A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A Reduction Strategy for the Taylor Resolution
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Buchberger's algorithm and staggered linear bases
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
On the construction of Gröbner bases using syzygies
Journal of Symbolic Computation
Experimenting the Gröbner basis algorithm with the A1PI system
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
A heuristic selection strategy for lexicographic Gröner bases?
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
“One sugar cube, please” or selection strategies in the Buchberger algorithm
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
How we proved that there are exactly 924 cyclic 7-roots
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
An algorithm for solving parametric linear systems
Journal of Symbolic Computation
Gröbner bases computation using syzygies
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
A dynamic algorithm for Gröbner basis computation
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
A case study of multi-threaded Gröbner basis completion
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
Modular algorithms for computing Gröbner bases
Journal of Symbolic Computation
Are Buchberger's criteria necessary for the chain condition?
Journal of Symbolic Computation
Computation of discrete comprehensive Gröbner bases using modular dynamic evaluation
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Algebraic Attacks on the Courtois Toy Cipher
Cryptologia
Computing generating sets of lattice ideals and Markov bases of lattices
Journal of Symbolic Computation
Computing Gröbner Bases within Linear Algebra
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Detecting unnecessary reductions in an involutive basis computation
Journal of Symbolic Computation
Computational algebra for bifurcation theory
Journal of Symbolic Computation
Reduction relations for monoid semirings
Journal of Symbolic Computation
Computing gröbner bases within linear algebra and its implementation
ACM Communications in Computer Algebra
Gröbner bases for polynomial systems with parameters
Journal of Symbolic Computation
F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
Journal of Symbolic Computation
Computing inhomogeneous Gröbner bases
Journal of Symbolic Computation
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Linear algebra to compute syzygies and Gröbner bases
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Signature-based algorithms to compute Gröbner bases
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Applying IsRewritten criterion on Buchberger algorithm
Theoretical Computer Science
Modifying Faugère's F5 algorithm to ensure termination
ACM Communications in Computer Algebra
An interactive user interface for division algorithms and the buchberger algorithm
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Resolution of a system of fuzzy polynomial equations using the Gröbner basis
Information Sciences: an International Journal
Finding the exact rotation between two images independently of the translation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Parallel reduction of matrices in gröbner bases computations
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases
Programming and Computing Software
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Improving incremental signature-based Gröbner basis algorithms
ACM Communications in Computer Algebra
Involutive bases algorithm incorporating F5 criterion
Journal of Symbolic Computation
| Hi-index | 0.00 |
Buchberger's algorithm calculates Groebner bases of polynomial ideals. Its efficiency dependsstrongly on practical criteria for detecting superfluous reductions. Buchberger recommends two criteria. The more important one is interpreted in this paper as a criterion for detecting redundant elements in a basis of a module of syzygies. We present a method for obtaining a reduced, nearly minimal basis of that module. The simple procedure for detecting (redundant syzygies and) superfluous reductions is incorporated now in our installation of Buchberger's algorithm in SCRATCHPAD II and REDUCE 3.3. The paper concludes with statistics stressing the good computational properties of these installations.