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
Exponential space computation of Gröbner bases
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Some Effectivity Problems in Polynomial Ideal Theory
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
The division algorithm and the hilbert scheme
The division algorithm and the hilbert scheme
Space-efficient Gröbner basis computation without degree bounds
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Dimension-dependent bounds for Gröbner bases of polynomial ideals
Journal of Symbolic Computation
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Let K[X] be a ring of multivariate polynomials with coefficients in a field K, and let f1, ..., fs be polynomials with maximal total degree d which generate an ideal I of dimension r. Then, for every admissible ordering, the total degree of polynomials in a Gröbner basis for I is bounded by 2 (1/2dn-r + d)2r. This is proved using the cone decompositions introduced by Dubé in [5]. Also, a lower bound of similar form is given.