Degree Bounds for Gröbner Bases of Important Classes of Polynomial Ideals and Efficient Algorithms (GBiC PolyA)

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Since their introduction by Buchberger [1], Gröbner bases play a vital role in algorithmic algebra. However, often their calculation is infeasible for large examples, even though algorithms and computers improved. Thus, it is important to identify classes of ideals for which the calculation of Gröbner bases can be done efficiently, and to further develop known algorithms. The crucial parameter of Gröbner bases is the maximal degree of their polynomials as can be seen from all known proofs of complexity bounds. Hence, this parameter will be treated for different classes of ideal often occuring in practice (e.g. radical ideals, prime ideals, and toric ideals). The resulting insights shall be applied in order to enhance algorithms computing Gröbner bases and alike.