A Dimension Series for Multivariate Splines.
A new algorithm for the Quillen-Suslin theorem.
A procedure to compute prime filtration
Let K be a field, S = K[x 1, … x n] be a polynomial ring in n variables over K and I ⊂ S be an ideal. We give a procedure to compute a prime filtration of S/I. We proceed as in the classical case by constructing an ascending chain of ideals of S starting from I and ending at S. The procedure of this paper is developed and has been implemented in the computer algebra system Singular.
A remark on Hodge algebras and Gröbner bases
A standard basis approach to syzygies of canonical curves.
A terminal area topology-independent GB-based conflict detection system for A-SMGCS.
A module for conflict detection in A-SMGCS is presented. It supervises the operations that the ground controller has to perform. It doesn?t depend on the topology of the terminal area. The system guarantees the safety of the proposed situation, that is, the impossibility that a conflict arises among aircrafts (and also road vehicles) obeying the signaling. We suppose that the terminal area has stop bars (or semaphores) controlling all intersections and accesses between runways, taxiways, exits,...
Algebraic Methods for Studying Interactions Between Epidemiological Variables
BackgroundIndependence models among variables is one of the most relevant topics in epidemiology, particularly in molecular epidemiology for the study of gene-gene and gene-environment interactions. They have been studied using three main kinds of analysis: regression analysis, data mining approaches and Bayesian model selection. Recently, methods of algebraic statistics have been extensively used for applications to biology. In this paper we present...
Algebraic proofs for geometric statements.
Algebraically solvable problems: describing polynomials as equivalent to explicit solutions.
Algorithm for the Gröbner region of a principal ideal.
Algorithms for the computation of moduli spaces for semiquasihomogeneous singularities.
We present algorithms and their implementation in the computer algebra system Singular 2.0 for the computation of equations for moduli spaces for semiquasihomogeneous singularities w.r.t. right equivalence. In addition, we describe the structure of the stabilizer group of Brieskorn-Pham singularities.
An Algorithm for Lifting Points in a Tropical Variety
An algorithm to calculate the kernel of certain polynomial ring homomorphisms.
Border bases and kernels of homomorphisms and of derivations
Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.
Borel ideals in three variables.
Bounds on degrees of projective schemes.
Canonical bases for subalgebras on two generators in the univariate polynomial ring.
Castelnuovo-Mumford regularity of products of ideals.
The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...
Classification of solvable Lie algebras.
Cohen-Macaulay modifications of the vertex cover ideal of a graph
We study when the modifications of the Cohen-Macaulay vertex cover ideal of a graph are Cohen-Macaulay.