The Inverse Gröbner Basis Problem in Codimension Two

Inverse Gröbner Basis Problem in Codimension Two

Generic linkage is used to compute a prime ideal such that the radical of the initial ideal of the prime ideal is equal to the radical of a given codimension two monomial ideal that has a Cohen-Macaulay quotient ring.

Deformations of Codimension 2 Toric Varieties

We prove Sturmfels’ conjecture that toric varieties of codimension two have no other flat deformations than those obtained by Gröbner basis theory.

A New Algorithm for Discussing Gröbner Bases with Parameters

In many practical applications it is necessary to determine a Gröbner basis of an ideal of polynomials whose coefficients depend on some parameters. The main problem in this context is to obtain the distinct reduced Gröbner basis for all possible values of the parameters. Examples of this situation can be found, for instance, in constructive algebraic geometry when determining conditions for a ...

Lifting Problem in Codimension 2 and Initial Ideals

Determination of a Source Term in an Inverse Heat Conduction Problem by Radial Basis Functions

In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...