MPWide is a light-weight communication library for distributed computing. It is specifically developed to allow message passing over long-distance networks using path-specific optimizations. An early version of MPWide was used in the Gravitational Billion Body Project to allow simulations across multiple supercomputers.

Mister plotter (mr-plotter) creates paper-quality mass-radius diagrams based on a wide range of state-of-the-art models of planetary interiors and atmospheres. It can be used to contextualize planets and infer their possible internal structures. It can also be used to search for correlations at a population level with its color-coding option based on any property collected in the NASA Exoplanet Archive, PlanetS, and Exoplanet.eu catalogs. mr-plotter can also produce article-ready two-column plots.

MRExo performs non-parametric fitting and analysis of the mass-radius (M-R) relationship for exoplanets. Written in Python, it offers tools for fitting the M-R relationship to a given data set and also includes predicting (M->R, and R->M) and plotting functions.

The MRLENS package offers a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate which allows us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N-Body Lambda-CDM simulations with added noise corresponding to both ground-based and space-based observations.

MrMoose (Multi-Resolution Multi-Object/Origin Spectral Energy) fits user-defined models onto a set of multi-wavelength data using a Bayesian framework. The code can handle blended sources, large variation in resolution, and even upper limits consistently. It also generates a series of outputs allowing for an quick interpretation of the results. The code uses emcee (ascl:1303.002), and saves the emcee sampler object, thus allowing users to transfer the output to a personal graphical interface.

mrpy calculates the MRP parameterization of the Halo Mass Function. It calculates basic statistics of the truncated generalized gamma distribution (TGGD) with the TGGD class, including mean, mode, variance, skewness, pdf, and cdf. It generates MRP quantities with the MRP class, such as differential number counts and cumulative number counts, and offers various methods for generating normalizations. It can generate the MRP-based halo mass function as a function of physical parameters via the mrp_b13 function, and fit MRP parameters to data in the form of arbitrary curves and in the form of a sample of variates with the SimFit class. mrpy also calculates analytic hessians and jacobians at any point, and allows the user to alternate parameterizations of the same form via the reparameterize module.

MRrelation calculates the posterior predictive mass distribution for an individual planet. The probabilistic mass-radius relationship (M-R relation) is evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M-R relation parameters.

The MRS (The MOS Reduction Software) suite reduces the spectra taken with the multi-object spectrograph spectra used as the focal plane instrument of RTT150 telescope in the TÜBİTAK National Observatory.

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.

MSL applies simulation-based inference techniques to the problem of substructure inference in galaxy-galaxy strong lenses. It leverages additional information extracted from the simulator, then trains neural networks to estimate likelihood ratios associated with population-level parameters characterizing dark matter substructure. The package including five high-level scripts which run the simulation and create samples, combing multiple simulation runs into a single file to use for training, then train the neural networks. After training, the estimated likelihood ratio is tested, and calibrated network predictions are made based on histograms of the network output.

Multi-Source Self-Calibration (MSSC) provides direction-dependent calibration to standard phase referencing. The code combines multiple faint sources detected within the primary beam to derive phase corrections. Each source has its CLEAN model divided into the visibilities which results in multiple point sources that are stacked in the uv plane to increase the S/N, thus permitting self-calibration. This process applies only to wide-field VLBI data sets that detect and image multiple sources within one epoch.

MST (Minimum Spanning Tree) identifies velocity coherent large-scale filaments through ATLASGAL clumps. It can also isolate filaments embedded in a crowded position–position–velocity (PPV) space. One strength of this method is its repeatability compared to manual approaches.

MSWAVEF calculates hydrogenic and non-hydrogenic momentum-space electronic wavefunctions. Such wavefunctions are often required to calculate various collision processes, such as excitation and line broadening cross sections. The hydrogenic functions are calculated using the standard analytical expressions. The non-hydrogenic functions are calculated within quantum defect theory according to the method of Hoang Binh and van Regemorter (1997). Required Hankel transforms have been determined analytically for angular momentum quantum numbers ranging from zero to 13 using Mathematica. Calculations for higher angular momentum quantum numbers are possible, but slow (since calculated numerically). The code is written in IDL.

