Relevant bibliographies by topics / Base du Gröbner

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  2. Dissertations / Theses
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Academic literature on the topic 'Base du Gröbner'

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Published: 25 May 2024

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Journal articles on the topic "Base du Gröbner"

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Bokut, L. A., Yuqun Chen, and Zerui Zhang. "Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras." Journal of Algebra and Its Applications 16, no. 01 (January 2017): 1750001. http://dx.doi.org/10.1142/s0219498817500013.

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We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.
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Steiner, Matthias Johann. "Solving Degree Bounds for Iterated Polynomial Systems." IACR Transactions on Symmetric Cryptology 2024, no. 1 (March 1, 2024): 357–411. http://dx.doi.org/10.46586/tosc.v2024.i1.357-411.

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For Arithmetization-Oriented ciphers and hash functions Gröbner basis attacks are generally considered as the most competitive attack vector. Unfortunately, the complexity of Gröbner basis algorithms is only understood for special cases, and it is needless to say that these cases do not apply to most cryptographic polynomial systems. Therefore, cryptographers have to resort to experiments, extrapolations and hypotheses to assess the security of their designs. One established measure to quantify the complexity of linear algebra-based Gröbner basis algorithms is the so-called solving degree. Caminata & Gorla revealed that under a certain genericity condition on a polynomial system the solving degree is always upper bounded by the Castelnuovo-Mumford regularity and henceforth by the Macaulay bound, which only takes the degrees and number of variables of the input polynomials into account. In this paper we extend their framework to iterated polynomial systems, the standard polynomial model for symmetric ciphers and hash functions. In particular, we prove solving degree bounds for various attacks on MiMC, Feistel-MiMC, Feistel-MiMC-Hash, Hades and GMiMC. Our bounds fall in line with the hypothesized complexity of Gröbner basis attacks on these designs, and to the best of our knowledge this is the first time that a mathematical proof for these complexities is provided. Moreover, by studying polynomials with degree falls we can prove lower bounds on the Castelnuovo-Mumford regularity for attacks on MiMC, Feistel-MiMC and Feistel-MiMCHash provided that only a few solutions of the corresponding iterated polynomial system originate from the base field. Hence, regularity-based solving degree estimations can never surpass a certain threshold, a desirable property for cryptographic polynomial systems.
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Jha, Ranjan, Damien Chablat, and Luc Baron. "Influence of design parameters on the singularities and workspace of a 3-RPS parallel robot." Transactions of the Canadian Society for Mechanical Engineering 42, no. 1 (March 1, 2018): 30–37. http://dx.doi.org/10.1139/tcsme-2017-0011.

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This paper presents variations in the workspace, singularities, and joint space with respect to design parameter k, which is the ratio of the dimensions of the mobile platform to the dimensions of the base of a 3-RPS parallel manipulator. The influence of the design parameters on parasitic motion, which is important when selecting a manipulator for a desired task, is also studied. The cylindrical algebraic decomposition method and Gröbner-based computations are used to model the workspace and joint space with parallel singularities in 2R1T (two rotational and one translational) and 3T (three translational) projection spaces, where the orientation of the mobile platform is represented using quaternions. These computations are useful in selecting the optimum value for the design parameter k such that the parasitic motions can be limited to specific values. Three designs of the 3-RPS parallel robot, based on different values of k, are analyzed.
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Yoshida, Hiroshi. "A model for analyzing phenomena in multicellular organisms with multivariable polynomials: Polynomial life." International Journal of Biomathematics 11, no. 01 (January 2018): 1850007. http://dx.doi.org/10.1142/s1793524518500079.

