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.