MTNeedlet uses needlets to filter spherical (Healpix) maps and detect and analyze the maxima population using a multiple testing approach. It has been developed with the CMB in mind, but it can be applied to other spherical maps. It pivots around three basic steps: 1.) The calculation of several types of needlets and their possible use to filter maps; 2.) The detection of maxima (or minima) on spherical maps, their visualization and basic analysis; and 3.) The multiple testing approach in order to detect anomalies in the maxima population of the maps with respect to the expected behavior for a random Gaussian map. MTNeedlet relies on Healpy (ascl:2008.022) to efficiently deal with spherical maps.

mTransport computes the 2-point-correlation function of the curvature and tensor perturbations in multifield models of inflation in the presence of a curved field space. It is a Mathematica implementation of the transport method which encompasses scenarios with violations of slow-roll conditions and turns of the trajectory in field space. It can be used for an arbitrary mass spectrum, including massive modes, particle production and models with quasi-single-field dynamics.

muLAn analyzes and fits light curves of gravitational microlensing events. The code includes all classical microlensing models (for example, single and binary microlenses, ground- and space-based parallax effects, orbital motion, finite-source effects, and limb-darkening); these can be combined into several time intervals of the analyzed light curve. Minimization methods include an Affine-Invariant Ensemble Sampler to generate a multivariate proposal function while running several Markov Chain Monte Carlo (MCMC) chains, for the set of parameters which is chosen to be fit; non-fitting parameters can be either kept fixed or set on a grid defined by the user. Furthermore, the software offers a model-free option to align all data sets together and allow inspection the light curve before any modeling work. It also comes with many useful routines (export publication-quality figures, data formatting and cleaning) and state-of-the-art statistical tools.

Modeling results can be interpreted using an interactive html page which contains all information about the light curve model, caustics, source trajectory, best-fit parameters and chi-square. Parameters uncertainties and statistical properties (such as multi-modal features of the posterior density) can be assessed from correlation plots. The code is modular, allowing the addition of other computation or minimization routines by directly adding their Python files without modifying the main code. The software has been designed to be easy to use even for the newcomer in microlensing, with external, synthetic and self-explanatory setup files containing all important commands and option settings. The user may choose to launch the code through command line instructions, or to import muLAn within another Python project like any standard Python package.

MulensModel calculates light curves of microlensing events. Both single and binary lens events are modeled and various higher-order effects can be included: extended source (with limb-darkening), annual microlensing parallax, and satellite microlensing parallax. The code is object-oriented and written in Python3, and requires AstroPy (ascl:1304.002).

Multi_CLASS modifies the Boltzmann code CLASS (ascl:1106.020) to compute of the cross-tracer angular power spectra of the number count fluctuations for two different tracers of the underlying dark matter density field. In other words, it generalizes the standard nCl output option of CLASS to the case of two different tracers, for example, two different galaxy populations with their own redshift distribution, and galaxy and magnification bias parameters, among others.

Multi_CLASS also includes an implementation of the effect of primordial non-Gaussianities of the local type, parametrized by the parameter f_NL (following the large-scale structure convention), on the effective bias of the tracers. There is also the possibility of having a tilted non-Gaussian correction, parametrized by n_NG, with a pivot scale determined by k_pivot_NG. The package includes galaxy redshift distributions for forthcoming galaxy surveys, with the ease of choosing between them (or an input file) from the parameters input file (e.g., multi_explanatory.ini). In addition, Multi_CLASS includes the possibility of using resolved gravitational wave events as a tracer.

The multiband periodogram is a general extension of the well-known Lomb-Scargle approach for detecting periodic signals in time-domain data. In addition to advantages of the Lomb-Scargle method such as treatment of non-uniform sampling and heteroscedastic errors, the multiband periodogram significantly improves period finding for randomly sampled multiband light curves (e.g., Pan-STARRS, DES and LSST). The light curves in each band are modeled as arbitrary truncated Fourier series, with the period and phase shared across all bands.

MultiColorFits is a tool to colorize and combine multiple fits images for making visually aesthetic scientific plots. The standard method to make color composites by combining fits images programmatically in python is to assign three images as separate red, green, and blue channels. This can produce unsatisfactory results for a variety of reasons, such as when less than three images are available, or additional images are desired to be shown. MultiColorFits breaks these limitations by allowing users to apply any color to a given image, not just red, green, or blue. Composites can then be created from an arbitrary number of images. Controls are included for stretching brightness scales with common functions.

MULTIGRIS (also called mgris) uses the sequential Monte Carlo method in PyMC (ascl:1506.005) to extract the posterior distributions of primary grid parameters and predict unobserved parameters/observables. The code accepts either a discrete number of components and/or continuous (e.g., power-law, normal) distributions for any given parameter. MULTIGRIS, written in Python, infers the posterior probability functions of parameters in a multidimensional potentially incomplete grid with some observational tracers defined for each parameter set. Observed values and their potentially asymmetric uncertainties are used to calculate a likelihood which, together with predefined or custom priors, produces the posterior distributions. Linear combinations of parameter sets may be used with inferred mixing weights and nearest neighbor or linear interpolation may be used to sample the parameter space.

