An Algebraic Approach to the Residues in Algebraic Geometry.
An algebraic construction of the generic singularities of Boardman-Thom
An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
An algorithm for computing the kernel of a locally finite higher derivation up to a certain degree
This paper gives an algorithm for computing the kernel of a locally finite higher derivation on the polynomial ring k[x₁,..., xₙ] up to a given bound.
An Algorithm for Lifting Points in a Tropical Variety
An algorithm for primary decomposition in polynomial rings over the integers
We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals, resp. over finite fields, and the idea of Shimoyama-Yokoyama, resp. Eisenbud-Hunecke-Vasconcelos, to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular. Examples and timings are given at the end of the article.
An algorithm to calculate the kernel of certain polynomial ring homomorphisms.
An algorithm to compute the kernel of a derivation up to a certain degree
An algorithm is described which computes generators of the kernel of derivations on k[X₁,...,Xₙ] up to a previously given bound. For w-homogeneous derivations it is shown that if the algorithm computes a generating set for the kernel then this set is minimal.
An analogue of the Erdős-Ginzburg-Ziv theorem for quadratic symmetric polynomials.
An application of classical invariant theory to identifiability in nonparametric mixtures
It is known that the identifiability of multivariate mixtures reduces to a question in algebraic geometry. We solve the question by studying certain generators in the ring of polynomials in vector variables, invariant under the action of the symmetric group.
An Application of Jonsson Modules to Some Questions Concerning Proper Subrings.
An application of modules of generalized fractions to grades of ideals and Gorenstein rings
An application of type sequences to the blowing-up.
An approximation theorem for Dubrovin valuation rings.
An Arithmetic Characterization of the Rational Homotopy Groups of Certain Spaces.
An axiomatic approach to homological dimension.
An Effective Approach to Keller's Jacobian Conjecture.
An effective procedure for minimal bases of ideals in Z[x]
We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.