منابع مشابه
Stability Computation via Gröbner Basis
In this article, we discuss a Gröbner basis algorithm related to the stability of algebraic varieties in the sense of Geometric Invariant Theory. We implement the algorithm with Macaulay 2, and give some applications to the moduli theory of curves. Given an algebraic group G acting on a projective variety X linearized by a line bundle L, the stability of a point x ∈ X can be determined by exami...
متن کاملComputation of Grobner Basis for Systematic Encoding of Generalized Quasi-Cyclic Codes
Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the systematic encoding of GQC codes is equivalent to the division algorithm in the theory of Gröbner basis of modules, there has been no algorithm that computes G...
متن کاملOn the computation of switching surfaces in optimal control: a Grobner basis approach
A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Gröbner bases. In this paper, we apply the Gröbner basis ...
متن کاملThe Computation of Grobner Bases Using an Alternative Algorithm
When Zharkov and Blinkov ([ZB93]) applied the classical ideas of involutive systems originating from the theory of partial dierential equations (c.f. [Ja29],[Po78]) to the computation of Gr obner bases (c.f. [Bu65],[BW93]) their theory seemed to be a rather marginal concept. But due to the opportunity of gaining a faster version for one of the most frequently applied algorithms the method came...
متن کاملAn algorithm for computing Grobner basis and the complexity evaluation
The first Gröbner basis algorithm was constructed by Buchberger in 1965; thus it bears his name to this day – Buchberger’s algorithm.[9] Though Buchberger’s algorithm looks relatively simple, it can take a very large amount of time. The step that creates 0 h via a normal form calculation is computationally very difficult. This is particularly frustrating (and wasteful) if the normal form calcul...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2010
ISSN: 0304-9914
DOI: 10.4134/jkms.2010.47.1.041