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Most of life maintains itself through turnover, namely cell proliferation, movement and elimination. Hydra’s cells, for example, disappear continuously from the ends of tentacles, but these cells are replenished by cell proliferation within the body. Inspired by such a biological fact, and together with various operations of polynomials, I here propose polynomial-life model toward analysis of some phenomena in multicellular organisms. Polynomial life consists of multicells that are expressed as multivariable polynomials. A cell is expressed as a term of polynomial, in which point [Formula: see text] is described as a term [Formula: see text] and the condition is described as its coefficient. Starting with a single term and following reductions by set of polynomials, I simulate the development from a cell to a multicell. In order to confirm uniqueness of the eventual multicell-pattern, Gröbner base can be used, which has been conventionally used to ensure uniqueness of normal form in the mathematical context. In this framework, I present various patterns through the polynomial-life model and discuss patterns maintained through turnover. Cell elimination seems to play an important role in turnover, which may shed some light on cancer or regenerative medicine.
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Gräbe, Hans-Gert, and Franz Pauer. "A remark on Hodge algebras and Gröbner bases." Czechoslovak Mathematical Journal 42, no. 2 (1992): 331–38. http://dx.doi.org/10.21136/cmj.1992.128327.

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Bellini, Emanuele, Massimiliano Sala, and Ilaria Simonetti. "Nonlinearity of Boolean Functions: An Algorithmic Approach Based on Multivariate Polynomials." Symmetry 14, no. 2 (January 22, 2022): 213. http://dx.doi.org/10.3390/sym14020213.

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We review and compare three algebraic methods to compute the nonlinearity of Boolean functions. Two of them are based on Gröbner basis techniques: the first one is defined over the binary field, while the second one over the rationals. The third method improves the second one by avoiding the Gröbner basis computation. We also estimate the complexity of the algorithms, and, in particular, we show that the third method reaches an asymptotic worst-case complexity of O(n2n) operations over the integers, that is, sums and doublings. This way, with a different approach, the same asymptotic complexity of established algorithms, such as those based on the fast Walsh transform, is reached.
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Eder, Christian. "Improving incremental signature-based Gröbner basis algorithms." ACM Communications in Computer Algebra 47, no. 1/2 (July 15, 2013): 1–13. http://dx.doi.org/10.1145/2503697.2503699.

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Eder, Christian, and Jean-Charles Faugère. "A survey on signature-based Gröbner basis computations." ACM Communications in Computer Algebra 49, no. 2 (August 14, 2015): 61. http://dx.doi.org/10.1145/2815111.2815156.

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Francis, Maria, and Thibaut Verron. "A Signature-Based Algorithm for Computing Gröbner Bases over Principal Ideal Domains." Mathematics in Computer Science 14, no. 2 (December 17, 2019): 515–30. http://dx.doi.org/10.1007/s11786-019-00432-5.

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AbstractSignature-based algorithms have become a standard approach for Gröbner basis computations for polynomial systems over fields, but how to extend these techniques to coefficients in general rings is not yet as well understood. In this paper, we present a proof-of-concept signature-based algorithm for computing Gröbner bases over commutative integral domains. It is adapted from a general version of Möller’s algorithm (J Symb Comput 6(2–3), 345–359, 1988) which considers reductions by multiple polynomials at each step. This algorithm performs reductions with non-decreasing signatures, and in particular, signature drops do not occur. When the coefficients are from a principal ideal domain (e.g. the ring of integers or the ring of univariate polynomials over a field), we prove correctness and termination of the algorithm, and we show how to use signature properties to implement classic signature-based criteria to eliminate some redundant reductions. In particular, if the input is a regular sequence, the algorithm operates without any reduction to 0. We have written a toy implementation of the algorithm in Magma. Early experimental results suggest that the algorithm might even be correct and terminate in a more general setting, for polynomials over a unique factorization domain (e.g. the ring of multivariate polynomials over a field or a PID).
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Eder, Christian. "An analysis of inhomogeneous signature-based Gröbner basis computations." Journal of Symbolic Computation 59 (December 2013): 21–35. http://dx.doi.org/10.1016/j.jsc.2013.08.001.

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Dissertations / Theses on the topic "Base du Gröbner"

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Amendola, Teresa. "Basi di Gröbner e anelli polinomiali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19458/.

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In questo elaborato ci proponiamo di fornire alcuni strumenti utili per illustrare il collegamento tra varietà affini e ideali polinomiali. La tesi segue l'approccio computazionale e sfrutta quindi alcuni algoritmi per la dimostrazione dei risultati principali. Si prova il Teorema della Base di Hilbert e si introducono le basi di Gröbner per la dimostrazione del Nullstellensatz.
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Vilanova, Fábio Fontes. "Sistemas de equações polinomiais e base de Gröbner." Universidade Federal de Sergipe, 2015. https://ri.ufs.br/handle/riufs/6524.