MultiModeCode facilitates efficient Monte Carlo sampling of prior probabilities for inflationary model parameters and initial conditions and efficiently generates large sample-sets for inflation models with O(100) fields. The code numerically solves the equations of motion for the background and first-order perturbations of multi-field inflation models with canonical kinetic terms and arbitrary potentials, providing the adiabatic, isocurvature, and tensor power spectra at the end of inflation. For models with sum-separable potentials MultiModeCode also computes the slow-roll prediction via the δN formalism for easy model exploration and validation.

MultiModes extracts the most significant frequencies of a sample of classical pulsating stars. The code takes a directory with light curves and initial parameters as input. For every light curve, the code calculates the frequencies spectrum, or periodogram, with the Fast Lomb Scargle algorithm, extracts the higher amplitude peak, and evaluates whether it is a real signal or noise. It fits frequency, amplitude, and phase through non-linear optimization, using a multisine function. This function is redefined with the new calculated parameters. MultiModes then does a simultaneous fit of a number of peaks (20 by default), subtracts them from the original signal, and goes back to the beginning of the loop with the residual, repeating the same process until the stop criterion is reached. After that, the code can filter suspicious spurious frequencies, those of low amplitude below the Rayleigh resolution, and possible combined frequencies.

We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson (2008), which itself significantly outperformed existing MCMC techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm is demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla $Lambda$CDM model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software is fully parallelized using MPI and includes an interface to CosmoMC (ascl:1106.025). It will also be released as part of the SuperBayeS package (ascl:1109.007) for the analysis of supersymmetric theories of particle physics.

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order l is represented by l unit vectors pointing in directions on the sky and an overall magnitude. These "multipole vectors and scalars" transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). However, they are related to the familiar spherical harmonic coefficients, alm, in a nonlinear way, and are therefore sensitive to different aspects of the CMB anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. Using the WMAP full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs 2<=l1!=l2<=8 is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the ILC map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the l=3 and l=8 multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

Multipoles, written in Python, calculates the quadrupole and hexadecapole approximations of the finite-source magnification: quadrupole (Wk,rho,Gamma) and hexadecapole (Wk,rho,Gamma). The code is efficient and faster than previously available methods, and could be generalized for use on large portions of the light curves.

Munipack provides easy-to-use tools for all astronomical astrometry and photometry, access to Virtual Observatory as well as FITS files operations and a simple user interface along with a powerful processing engine. Its many features include a FITS images viewer that allows for basic (astronomical) operations with frames, advanced image processor supporting an infinite dynamic range and advanced color management, and astrometric calibration of images. The astrometry module uses robust statistical estimators and algorithms. The photometry module provides the classical method detection of stars and implements the aperture photometry, calibrated on the basis of photon statistics, and allows for the automatic detection and aperture photometry of stars; calibration on absolute fluxes is possible. The software also provides a standard way to correct for all the bias, dark and flat-field frames, and many other features.

MuSCAT2_transit_pipeline provides photometry and transit analysis pipelines for MuSCAT2. It consists of a set of executable scripts and two Python packages: muscat2ph for photometry, and muscat2ta for transit analysis. The MuSCAT2 photometry can be carried out using the scripts only. The transit analysis can also in most cases be done using the main transit analysis script m2fit, but the muscat2ta package also offers high-level classes that can be used to carry out more customized transit analysis as a Python script (or Jupyter notebook).

MUSCLE (MUltiscale Spherical ColLapse Evolution) produces low-redshift approximate N-body realizations accurate to few-Megaparsec scales. It applies a spherical-collapse prescription on multiple Gaussian-smoothed scales. It achieves higher accuracy than perturbative schemes (Zel'dovich and second-order Lagrangian perturbation theory - 2LPT), and by including the void-in-cloud process (voids in large-scale collapsing regions), solves problems with a single-scale spherical-collapse scheme.

The MUSE pipeline turns the complex raw data of the MUSE integral field spectrograph into a ready-to-use datacube for scientific analysis.

MUSE-PSFR reconstructs a PSF for the MUSE WFM-AO mode using telemetry data from SPARTA. The algorithm conducts a Fourier analysis of the laser-assisted ground layer adaptive optics (GLAO) residual phase statistics and has been test in end-to-end simulations. A sensitivity analysis was conducted to determine the required accuracy in terms of input parameters. MUSE-PSFR is capable of reconstructing the critical parameters of a PSF and can be used with MUSE 3D data by all MUSE users.

