ISSN:
1432-0622
Keywords:
Gröbner bases
;
Polynomial ideals
;
Dual bases
;
Interpolation
;
0-dimensional schemes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
,
Technology
Notes:
Abstract In this paper we study 0-dimensional polynomial ideals defined by a dual basis, i.e. as the set of polynomials which are in the kernel of a set of linear morphisms from the polynomial ring to the base field. For such ideals, we give polynomial complexity algorithms to compute a Gröbner basis, generalizing the Buchberger-Möller algorithm for computing a basis of an ideal vanishing at a set of points and the FGLM basis conversion algorithm. As an application to Algebraic Geometry, we show how to compute in polynomial time a minimal basis of an ideal of projective points.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01386834
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