A superexponential lower bound for Gro¨bner bases and church-Rosser Commutative Thue systems
Information and Control
The structure of polynomial ideals and Grobner bases
SIAM Journal on Computing
A new lower bound construction for commutative thue systems with applications
Journal of Symbolic Computation
The membership problem for unmixed polynomial ideals is solvable in single exponential time
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
Exponential space computation of Gröbner bases
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Upper and Lower Bounds for the Degree of Groebner Bases
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Degree bounds for Gröbner bases of low-dimensional polynomial ideals
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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Given a basis F of a polynomial ideal I in K[x"1,...,x"n] with degrees deg(F)@?d, the degrees of the reduced Grobner basis G w.r.t. any admissible monomial ordering are known to be double exponential in the number of indeterminates in the worst case, i.e. deg(G)=d^2^^^@Q^^^(^^^n^^^). This was established in Mayr and Meyer (1982) andDube (1990). We modify both constructions in order to give worst case bounds depending on the ideal dimension proving that deg(G)=d^n^^^@Q^^^(^^^1^^^)^2^^^@Q^^^(^^^r^^^) for r-dimensional ideals (in the worst case).