Related papers: Cylindrical Algebraic Decompositions for Boolean C…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
We adress the problem of the algebraic decoding of any cyclic code up to the true minimum distance. For this, we use the classical formulation of the problem, which is to find the error locator polynomial in terms of the syndroms of the…
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…
New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Canonical Polyadic Decomposition (CPD) of a third-order tensor is a minimal decomposition into a sum of rank-$1$ tensors. We find new mild deterministic conditions for the uniqueness of individual rank-$1$ tensors in CPD and present an…
For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In…
A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…
Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
This paper investigates the problem of decomposition with respect to outputs for Boolean control networks (BCNs). First, with the linear expression of BCNs and the matrix semi-tensor product, some algebraic equivalent conditions for the…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
A new algorithm for deciding the satisfiability of polynomial formulas over the reals is proposed. The key point of the algorithm is a new projection operator, called sample-cell projection operator, custom-made for Conflict-Driven Clause…
In 1994 Lazard proposed an improved method for cylindrical algebraic decomposition (CAD). The method comprised a simplified projection operation together with a generalized cell lifting (that is, stack construction) technique. For the proof…
Cylindrical Algebraic Decomposition (CAD) algorithms typically produce a decomposition adapted to a finite family of semi-algebraic sets $\mathcal{F}$ (i.e. every member of $\mathcal{F}$ is a union of cells). Different algorithms may…
We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$.…
Uncertain information is commonplace in real-world data management scenarios. The ability to represent large sets of possible instances (worlds) while supporting efficient storage and processing is an important challenge in this context.…
Determining the satisfiability of Boolean constraint-satisfaction problems with different types of constraints, that is hybrid constraints, is a well-studied problem with important applications. We study here a new application of hybrid…