Related papers: Elimination Templates in Macaulay2
To locate all eigenvalues of a matrix more precisely, we exclude some sets which do not include any eigenvalue of the matrix from the well-known Brauer set to give two new Brauer-type eigenvalue inclusion sets. And it is also shown that the…
We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. Minimal differential…
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…
This paper presents a new algorithm based on interval methods for rigorously constructing inner estimates of feasible parameter regions together with enclosures of the solution set for parameter-dependent systems of nonlinear equations in…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment…
The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…
The CompModels package for R provides a suite of computer model test functions that can be used for computer model prediction/emulation, uncertainty quantification, and calibration, but in particular, the sequential optimization of computer…
We formalise, in Coq, the opening sections of Parity Complexes [Street1991] up to and including the all important excision of extremals algorithm. Parity complexes describe the essential combinatorial structure exhibited by simplexes, cubes…
For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded…
The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomial ideals related to integral dependence. We discuss two…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
We develop a package using the computer algebra system GAP for computing the decomposition of a representation $\rho$ of a finite group $G$ over $\mathbb{C}$ into irreducibles, as well as the corresponding decomposition of the centraliser…
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
This note introduces the Macaulay2 package SchurVeronese, which gathers together data about Veronese syzygies and makes it readily accessible in Macaulay2. In addition to standard Betti tables, the package includes information about the…
In recent years, the combinatorial properties of monomials ideals and binomial ideals have been widely studied. In particular, combinatorial interpretations of free resolution algorithms have been given in both cases. In this present work,…