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

Tropical geometry | Study and teaching (Graduate) | Geometry, Algebraic

Book

2005, ISBN 3540255273, x, 586

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

.... In this paper we apply the method of Gröbner–Shirshov bases to construct the free (noncommutative) integro-differential algebra on a set...

Rota–Baxter algebra | Differential Rota–Baxter algebra | Free objects | Gröbner–Shirshov bases | Integro-differential algebra | Gröbner-Shirshov bases | Rota-Baxter algebra | Differential Rota-Baxter algebra | MATHEMATICS | ROTA-BAXTER ALGEBRAS | DIAMOND LEMMA | Grobner-Shirshov bases | DIFFERENTIAL-EQUATIONS | Computer science | Analysis | Algebra

Rota–Baxter algebra | Differential Rota–Baxter algebra | Free objects | Gröbner–Shirshov bases | Integro-differential algebra | Gröbner-Shirshov bases | Rota-Baxter algebra | Differential Rota-Baxter algebra | MATHEMATICS | ROTA-BAXTER ALGEBRAS | DIAMOND LEMMA | Grobner-Shirshov bases | DIFFERENTIAL-EQUATIONS | Computer science | Analysis | Algebra

Journal Article

Bulletin of Mathematical Sciences, ISSN 1664-3607, 12/2014, Volume 4, Issue 3, pp. 325 - 395

In this survey we give an exposition of the theory of Gröbner–Shirshov bases for associative algebras, Lie algebras, groups, semigroups, Ω...

Rota–Baxter algebra | 16Y60 | Category | Associative algebra | Lyndon–Shirshov word | 13P10 | Dialgebra | Mathematics | 17-xx | 17B37 | 17B66 | 17B01 | 18D50 | Plactic monoid | Lyndon–Shirshov basis | 20Mxx | Mathematics, general | 20F05 | Free semigroup | PBW theorem | 20M18 | Congruence | 16-xx | Gröbner basis | Ω -algebra | Normal form | Composition-Diamond lemma | Semiring | Pre-Lie algebra | 17D99 | Braid group | 18Axx | Gröbner–Shirshov basis | Chinese monoid | Lie algebra | Module | 16S35 | 20F36 | 16S15 | 16W99 | Ω-algebra | EXTENSIONS | CONJUGACY PROBLEMS | MATHEMATICS | NORMAL-FORM | WORD | Omega-algebra | Rota-Baxter algebra | ALGORITHMS | Grobner-Shirshov basis | Lyndon-Shirshov word | Grobner basis | LIE-ALGEBRAS | Lyndon-Shirshov basis | CONSTRUCTION | QUANTUM GROUP

Rota–Baxter algebra | 16Y60 | Category | Associative algebra | Lyndon–Shirshov word | 13P10 | Dialgebra | Mathematics | 17-xx | 17B37 | 17B66 | 17B01 | 18D50 | Plactic monoid | Lyndon–Shirshov basis | 20Mxx | Mathematics, general | 20F05 | Free semigroup | PBW theorem | 20M18 | Congruence | 16-xx | Gröbner basis | Ω -algebra | Normal form | Composition-Diamond lemma | Semiring | Pre-Lie algebra | 17D99 | Braid group | 18Axx | Gröbner–Shirshov basis | Chinese monoid | Lie algebra | Module | 16S35 | 20F36 | 16S15 | 16W99 | Ω-algebra | EXTENSIONS | CONJUGACY PROBLEMS | MATHEMATICS | NORMAL-FORM | WORD | Omega-algebra | Rota-Baxter algebra | ALGORITHMS | Grobner-Shirshov basis | Lyndon-Shirshov word | Grobner basis | LIE-ALGEBRAS | Lyndon-Shirshov basis | CONSTRUCTION | QUANTUM GROUP

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

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

1993, ISBN 9783540979715, Volume 141., xxii, 574

Book

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

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

1993, ISBN 9783540979715, Volume 141., xxii, 574

Book

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

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

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

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

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

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

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

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

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

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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