منابع مشابه
Computing Ideals of Points
The easiest geometric object in affine or projective space is a single rational point. It has no secrets, in particular its defining ideal, i.e. the set of all the polynomials which vanish at the point, is straightforward to describe. Namely, for an affine point with coordinates (a1, . . . , an), the corresponding ideal is p = (x1 − a1, . . . , xn − an); while for a projective point with coordi...
متن کاملEfficiently Computing Gröbner Bases of Ideals of Points
We present an algorithm for computing Gröbner bases of vanishing ideals of points that is optimized for the case when the number of points in the associated variety is less than the number of indeterminates. The algorithm first identifies a set of essential variables, which reduces the time complexity with respect to the number of indeterminates, and then uses PLU decompositions to reduce the t...
متن کاملGenerating Loop Invariants by Computing Vanishing Ideals of Sample Points
Loop invariants play a very important role in proving correctness of programs. In this paper, we address the problem of generating invariants of polynomial loop programs. We present a new approach, for generating polynomial equation invariants of polynomial loop programs through computing vanishing ideals of sample points. We apply rational function interpolation, based on early termination tec...
متن کاملComputing Spectral Elimination Ideals
We present here an overview of the hypermatrix spectral decomposition deduced from the Bhattacharya-Mesner hypermatrix algebra [BM1, BM2]. We describe necessary and sufficient conditions for the existence of a spectral decomposition. We further extend to hypermatrices the notion of resolution of identity and use them to derive hypermatrix analog of matrix spectral bounds. Finally we describe an...
متن کاملComputing Gröbner Bases for Vanishing Ideals of Finite Sets of Points
We present an algorithm that incrementally computes a Gröbner basis for the vanishing ideal of any finite set of points in an affine space under any monomial order, and we apply this algorithm to polynomial interpolation in multiple variables. For the case of distinct points, the algorithm is natural generalization of Newton’s interpolation for univariate polynomials. The time complexity in the...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2000
ISSN: 0747-7171
DOI: 10.1006/jsco.2000.0411