Related papers: Maple+GrTensorII libraries for cosmology
We present a new open source C library \texttt{msolve} dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic framework of \texttt{msolve} relies on Gr\''obner bases and…
We present our implementation of an algorithm which functions as a numerical oracle for the Newton polytope of a hypersurface in the Macaulay2 package NumericalNP.m2. We propose a tropical membership test, relying on this algorithm, for…
CLIFFORD performs various computations in Grassmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in Cl(B) - the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B.…
We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight…
We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.
This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety…
Weak gravitational lensing is a promising tool for the study of the mass distribution in the Universe. Here we report some partial results that show how lensing maps can be used to differentiate between cosmological models. We pay special…
We review several aspects of clusters of galaxies and their application to cosmology. We present first results of numerical simulations of the dynamics of the intra-cluster gas and of different interaction processes between cluster galaxies…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…
On the basis of the relativistic kinetic theory the relativistic statistical systems with scalar interaction particles are investigated. The self-consistent system of the equations describing self-gravitating plasma with interpartial scalar…
This paper is a sequel in which we further analyze the recently derived quantum gravity equations which apply in accelerating cosmological spacetimes and whose solutions should be equivalent to all order re-summations of the perturbative…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical…
We present the Macaulay2 package TropicalToric.m2 for toric intersection theory computations using tropical geometry.
The purpose of these lectures is to give a short introduction into a very vast field of numerical simulations for cosmological applications. I focus on major features of the simulations: the equations, main numerical techniques, effects of…
We describe a new software package for computing multiplier ideals in certain cases, including monomial ideals, monomial curves, generic determinantal ideals, and hyperplane arrangements. In these cases we take advantage of combinatorial…
This paper represents the first investigation of the suitability and performance of Graphcore Intelligence Processing Units (IPUs) for deep learning applications in cosmology. It presents the benchmark between a Nvidia V100 GPU and a…
This tutorial illustrates how to use Grayson and Stillman's computer algebra system, Macaulay2, to study schemes. The examples are taken from the homework for an algebraic geometry class given at the University of California, Berkeley in…