MUSIC generates multi-scale initial conditions with multiple levels of refinements for cosmological ‘zoom-in’ simulations. The code uses an adaptive convolution of Gaussian white noise with a real-space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first- (1LPT) or second-order Lagrangian perturbation theory (2LPT). MUSIC achieves rms relative errors of the order of 10−4 for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches. In addition, errors are localized at coarse-fine boundaries and do not suffer from Fourier space-induced interference ringing.

The original MUSIC code (ascl:1311.011) was designed to provide initial conditions for zoom initial conditions and is limited for applications to large-scale cosmological simulations. MUSIC2-monofonIC generates high order LPT/PPT cosmological initial conditions for single resolution cosmological simulations, and can be used for rapid predictions of large-scale structure. MUSIC2-monofonIC offers support for up to 3rd order Lagrangian perturbation theory, PPT (Semiclassical PT for Eulerian grids) up to 2nd order, and for mixed CDM+baryon sims. It direct interfaces with CLASS and can use file input from CAMB; it offers multiple output modules for RAMSES (ascl:1011.007), Arepo (ascl:1909.010), Gadget-2/3 (ascl:0003.001), and HACC via plugins, and new modules/plugins can be easily added.

myRadex solves essentially the same problem as RADEX (ascl:1010.075), except that it takes a different approach to solve the statistical equilibrium problem. Given an initial distribution, myRadex evolves the system towards equilibrium using an ODE solver. Frequencies in the input file are used by default, and a function for calculating critical densities of all the transitions of a molecule is included.

MYRaf is a practicable astronomical image reduction and photometry software and interface for IRAF (ascl:9911.002). The library uses IRAF, PyRAF (ascl:1207.011), Ginga (ascl:1303.020), and other python packages with a Qt framework for automated software processing of data from robotic telescopes.

MYRIAD is a C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, binary and multiple sub-systems that either form dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6 could be replaced by another module that uses other accelerating-hardware like the Graphics Processing Units (GPUs). Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. The code accuracy becomes comparable and even better than the accuracy of existing codes when a number of close binary systems is dynamically created in a simulation; this is due to the high accuracy of the method that is used for close binary and multiple sub-systems. The code can be used for evolving star clusters containing equal-mass stars or star clusters with an initial mass function (IMF) containing an intermediate mass black hole (IMBH) at the center and/or a fraction of primordial binaries, which are systems of particular astrophysical interest.

N-GenIC is an initial conditions code for cosmological structure formation that can be used to set-up random N-body realizations of Gaussian random fields with a prescribed power spectrum in a homogeneously sampled periodic box. The code creates cosmological initial conditions based on the Zeldovich approximation, in a format directly compatible with GADGET (ascl:0003.001) or AREPO (ascl:1909.010).

N-MODY is a parallel particle-mesh code for collisionless N-body simulations in modified Newtonian dynamics (MOND). N-MODY is based on a numerical potential solver in spherical coordinates that solves the non-linear MOND field equation, and is ideally suited to simulate isolated stellar systems. N-MODY can be used also to compute the MOND potential of arbitrary static density distributions. A few applications of N-MODY indicate that some astrophysically relevant dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter.

NAFE (Noise Adaptive Fuzzy Equalization) is an image processing method allowing for visualization of fine structures in SDO AIA high dynamic range images. It produces artifact-free images and gives significantly better results than methods based on convolution or Fourier transform.

Nahoon is a gas-phase chemical model that computes the chemical evolution in a 1D temperature and density structure. It uses chemical networks downloaded from the KInetic Database for Astrochemistry (KIDA) but the model can be adapted to any network. The program is written in Fortran 90 and uses the DLSODES (double precision) solver from the ODEPACK package (ascl:1905.021) to solve the coupled stiff differential equations. The solver computes the chemical evolution of gas-phase species at a fixed temperature and density and can be used in one dimension (1D) if a grid of temperature, density, and visual extinction is provided. Grains, both neutral and negatively charged, and electrons are considered as chemical species and their concentrations are computed at the same time as those of the other species. Nahoon contains a test to check the temperature range of the validity of the rate coefficients and avoid extrapolations outside this range. A test is also included to check for duplication of chemical reactions, defined over complementary ranges of temperature.

naif extracts frequencies and respective amplitudes from time-series, such as that of an orbital coordinate. Based on the Numerical Analysis of Fundamental Frequencies (NAFF) algorithm and written in Python, naif offers some improvements, particularly in computation time. It also offers functions to plot the power-spectrum before extraction of each frequency, which can be useful for debugging particular orbits.

