Related papers: RationalMaps, a package for Macaulay2
We offer a Maple package SL\_2\_Inv\_Ker for calculating of minimal generating sets for the algebras of joint invariants/semi-invariants of binary forms and for calculations of the kernels of Weitzenb\"ock derivations.
The tautological ring of the moduli space of stable curves has been studied extensively in the last decades. We present a SageMath implementation of many core features of this ring. This includes lists of generators and their products,…
Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular…
This paper presents a MATLAB toolbox for computing the conformal mapping from a given polygonal multiply connected domain onto a circular multiply connected domain and its inverse. The toolbox can be used for multiply connected domains with…
In our understanding, a mind-map is an adaptive engine that basically works incrementally on the fundament of existing transactional streams. Generally, mind-maps consist of symbolic cells that are connected with each other and that become…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
Normaliz is a tool for the computation of Hilbert bases of normal affine monoids and related tasks. We describe the Macaulay 2 interface to Normaliz. It makes Normaliz accessible for operations on monoid algebras in Macaulay 2 and,…
Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…
Instead of a monolithic programming language trying to cover all features of interest, some programming systems are designed by combining together simpler languages that cooperate to cover the same feature space. This can improve usability…
We introduce the $\textit{Macaulay2}$ package $\texttt{OIGroebnerBases}$ for working with OI-modules over Noetherian polynomial OI-algebras. The main methods implement OI-analogues of Buchberger's algorithm and Schreyer's theorem to compute…
This paper presents maplet, an open-source R package for the creation of highly customizable, fully reproducible statistical pipelines for omics data analysis, with a special focus on metabolomics-based methods. It builds on the…
Humans are expert explorers. Understanding the computational cognitive mechanisms that support this efficiency can advance the study of the human mind and enable more efficient exploration algorithms. We hypothesize that humans explore new…
The article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmology
We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…
We introduce a diagrammatic language for compact, orientable 3-dimensional manifolds with boundary. A diagrammatic calculus (both integral and rational version) appropriate for this language is introduced and its completeness is proved in…
This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct…
We present three equivalence classes of rational non-invertible multidimensional compatible maps. These maps turns out to be idempotent and by construction they admit birational partial inverses (companion maps) which are Yang-Baxter maps.…
We introduce the Macaulay2 package BooleanGB, which computes a Gr\"obner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an…
This is, mostly, a survey of results about the birational geometry of rationally connected manifolds, using rational curves analogous to lines in ${\mathbb P}^n$ ({\it quasi-lines}). Various characterizations of a Zariski neighbourhood of a…
We describe the \texttt{Imeall} package for the calculation and indexing of atomistic properties of grain boundaries in materials. The package provides a structured database for the storage of atomistic structures and their associated…