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A criterion for detecting unnecessary reductions in the construction of Groebner bases
TLDR
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.
Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
  • B. Buchberger
  • Computer Science, Mathematics
    J. Symb. Comput.
  • 1 March 2006
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
The Construction of Multivariate Polynomials with Preassigned Zeros
TLDR
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.
Applications of Gröbner Bases in Non-linear Computational Geometry
  • B. Buchberger
  • Computer Science, Mathematics
    Trends in Computer Algebra
  • 1987
Computer algebra symbolic and algebraic computation
TLDR
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.
A theoretical basis for the reduction of polynomials to canonical forms
TLDR
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.
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