Abstract
A method is proposed for the short description of an algebraic hypersurface with the help of descriptors that depend on a small number of coefficients of the corresponding polynomial form and are invariant with respect to the orthogonal transformations of the enveloping space. These invariants, which can easily be computed even for high dimensionalities, allow to compare quickly the shapes of hypersurfaces in the general position and can be used as features in applied problems of object description and recognition as well as for the solution of combinatorial problems. The transformation of real multilinear cubic forms is specially considered.
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