Generic realizations of configurations of lines as reducible projective varieties in Pn are constructed numerically. Examples are taken from projections of abstract seminormal configurations and the classical geometry related to Schläfli’s double-six configuration. The ideal defining the homogeneous coordinate ring of a realization is calculated along with its Hilbert Function, identifying whic...

In this paper, we consider a finite, torsion-free module E over Gorenstein local ring. We provide sufficient conditions for to be of linear type and the Rees algebra R ( ) Cohen-Macaulay. Our results are obtained by constructing generic Bourbaki ideal I exploiting properties residual intersections .

In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive an...

For an ideal I with a positive dimensional real variety VR(I), based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Gröbner basis of an ideal J generated by the kernel of a truncated moment matrix and satisfying I ⊆ J ⊆ I(VR(I)), VR(I) = VC(J) ∩ R. We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algo...

This work is devoted to the study of a network on chip [3] model: IPNoSys (Integrated On-chip Network Processing System), having as main objective to obtain an optimal configuration of the network, comparing performance and power consumption. In this work, the platform IPNoSys shall be subject to execution of a set of synchronous dataflow generic applications. The term “generic” means that they...

Let {f1, f2, . . . , ft} ⊂ Q[z1, . . . , zN ] be a set of homogeneous polynomials. Let Z denote the complex, projective, algebraic set determined by the homogeneous ideal I = (f1, f2, . . . , ft) ⊂ C[z1, . . . , zN ]. Numerical continuation-based methods can be used to produce arbitrary precision numerical approximations of generic points on each irreducible component of Z. Consider the prime d...

This report presents a perspective on software reuse in the context of "ideal" software development capabilities. Software reuse is viewed as a means of achieving—or at least approximating—the ideal capabilities. A generic application and development model is proposed for unifying various types of software reuse. The model can be initially formulated as a project family architecture and produce...

An efficient algorithm is presented for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the ideal is given by its Gröbner basis, no extra Gröbner basis computation is needed for factoring a polynomial over the extension field. We will only use linear algebra to get a polynomial over the base field by a gener...

Let I be an ideal in a polynomial ring over a perfect field. We give new methods for comput ing the equidimensional parts and radical of I, for localizing I with respect to another ideal, and thus for finding the pr imary decomposit ion of / . Our methods rest on modern ideas from commutat ive algebra, and are direct in the sense that they avoid the generic projections used by Hermann (1926) an...

A generic 3D laser-pulse-shaping scheme is proposed towards the generation of a uniform ellipsoidal particle distribution, an ideal distribution due to the linear dependence of the space-charge force on the particle position. The shaping is accomplished via spatiotemporal coupling of the laser dynamics via chromatic aberration in an optical lens. Particle tracking simulations show that the elec...