Naima computes non-thermal radiation from relativistic particle populations. It includes tools to perform MCMC fitting of radiative models to X-ray, GeV, and TeV spectra using emcee (ascl:1303.002), an affine-invariant ensemble sampler for Markov Chain Monte Carlo. Naima is an Astropy (ascl:1304.002) affiliated package.

NaMaster computes full-sky angular cross-power spectra of masked, spin-0 and spin-2 fields with an arbitrary number of known contaminants using a pseudo-Cl (aka MASTER) approach. The code also implements E/B-mode purification and offers both full-sky and flat-sky modes. NaMaster is available as a C library, Python module, and standalone program.

nanopipe is a data reduction pipeline for calibration, RFI removal, and pulse time-of-arrival measurement from radio pulsar data. It was developed primarily for use by the NANOGrav project. nanopipe is written in Python, and depends on the PSRCHIVE (ascl:1105.014) library.

NAPLES (Numerical Analysis of PLanetary EncounterS) performs batch propagations of close encounters in the three-body problem and computes the numerical error with respect to reference trajectories computed in quadruple precision. It uses the LSODAR integrator from ODEPACK (ascl:1905.021) and the equations of motion correspond to several regularized formulations.

Nauyaca infers planetary masses and orbits from mid-transit times fitting. The code requires transit ephemeris per planet and stellar mass and radius, and uses minimization routines and a Markov chain Monte Carlo method to find planet parameters that best reproduce the transit times based on numerical simulations. The code package provides customized plotting tools for analyzing the results.

NAVanalysis studies the non-baryonic, or non-Newtonian, contribution to galaxy rotation curves straight from a given data sample. Conclusions on the radial profile of a given model can be drawn without individual galaxy fits to provide an efficient sample comparison. The method can be used to eliminate model parameter regions, find the most probable parameter regions, and uncover trends not easy to find from standard fits. Further, NAVanalysis can compare different approaches and models.

I review the development of direct N-body codes at Cambridge over nearly 40 years, highlighting the main stepping stones. The first code (NBODY1) was based on the simple concepts of a force polynomial combined with individual time steps, where numerical problems due to close encounters were avoided by a softened potential. Fortuitously, the elegant Kustaanheimo-Stiefel two-body regularization soon permitted small star clusters to be studied (NBODY3). Subsequent extensions to unperturbed three-body and four-body regularization proved beneficial in dealing with multiple interactions. Investigations of larger systems became possible with the Ahmad-Cohen neighbor scheme which was used more than 20 years ago for expanding universe models of 4000 galaxies (NBODY2). Combining the neighbor scheme with the regularization procedures enabled more realistic star clusters to be considered (NBODY5). After a period of simulations with no apparent technical progress, chain regularization replaced the treatment of compact subsystems (NBODY3, NBODY5). More recently, the Hermite integration method provided a major advance and has been implemented on the special-purpose HARP computers (NBODY4) together with an alternative version for workstations and supercomputers (NBODY6). These codes also include a variety of algorithms for stellar evolution based on fast lookup functions. The treatment of primordial binaries contains efficient procedures for chaotic two-body motion as well as tidal circularization, and special attention is paid to hierarchical systems and their stability. This family of N-body codes constitutes a powerful tool for dynamical simulations which is freely available to the astronomical community, and the massive effort owes much to collaborators.

nbody6tt, based on Aarseth's nbody6 (ascl:1102.006) code, includes the treatment of complex galactic tides in a direct N-body simulation of a star cluster through the use of tidal tensors (tt) and offers two complementary methods. The first allows consideration of any kind of galaxy and orbit, thus offering versatility; this method cannot be used to study tidal debris, as it relies on the tidal approximation (linearization of the tidal force). The second method is not limited by this and does not require a galaxy simulation; the user defines a numerical function which takes position and time as arguments, and the galactic potential is returned. The space and time derivatives of the potential are used to (i) integrate the motion of the cluster on its orbit in the galaxy (starting from user-defined initial position and velocity vector), and (ii) compute the tidal acceleration on the stars.

NbodyGradient computes gradients of N-body integrations for Newtonian gravity and arbitrary N-body hierarchies. Developed for transit-timing analyses and written in Julia, NbodyGradient gives derivatives of the transit times with respect to the initial conditions, either masses and Cartesian coordinates/velocities or orbital elements.