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2015, Graduate studies in mathematics, ISBN 9780821851982, Volume 161, xii, 363
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on... 
Tropical geometry | Study and teaching (Graduate) | Geometry, Algebraic
Book
2012, Graduate studies in mathematics, ISBN 9780821872871, Volume 130, xi, 164
Book
Journal of Algebra, ISSN 0021-8693, 11/2015, Volume 442, pp. 354 - 396
Journal Article
Journal Article
Communications in Algebra, ISSN 0092-7872, 04/2019, Volume 47, Issue 4, pp. 1671 - 1689
We establish Gröbner-Shirshov bases theory for commutative dialgebras. We show that for any ideal I of , I has a unique reduced... 
Commutative dialgebra | Gröbner-Shirshov basis | normal form | commutative disemigroup | word problem | MATHEMATICS | DIAMOND LEMMA | 17A99 | 13P10 | 08A50 | Grobner-Shirshov basis | 16S15 | Canonical forms
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2017, Volume 45, Issue 5, pp. 1996 - 2017
We consider the problem of describing Gröbner-Shirshov bases for free associative algebras in finite terms... 
Free associative algebra | Gröbner-Shirsov bases | HNN extension | normal form | group | Gröbner–Shirsov bases | MATHEMATICS | Grobner-Shirsov bases | Parameterization | Algebra | Associative | Algorithms | Mathematical analysis | Standards
Journal Article
Journal of symbolic computation, ISSN 0747-7171, 10/2019
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 6/2019, Volume 59, Issue 2, pp. 417 - 442
...BIT Numerical Mathematics (2019) 59:417–442 https://doi.org/10.1007/s10543-018-0733-x Numerical computation of H-bases Masoumeh Javanbakht 1 · Tomas Sauer 2... 
SVD | Computational Mathematics and Numerical Analysis | Syzygy | H-basis | 65F30 | Numeric Computing | 13P10 | Mathematics, general | Mathematics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SCHEME | MATHEMATICS, APPLIED | GROBNER
Journal Article
Communications in Algebra, ISSN 0092-7872, 12/2017, Volume 45, Issue 12, pp. 5283 - 5296
We develop Gröbner-Shirshov bases technique for pre-associative (dendriform) algebras and prove a version of composition-diamond lemma. 
Dendriform algebra | Gröbner-Shirshov basis | Gröbner—Shirshov basis | MATHEMATICS | KOSZUL DUALITY | Grobner-Shirshov basis | Diamonds
Journal Article
BULLETIN OF MATHEMATICAL BIOLOGY, ISSN 0092-8240, 07/2019, Volume 81, Issue 7, pp. 2691 - 2705
Model selection based on experimental data is an important challenge in biological data science. Particularly when collecting data is expensive or... 
NETWORK | Staircases of monomial ideals | Grobner bases | LAC OPERON | Algebraic design of experiments | GROWTH | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | MODEL | Ideals of points | Biological data science | IDEALS | Chromosomes | Analysis | Boolean algebra | Lactose operon | E coli | Uniqueness
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 06/2019, Volume 107, pp. 74 - 101
In this work we consider the computation of Gröbner bases of the steady state ideal of reaction networks equipped with mass-action kinetics... 
Invariant | Binomial ideals | Mass-action kinetics | Steady state ideal | Gröbner basis | Grobner basis | MATHEMATICS, APPLIED | MODEL | Algebra
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 11/2018, Volume 89, pp. 227 - 254
... of Gröbner bases taking into account the valuation of K. Because of the use of the valuation, this theory is promising for stable computations over polynomial rings over a p-adic field... 
Gröbner bases | Tropical geometry | F5 algorithm | p-Adic precision | p-Adic algorithm | MATHEMATICS, APPLIED | GrObner bases | COMPUTER SCIENCE, THEORY & METHODS | Valuation | Algorithms
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 06/2018, Volume 28, Issue 4, pp. 553 - 571
... — canonical forms and Gröbner bases — related? Our main result states that if the canonical form of a neural... 
Neural code | Receptive field | Gröbner basis | Boolean lattice | Canonical form | Grobner basis | MATHEMATICS | receptive field | CODES | canonical form
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 05/2017, Volume 80, pp. 719 - 784
In 1965 Buchberger introduced an algorithmic approach to compute Gröbner bases. Later on, he and many others presented various attempts to improve the computation by removing useless elements a priori... 
Gröbner bases | GVW | Signature-based algorithms | Syzygies | MATHEMATICS, APPLIED | Grobner bases | COMPUTER SCIENCE, THEORY & METHODS | F5 ALGORITHM | IDEALS | Surveys | Algebra | Algorithms
Journal Article
2000, Lecture notes in mathematics, ISBN 9783540671619, Volume 1728., xi, 153
This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems... 
Gröbner bases | Data processing | Algebra | Differentiable dynamical systems | Computer science | Mathematics of Computing | Analysis | Global analysis | Global Analysis and Analysis on Manifolds | Global analysis (Mathematics) | Math Applications in Computer Science | Computational Science and Engineering
Book
1993, Graduate texts in mathematics, ISBN 0387979719, Volume 141, xxii, 574
Book
Journal of Algebra, ISSN 0021-8693, 07/2013, Volume 385, pp. 47 - 63
.... As applications, we obtain Gröbner–Shirshov bases and A. Blassʼs (1995) and M. Fiore and T. Leinsterʼs (2004) normal forms of the semirings N... 
Gröbner–Shirshov basis | Semiring | Congruence | Normal form | Gröbner-Shirshov basis | LIE-ALGEBRAS | MATHEMATICS | COMPOSITION-DIAMOND LEMMA | Grobner-Shirshov basis | FREE ALGEBRAS | Algorithms
Journal Article
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