Related papers: Elimination Templates in Macaulay2
We review the enveloping algebra of the 10 dimensional chiral sigma matrices. To facilitate the computation of the product of several chiral sigma matrices we have developed a symbolic program. Using this program one can reduce the…
Proving program termination is key to guaranteeing absence of undesirable behaviour, such as hanging programs and even security vulnerabilities such as denial-of-service attacks. To make termination checks scale to large systems,…
We present a novel method for predicting binary phase diagrams through the automatic construction of a minimal basis set of representative templates. The core assumption is that any materials space can be divided into a small number of…
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…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the…
Explainability techniques for data-driven predictive models based on artificial intelligence and machine learning algorithms allow us to better understand the operation of such systems and help to hold them accountable. New transparency…
Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning…
We present in this paper a routine which construct the ideal generated by a list of elements in a matrix Lie algebra at any particular characteristic. We have used this algorithm to analyze the problem of the simplicity of some Lie…
We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce…
We introduce DDE-Solver, a Maple package designed for solving Discrete Differential Equations (DDEs). These equations are functional equations relating algebraically a formal power series F(t, u) with polynomial coefficients in a…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
We introduce the AdditiveToricVarieties package for Macaulay2, a software system for algebraic geometry and commutative algebra, with methods for working with additive group actions on complete toric varieties. More precisely, we implement…
This paper represents notes of the mini-courses given by the authors at the GCGTA conference in Dortmund (2007), Ottawa-Saint Sauveur conference (2007), Escola d'Algebra in Rio de Janeiro (2008) and Alagna (Italy, 2008) conference on…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
We present a methodology for formulating simplifying abstractions in machine learning systems by identifying and harnessing the utility structure of decisions. Machine learning tasks commonly involve high-dimensional output spaces (e.g.,…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…
Recognising and locating image patches or sets of image features is an important task underlying much work in computer vision. Traditionally this has been accomplished using template matching. However, template matching is notoriously…
The \texttt{StronglyStableIdeals} package for \textit{Macaulay2} provides a method to compute all saturated strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. A description of the main method and auxiliary…