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Authors: Alexey Yu. Zharkov and Yuri A. Blinkov

Involutive bases are a tool for solving problems in connection with multivariate polynomials, such as solving systems of polynomial equations and analyzing polynomial ideals.

An involutive basis of a polynomial ideal is a special form of a redundant Gröbner basis. The construction of involutive bases reduces the problem of solving polynomial systems to simple linear algebra. The package can be used over a variety of different coefficient domains, and for different variable and term orderings. The algorithm implemented in the INVBASE package is proved to be valid for any zero-dimensional ideal as well as for positive-dimensional ideals in generic form. However, the algorithm does not terminate for "sparse" positive-dimensional systems.