A new criterion is presented that may be applied in an algorithm for constructing Grobner-bases of polynomial ideals and allows to derive a realistic upper bound for the degrees of the polynomials in the GroBner-Bases computed by the algorithm in the case of poylemials in two variables.Expand

This is the English translation (by Michael P. Abramson) of the PhD thesis of Bruno Buchberger, in which he introduced the algorithmic theory of Grobner bases. Some comments by Buchberger on the… Expand

An algorithm for constructing a basis of the ideal of all polynomials, which vanish at a preassigned set of points, is presented, which yields also Newton-type poynomials for pointwise interpolation.Expand

This volume is the first systematic and complete treatment of computergebra and presents the basic problems of computer algebra and the best algorithms now known for their solution with their mathematical foundations, and complete references to the original literature.Expand

A characterization theorem is proved for a certain type of bases of polynomial ideals whose usefulness stems from the fact that a number of computability problems in the theory of poynomial ideals is reducible to the construction of bases in this type.Expand