Insight on the structure of differential ideals defined by coherent autoreduced set allows one
to uncouple the differential and algebraic computations in a decomposition algorithm …

This is the first in a series of two tutorial articles devoted to triangulation-decomposition
algorithms. The value of these notes resides in the uniform presentation of triangulation …

We propose an efficient algorithm for computing triangular decompositions of algebraic
varieties. It is based on an incremental process and produces components in order of …

Regular chains and triangular decompositions are fundamental and well-developed tools for
describing the complex solutions of polynomial systems. This paper proposes adaptations of …

We study the triangular representation of zero-dimensional varieties defined over the
rational field (resp. a rational function field). We prove polynomial bounds in terms of intrinsic …

Efficient characteristic set methods for computing zeros of polynomial equation systems in a
finite field are proposed. The concept of proper triangular sets is introduced and an explicit …

We study the representation of the solutions of a polynomial system by triangular sets, and
concentrate on the positive-dimensional case. We reduce to dimension zero by placing the …

Ritt–Wuʼs algorithm of characteristic sets is the most representative for triangularizing sets
of multivariate polynomials. Pseudo-division is the main operation used in this algorithm. In …

In this paper the chordal graph structures of polynomial sets appearing in triangular
decomposition in top-down style are studied when the input polynomial set has a chordal …

The complexity of computing the Galois group of a linear differential equation is of general
interest. In a recent work, Feng gave the first degree bound on Hrushovski's algorithm for …