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TitleOn the Macaulay Inverse System and Its Importance for the Theory of Linear Differential Equations with Constant Coefficients
Author(s) Wolfgang Gröbner
TypeArticle in Journal
AbstractWhen first studying Macaulay's inverse systems (for this, see [2, p. 65ff] first, then [3, page 37ff], and the excellent short exposition [1, page 66ff]), one can easily fall for the mistake that this is a difficult to understand, artificial construction of little value. Subsequent applications, which lead to a very suprising new insight, teach us better. In what follows, it will be shown how this shortcoming, insofar as it even exists, can be corrected in a simple way that draws on a new interpretation of the polynomial ring, which may be useful in and of itself. Macaulay's inverse system is thereby connected to the system of integrals of linear homogeneous differential equations with constant coefficients and loses its character of possible foreignness. At the same time, this work represents an attempt to establish relationships between two seemingly completely separate branches of mathematics, which may be useful and fruitful for both sides.
URL http://doi.acm.org/10.1145/1838599.1838608
JournalACM Commun. Comput. Algebra
AddressNew York, NY, USA
Translation No
Refereed No