Determination of the basis of the space of all root functionals of a   system of polynomial equations and of the basis of its ideal by the operation   of the extension of bounded root functionals
  It is proposed the algorithm that find a basis of the ideal and a basis of the space of all root functionals by using the extension operation for bounded root functionals, when the number of polynomials is equal to the number of variables, if it is known that the ideal of polynomials is 0-dimensional. The asyptotic complexity of this algorithm is d^{O(n)} operations, where n is the number of polynomials and the number of variables, d is the maximal degree of polynomials. The extension operation has connection with the multivariate Bezoutian construction. 
Timur R. Seifullin