Algorithms in Singular by Hans Schonemann

“…Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. …”
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On Solving The Systems of Algebraic Equations Using Gröbner Bases by Alexander Shokurov

“…Described and proved the algorithm for finding some solution of algebraic equations over arbitrary field k for zero dimension ideals if Gröbner basis of this ideal over lexicographic order is given. …”
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Rewrite Rules and Simplification of Matrix Expressions by John J Wavrik

“…The non-commutative variant of the Grobner Basis Algorithm is used to generate rewrite rules. …”
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Border Basis of an Ideal of Points and its Application in Experimental Design and Regression by Samira Poukhajouei, Sare Goli, Amir Hashemi

“…In 2006, Farr and Gao presented an incremental algorithm to compute a Gröbner basis for an ideal of points. The main goal of their paper is to calculate a Gröbner basis for the vanishing ideal of any finite set of points under any monomial ordering, and for points with nontrivial multiplicities they adapt their algorithm to compute the vanishing ideal via Taylor expansions. …”
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On the first fall degree of summation polynomials by Kousidis Stavros, Wiemers Andreas

“…We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.…”
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On the computation of Hilbert series and Poincare series for algebras with infinite Grobner bases by Jonas Mansson

“…We also show how these automata can be used to compute the Hilbert series and Poincaré series for any algebra with a rational set of leading words of its minimal Gröbner basis.…”
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BERGMAN under MS-DOS and Anick's resolution by V. Ufnarovski, S. Cojocaru

“…The definition and main results connected with the Gröbner basis, Hilbert series and Anicks resolution are formulated. …”
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Resonances in a spring-pendulum: algorithms for equivariant singularity theory by Broer, H, Hoveijn, I, Lunter, G, Vegter, G

“…The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.…”

Algebraic Analysis of Zero-Hopf Bifurcation in a Chua System by Bo Huang, Wei Niu, Shaofen Xie

“…After, using the averaging method, as well as the methods of the Gröbner basis and real solution classification, we provide sufficient conditions for the existence of three limit cycles bifurcating from a zero-Hopf equilibrium of the Chua system. …”
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Evaluating software packages for attacks against elliptic curve cryptography by Moore, N

“…In this paper, we will be looking at how some attacks on elliptic curve cryptography work and evaluate a number of programming languages to test their suitability for implementing an attack that uses a Grobner basis calculation.…”

Non-commutative computer algebra and molecular computing by Svetlana Cojocaru, Victor Ufnarovski

“…The restrictions, connected with the coefficient handling in Grobner basis calculations are investigated. Semigroup and group cases are considered as more appropriate. …”
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On the brane expansion of the Schur index by M. Beccaria, A. Cabo-Bizet

“…This is evaluated by a novel deformation algorithm that avoids Gröbner basis methods. Various terms of the brane expansion are computed and their sum is shown to be free of wall-crossing singularities to the order we explored. …”
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Dynamics of a System of Two Connected Bodies Moving along a Circular Orbit around the Earth by Gutnik Sergey A., Sarychev Vasily A.

“…Nine distinct solutions are found within an approach which uses the computer algebra method based on the algorithm for the construction of a Gröbner basis.…”
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On cogrowth function of algebras and its logarithmical gap by Kanel-Belov, Alexei Ya., Melnikov, Igor, Mitrofanov, Ivan

“…If the number of obstructions is finite then $I$ has a finite Gröbner basis, and the word problem for the algebra is decidable. …”
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Chiral rings, Futaki invariants, plethystics, and Gröbner bases by Jiakang Bao, Yang-Hui He, Yan Xiao

“…All of these are illustrated with a host of examples, by considering vacuum moduli spaces of various theories. Using Gröbner basis and plethystic techniques, many non-complete intersections can also be addressed, thus expanding the list of known theories in the literature.…”
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Unveiling regions in multi-scale Feynman integrals using singularities and power geometry by B. Ananthanarayan, Abhishek Pal, S. Ramanan, Ratan Sarkar

“…Furthermore, the elements of the Gröbner Basis of the Landau Equations give a family of transformations, which when applied, reveal regions like potential and Glauber. …”
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Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE by Yunfeng Jiang, Yang Zhang

“…In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gröbner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. …”
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Efficient calculation of all steady states in large-scale overlapping generations models by Monireh Riahi, Felix Kuebler, Abdolali Basiri, Sajjad Rahmany

“…Instead, we use the specific structure of the economic problem to develop a new algorithm that does not employ the usual steps for the computation of Grobner basis such as the computation of successive S-polynomial and expensive division.…”
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Twisted indices, Bethe ideals and 3d N $$ \mathcal{N} $$ = 2 infrared dualities by Cyril Closset, Osama Khlaif

“…Abstract We study the topologically twisted index of 3d N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories with unitary gauge groups. We implement a Gröbner basis algorithm for computing the Σ g × S 1 index explicitly and exactly in terms of the associated Bethe ideal, which is defined as the algebraic ideal associated with the Bethe equations of the corresponding 3d A-model. …”
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Monomization of power Ideals and parking functions by Desjardins, Craig J. (Craig Jeffrey)

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