Related papers: Maple+GrTensorII libraries for cosmology
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
The paper-and-pencil calculator is a cosmological nomogram which allows to find relations between redshift, distance, age of the Universe, physical and angular sizes, luminosity and apparent magnitude for the standard cosmological model…
We develop a link between degree estimates for rational sphere maps and compressed sensing. We provide several new ideas and many examples, both old and new, that amplify connections with linear programming. We close with a list of ten open…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
Aims: The interactive software package iCosmo, designed to perform cosmological calculations is described. Methods: iCosmo is a software package to perform interactive cosmological calculations for the low redshift universe. Computing…
We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It contains routines for vertex and facet enumeration, computation of…
This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
`ronswanson` provides a simple-to-use framework for building so-called table or template models for `astromodels`the modeling package for multi-messenger astrophysical data-analysis framework, `3ML`. With `astromodels` and `3ML` one can…
Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from…
A combined N--body/SPH code is presented which benefits from the high speed of the special purpose hardware GRAPE (GRAvity PipE). Besides gravitational forces, GRAPE also returns the list of neighbours and can, therefore, be used to speed…
Within the framework of the German Astrophysical Virtual Observatory (GAVO), we provide synthetic spectra, simulation software for the calculation of NLTE model atmospheres, as well as necessary atomic data. This will enable a VO user to…
With the help of our own software package DifEqTools, numerical modeling of the cosmological evolution of a system consisting of an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields, a classical field and a phantom…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…
This article provides a method for quick computation of galaxy two-point correlation function(2pCF) from redshift surveys using python. One of the salient features of this approach is that it can be used for calculating galaxy clustering…
Gravitational lensing is a fundamental tool for cosmology. A recent instrument which will provide more information for models of these objects is ALMA. Our goal is to select lens candidates to observe with ALMA and then model them using…
We present a small computer algebra program for use in Maxwell's theory. The Maxwell equations and the energy-momentum current of the electromagnetic field are formulated in the language of exterior differential forms. The corresponding…
We discuss the construction of cosmological models within the framework of Macroscopic Gravity (MG), which is a theory that models the effects of averaging the geometry of space-time on large scales. We find new exact spatially homogeneous…
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…