N ov 2 00 6 Minimal Canonical Comprehensive Gröbner System ∗
نویسندگان
چکیده
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 canonical description of the partition and the reduced bases.
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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متن کامل2 9 Ja n 20 06 Canonical discussion of polynomial systems with parameters ∗
Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Gröbner bases depending on the values of the parameters. An improvement using a discriminant ideal to rewrite the tree was described by Manubens and the author in 2005. In this paper we describe how to iterate the use ...
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