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تسجيل مستخدم جديدThe Geometry of Border Bases
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The main topic of the paper is the construction of various explicit flat families of border bases. To begin with, we cover the punctual Hilbert scheme Hilb^mu(A^n) by border basis schemes and work out the base changes. This enables us to control flat families obtained by linear changes of coordinates. Next we provide an explicit construction of the principal component of the border basis scheme, and we use it to find flat families of maximal dimension at each radical point. Finally, we connect radical points to each other and to the monomial point via explicit flat families on the principal component.
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Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the deformation to
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In modeling physical systems it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases, provide som
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In this paper we consider the problem of computing all possible order ideals and also sets connected to 1, and the corresponding border bases, for the vanishing ideal of a given finite set of points. In this context two different approaches are discu
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