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Showing 1 to 7 of 7 for “"Groebner Bases"”.
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On Groebner Bases of (Non)commutative Free Algebras
… structure called ideals. The theory of Groebner bases provide a theoretical foundation for answering questions involving ideals. The original algorithm used to produce a Groebner basis was developed in 1976 by Buchberger. It has been implemented in many computer algebra systems. In a …
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Infinite Groebner Bases And Noncommutative Polly Cracker Cryptosystems
… (over finite fields) that have infinite reduced Groebner bases, and can be used to generate a public key. We present classes of such ideals and prove that they do not have a finite Groebner basis under any admissible order. We also examine various techniques to realize finite Groebner bases, in …
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Macaulay Bases of Modules
We introduce fully general Macaulay bases of modules, which are a common generalization of Groebner bases and Macaulay 𝐻-bases to suitably graded modules over a commutative graded k-algebra, where the index sets of the two gradings may differ. The additional generality includes Groebner bases of …
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Groebner Finite Path Algebras
… of their finitely generated ideals have finite Groebner bases.
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Computational Algebraic Geometry Applied to Invariant Theory
… lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer algebra system Mathematica. Number 14 of Hilbert\'s 23 problems is discussed along with the notion of invariance under a group action of GLn(C). Computational difficulties are …
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A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices
… to this proof involves the ideas of strong Groebner bases for ideals of polynomials with integral coefficients and ``leading coefficient ideals.'' </p> <p>Moving to projective dimension two, we fix the ring B = k[x,y], with k a field, and consider homogeneous height two perfect ideals I = …
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Real root counting for parametric polynomial systems and applications.
… quadratic forms. Recently developed tools like Groebner bases make it possible to let computers perform symbolic computations of polynomials and count zeros by applying classic results. A computer algebra system (CAS), for example Mathematica, is the software to do such computations. In Chapter …