Minimal Primary Decomposition and Factorized Gröbner Bases
نویسندگان
چکیده
منابع مشابه
Triangular Systems and Factorized Gröbner Bases
Solving systems of polynomial equations in an ultimate way means to nd the isolated primes of the associated variety and to present them in a way that is well suited for further computations. [5] proposes an algorithm, that uses several Grobner basis computations for a dimension reduction argument, delaying factorization to the end of the algorithm. In this paper we investigate the opposite ap...
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We present an algorithm to compute the primary decomposition of any ideal in a polynomial ring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a constructive PID and that we are given an algorithm to factor polynomials over fields which are finitely generated over R or residue fields of R. We show how basic ideal theoretic operations can be performe...
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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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We focus on Gröbner bases for modules of univariate polynomial vectors over a ring. We identify a useful property, the " predictable leading monomial (PLM) property " that is shared by minimal Gröbner bases of modules in F[x] q , no matter what positional term order is used. The PLM property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable deg...
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Gröbner Bases [Buc70] and Cylindrical Algebraic Decomposition [Col75,CMMXY09] are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gröbner bases to the (conjoined) equalities before invoking CAD. ...
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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 1997
ISSN: 0938-1279,1432-0622
DOI: 10.1007/s002000050064