++. The MATLAB version ofKERTAP is parallelized using the MATLAB Parallel Computing Toolbox and theDistributed Computing Server. The Python code was sped up using Cython andsupports full implementation of MPI using 'mpi4py' package. As an example, weinvestigate the inclination angle dependence of the observed polarization andthe strong lensing magnification of AGN X-ray emission. We conclude that it ispossible to perform complex numerical-relativity-related computations usinginterpreted languages such as MATLAB and Python.Comment: 11 pages, 7 figure

ALGORITHMS AND PROGRAMS FOR STRONG GRAVITATIONAL LENSING IN KERR SPACE-TIME INCLUDING POLARIZATION