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Multivariate Interpolation and Standard Bases for Macaulay Modules

✍ Scribed by Luigi Cerlienco; Marina Mureddu

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
304 KB
Volume
251
Category
Article
ISSN
0021-8693

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✦ Synopsis

The K-linear space of all n-linearly recursive functions (1.1) =evaluated differential forms) for which a zero-dimensional ideal βŠ‚ K x 1

x n is the largest ideal which is contained in the kernel of all of them turns out to be the orthogonal K-space βŠ₯ βŠ‚ K x 1

x n * of and is known as Macaulay's inverse system of . Making use of the antiderivative operator , the whole space of all differential forms can be endowed with a structure of K x 1

x n -module; with respect to finitely generated submodules of it (which we call Macaulay modules), we describe a dual analog of the Grâbner bases theory. The motivation for studying Macaulay modules has to be found mainly in multivariate interpolation problems and in the theory of polynomial bialgebras, though some application to algebraic geometry is not excluded.  2002 Elsevier Science (USA)

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