Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into well constrained, over-, and underconstrained subsystems. This paper also gives an efficient method to decompose well constrained systems into irreducible ones....

Unprojection theory analyzes and constructs complicated commutative rings in terms of simpler ones. Our main result is that, on the algebraic level of Stanley-Reisner rings, stellar subdivisions of Gorenstein* simplicial complexes correspond to unprojections of type Kustin-Miller. As an application of our methods we study the minimal resolution of Stanley– Reisner rings associated to stacked po...

Many inequalities involving the functions ln, exp, sin, cos, etc., can be proved automatically by MetiTarski: a resolution theorem prover (Metis) modified to call a decision procedure (QEPCAD) for the theory of real closed fields. The decision procedure simplifies clauses by deleting literals that are inconsistent with other algebraic facts, while deleting as redundant clauses that follow algeb...

We study the local topological structure of generic multijet preimages of algebraic varieties and prove their stratifiability with additional quantitative estimates. The result is a necessary technical tool for analyzing bifurcations of periodic orbits from heteroclinic polygons of vector fields in space. The proof is based on interpretation of Newton interpolation formula as a resolution of si...

We describe a IJirect Linear Algebraic I)econvolution (DI,AI)) approach to imaging of data from Compton ~-ray telescopes. lrnposition of the additional physical constraint, that all components of the model bc non-negative, has been found to have a powerful effect in stabilizing the results, giving spatial resolution at or near the instrumental limit. A companion paper (Dixon et al. 1993) presen...

WC Abstract CIT image reconstruction using information regarding shape of the electron density distribution in the plane of interested is implemented using a volumetric iterative techinique. Shape estimation and guidance is provided on a localized basis both in the projection and image domains of the algebraic reconstruction process. Preliminary results ofIRl-90 based simulations indicate subst...

We propose two local invariants for the inductive proof of the embedded resolution of purely inseparable surface singularities of order equal to the characteristic. The invariants are built on an detailed analysis of the so called kangaroo phenomenon in positive characteristic. They thus measure accurately the algebraic complexity of an equation defining a surface singularity in characteristic ...

Motivic integration is a powerful technique to prove that certain quantities associated to algebraic varieties are birational invariants or are independent of a chosen resolution of singularities. We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals of a very general typ...

We propose to design new algorithms for motion planning problems based on the Domain Subdivision paradigm, but coupled with numerical primitives. Although weaker than exact algebraic primitives, our primitives are safe and are exact in the limit. Our algorithms are practical, easy to implement, and have adaptive complexity. A simple but useful example of our approach is presented here. In contr...

Abstract. Three-dimensional transonic flow over a delta wing is investigated using several turbulence models. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition aft of the leading edge o...