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Showing 1 to 5 of 5 for “"border bases"”.
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Generalizations and Applications of Border Bases
This doctoral thesis is devoted to generalize border bases to the module setting and to apply them in various ways. First, we generalize the theory of border bases to finitely generated modules over a polynomial ring. We characterize these generalized border bases and show that we can compute them. …
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Computation of Approximate Border Bases and Applications
… associated with the computation of approximate border bases, a generalisation of border bases, in the context of the oil and gas industry. The concept of approximate border bases was introduced by D. Heldt, M. Kreuzer, S. Pokutta and H. Poulisse in "Approximate computation of zero-dimensional …
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Algebraic and Logic Solving Methods for Cryptanalysis
… SAT solving and techniques that are related to border bases and Gröbner bases. In particular, we describe in detail the Border Basis Algorithm and discuss its specialized version for Boolean polynomials called the Boolean Border Basis Algorithm. In the second part of the thesis, we deal with …
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New Techniques for Polynomial System Solving
… kind uses the concept of mutants to optimize the Border Basis Algorithm. We study recent suggestions of transferring a system of polynomial equations over the finite field with two elements into a system of polynomial equalities and inequalities over the set of integers (respectively over the set …
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Border Basis Schemes
The basic idea of border basis theory is to describe a zero-dimensional ring P/I by an order ideal of terms whose residue classes form a K-vector space basis of P/I. The O-border basis scheme is a scheme that parametrizes all zero-dimensional ideals that have an O-border basis. In general, the …