: Three algorithms for multiple lensing with contour integration

Context. Modeling of microlensing events poses computational challenges for the resolution of the lens equation and the high dimensionality of the parameter space. In particular, numerical noise represents a severe limitation to fast and efficient calculations of microlensing by multiple systems, which are of particular interest in exoplanetary searches. Aims. We present a new public code built on our previous experience on binary lenses that introduces three new algorithms for the computation of magnification and astrometry in multiple microlensing. Methods. In addition to the classical polynomial resolution, we introduce a multi-polynomial approach in which each root is calculated in a frame centered on the closest lens. In addition, we propose a new algorithm based on a modified Newton-Raphson method applied to the original lens equation without any numerical manipulation. Results. These new algorithms are more accurate and robust compared to traditional single-polynomial approaches at a modest computational cost, opening the way to massive studies of multiple lenses. The new algorithms can be used in a complementary way to optimize efficiency and robustness.