Canonical comprehensive Gröbner bases
نویسندگان
چکیده
منابع مشابه
Minimal canonical comprehensive Gröbner systems
This is the continuation of Montes’ paper ‘‘On the canonical discussion of polynomial systems with parameters’’. In this paper, we define the Minimal Canonical Comprehensive Gröbner System of a parametric ideal and fix under which hypothesis it exists and is computable. An algorithm to obtain a canonical description of the segments of the Minimal Canonical CGS is given, thus completing the whol...
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Before surveying the results of the paper, we introduce path algebras. Path algebras play a central role in the representation theory of finite-dimensional algebras (Gabriel, 1980; Auslander et al., 1995; Bardzell, 1997) and the theory of Gröbner bases (Bergman, 1978; Mora, 1986; Farkas et al., 1993) has been an important tool in some results (Feustel et al., 1993; Green and Huang, 1995; Bardze...
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In this paper we complete the algorithm DISPGB (Discussing Parametric Gröbner Basis) from the last paper by Montes, in order to obtain the Minimal Canonical Comprehensive Gröbner System (MCCGS). Given a parametric ideal, the MCCGS algorithm provides the minimal partition of the parameter space with associated Gröbner bases having the same type of solutions over each segment and provides a canon...
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a r t i c l e i n f o a b s t r a c t A new approach is proposed for computing a comprehensive Gröb-ner basis of a parameterized polynomial system. The key new idea is not to simplify a polynomial under various specialization of its parameters, but rather keep track in the polynomial, of the power products whose coefficients vanish; this is achieved by partitioning the polynomial into two parts...
متن کاملComprehensive Gröbner Bases in a Java Computer Algebra System
We present an implementation of the algorithms for computing comprehensive Gröbner bases in a Java computer algebra system (JAS). Contrary to approaches to implement comprehensive Gröbner bases with minimal requirements to the computer algebra system, we aim to provide and utilize all necessary algebraic structures occurring in the algorithm. In the implementation of a condition we aim at the m...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2003
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(03)00099-3