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Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm.
Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal
Buchberger, B · 1965
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An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
Buchberger, B · 1965
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The complexity of the word problems for commutative semigroups and polynomial ideals
Mayr, E. W. and Meyer, A. R · 1982
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A criterion for detecting m m -regularity
Bayer, D. and Stillman, M · 1987
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On the complexity of computing syzygies
Bayer, D. and Stillman, M · 1988
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On an installation of Buchberger’s algorithm
Gebauer, R. and Möller, H. M · 1988
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The structure of polynomial ideals and Gröbner bases
Dubé, T. W · 1990
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Buchberger algorithm and integer programming
Conti, P. and Traverso, C · 1991
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“One sugar cube, please” or selection strategies in the Buchberger algorithm
Giovini, A., Mora, T., Niesi, G., Robbiano, L., and Traverso, C · 1991
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What can be computed in algebraic geometry?
Bayer, D. and Mumford, D · 1993
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Commutative algebra
Eisenbud, D · 1995
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Diaconis, P. and Sturmfels, B · 1998
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Ideals generated by quadrics exhibiting double exponential degrees
Koh, J · 1998
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A new efficient algorithm for computing Gröbner bases ( F 4 ) (F_{4})
Faugère, J.-C · 1999
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A new efficient algorithm for computing Gröbner bases without reduction to zero ( F 5 ) (F_{5})
Faugère, J.-C · 2002
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Modular algorithms for computing Gröbner bases
Arnold, E. A · 2003
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Applications of Gröbner bases to signal and image processing: a survey
Lin, Z., Xu, L., and Wu, Q · 2004
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Using algebraic geometry
Cox, D. A., Little, J., and O’Shea, D · 2005
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Solving polynomial equation systems. II , volume 99 of Encyclopedia of Mathematics and its Applications
Mora, T · 2005
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Gröbner bases, coding, and cryptography
Sala, M., Mora, T., Perret, L., Sakata, S., and Traverso, C. (eds.) · 2009
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Some applications of Gröbner bases in robotics and engineering
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Spinning Up in Deep Reinforcement Learning
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Bengio, Y., Lodi, A., and Prouvost, A · 2018
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Sullivant, S · 2018
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A system for doing computations in commutative algebra, Abbott, J., Bigatti, A. M., and Robbiano, L., 2019
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