In nice cases, a zero-dimensional complete intersection ideal over a field has a Shape
Lemma. There are also cases where the ideal is generated by the resultant and first …

We present a bounded probability algorithm for the computation of the Chowforms of the
equidimensional components of an algebraic variety. In particular, this gives an alternative …

This paper is concerned with certifying that a given point is near an exact root of an
overdetermined or singular polynomial system with rational coefficients. The difficulty lies in …

In this paper, we consider the problem of formulating the subresultant polynomials for
several univariate polynomials in Newton basis. It is required that the resulting subresultant …

In this paper, we tackle the following problem: compute the gcd for several univariate
polynomials with parametric coefficients. It amounts to partitioning the parameter space …

Given a birational parameterization ϕ of an algebraic surface S⊂ P 3, the purpose of this
paper is to investigate the sets of points on S whose pre-image consists of k or more points …

Subresultant of two univariate polynomials is a fundamental object in computational algebra
and geometry with many applications (for instance, parametric GCD and parametric …

Grö bner bases is one the most powerful tools in algorithmic nonlinear algebra. Their
computation is an intrinsically hard problem with a complexity at least single exponential in …

We give a rational expression for the subresultants of n+ 1 generic polynomials f1,…, fn+ 1
in n variables as a function of the coordinates of the common roots of f1,…, fn and their …

For a reduced hypersurface V (f)⊆ P n of degree d, the Castelnuovo-Mumford regularity of
the Milnor algebra M (f) is well understood when V (f) is smooth, as well as when V (f) has …