On radical zero-dimensional ideals
نویسندگان
چکیده
منابع مشابه
Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals
For an ideal I ⊆ R[x] given by a set of generators, a new semidefinite characterization of its real radical I(VR(I)) is presented, provided it is zero-dimensional (even if I is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety VR(I) as well as a set of generators of the real r...
متن کاملUnivariate Representat ion of Zero - dimensional Ideals
To give an efficiently computable representation of the zeros of a zero-dimensional ideal I, Rouillier (1996) introduced the rational univariate representation (RUR) as an extension of the generalized shape lemma (GSL) proposed by Alonso et al. (1996). In this paper, we propose a new method to compute the RUR of the radical of I, and report on its practical implementation. In the new method, th...
متن کاملThe Core of Zero-dimensional Monomial Ideals
The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two an...
متن کاملApproximate computation of zero-dimensional polynomial ideals
The Buchberger-Möller algorithm is a well-known efficient tool for computing the vanishing ideal of a finite set of points. If the coordinates of the points are (imprecise) measured data, the resulting Gröbner basis is numerically unstable. In this paper we introduce a numerically stable Approximate Vanishing Ideal (AVI) Algorithm which computes a set of polynomials that almost vanish at the gi...
متن کاملA Survey on Combinatorial Duality Approach to Zero-dimensional Ideals
A Survey on Combinatorial Duality Approach to Zero-dimensional Ideals. ——————————— [email protected] ——————————— [email protected]
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1989
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(89)80060-4