
Macaulay bases of modules
We define Macaulay bases of modules, which are a common generalization o...
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A lattice formulation of the F4 completion procedure
We write a procedure for constructing noncommutative Groebner bases. Red...
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Criteria for Finite Difference Groebner Bases of Normal Binomial Difference Ideals
In this paper, we give decision criteria for normal binomial difference ...
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Confluence and Convergence in Probabilistically Terminating Reduction Systems
Convergence of an abstract reduction system (ARS) is the property that a...
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Gröbner Bases of Modules and Faugère's F_4 Algorithm in Isabelle/HOL
We present an elegant, generic and extensive formalization of Gröbner ba...
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Model Order Reduction for Rotating Electrical Machines
The simulation of electric rotating machines is both computationally exp...
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Accelerating combinatorial filter reduction through constraints
Reduction of combinatorial filters involves compressing state representa...
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Gröbner Bases with Reduction Machines
In this paper, we make a contribution to the computation of Gröbner bases. For polynomial reduction, instead of choosing the leading monomial of a polynomial as the monomial with respect to which the reduction process is carried out, we investigate what happens if we make that choice arbitrarily. It turns out not only this is possible (the fact that this produces a normal form being already known in the literature), but, for a fixed choice of reductors, the obtained normal form is the same no matter the order in which we reduce the monomials. To prove this, we introduce reduction machines, which work by reducing each monomial independently and then collecting the result. We show that such a machine can simulate any such reduction. We then discuss different implementations of these machines. Some of these implementations address inherent inefficiencies in reduction machines (repeating the same computations). We describe a first implementation and look at some experimental results.
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