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The main objective of this dissertation is to present an algebraic method capable of determining a solution, if any, of a non linear polynomial equation systems using Gröbner basis. In order to accomplish that, we first present some concepts and theorems linked to polynomial rings with several undetermined and monomial ideals where we highlight the division extended algorithm, the Hilbert Basis and the Buchberger´s algorithm. Beyond that, using basics of Elimination and Extension Theorems, we present an algebraic solution to the map coloring that use 3 colors as well as a general solution to the Sudoku puzzle.
O objetivo principal desse trabalho é, usando bases de Gröbner, apresentar um método algébrico capaz de determinar a solução, quando existir, de sistemas de equações polinomiais não necessariamente lineares. Para tanto, necessitamos inicialmente apresentar alguns conceitos e teoremas ligados a anéis de polinômios com várias indeterminadas e de ideais monomiais, dentre os quais destacamos o algoritmo extendido da divisão, o teorema da Base de Hilbert e o algoritmo de Buchberger. Além disso, usando noções básicas da Teoria de eliminação e extensão, apresentamos uma solução algébrica para o problema da coloração de mapas usando três cores, bem como um solução geral para o puzzle Sudoku.
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Hashemi, Amir. "Structure et compléxité des bases de Gröbner." Paris 6, 2006. http://www.theses.fr/2006PA066116.

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Bender, Matias Rafael. "Algorithms for sparse polynomial systems : Gröbner bases and resultants." Electronic Thesis or Diss., Sorbonne université, 2019. http://www.theses.fr/2019SORUS029.

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La résolution de systèmes polynomiaux est l’un des problèmes les plus anciens et importants en mathématiques informatiques et a des applications dans plusieurs domaines des sciences et de l’ingénierie. C'est un problème intrinsèquement difficile avec une complexité au moins exponentielle du nombre de variables. Cependant, dans la plupart des cas, les systèmes polynomiaux issus d'applications ont une structure quelconque. Dans cette thèse, nous nous concentrons sur l'exploitation de la structure liée à la faible densité des supports des polynômes; c'est-à-dire que nous exploitons le fait que les polynômes n'ont que quelques monômes à coefficients non nuls. Notre objectif est de résoudre les systèmes plus rapidement que les estimations les plus défavorables, qui supposent que tous les termes sont présents. Nous disons qu'un système creux est non mixte si tous ses polynômes ont le même polytope de Newton, et mixte autrement. La plupart des travaux sur la résolution de systèmes creux concernent le cas non mixte, à l'exception des résultants creux et des méthodes d'homotopie. Nous développons des algorithmes pour des systèmes mixtes. Nous utilisons les résultantes creux et les bases de Groebner. Nous travaillons sur chaque théorie indépendamment, mais nous les combinons également: nous tirons parti des propriétés algébriques des systèmes associés à une résultante non nulle pour améliorer la complexité du calcul de leurs bases de Groebner; par exemple, nous exploitons l’exactitude du complexe de Koszul pour déduire un critère d’arrêt précoce et éviter tout les réductions à zéro. De plus, nous développons des algorithmes quasi-optimaux pour décomposer des formes binaires
Solving polynomial systems is one of the oldest and most important problems in computational mathematics and has many applications in several domains of science and engineering. It is an intrinsically hard problem with complexity at least single exponential in the number of variables. However, in most of the cases, the polynomial systems coming from applications have some kind of structure. In this thesis we focus on exploiting the structure related to the sparsity of the supports of the polynomials; that is, we exploit the fact that the polynomials only have a few monomials with non-zero coefficients. Our objective is to solve the systems faster than the worst case estimates that assume that all the terms are present. We say that a sparse system is unmixed if all its polynomials have the same Newton polytope, and mixed otherwise. Most of the work on solving sparse systems concern the unmixed case, with the exceptions of mixed sparse resultants and homotopy methods. In this thesis, we develop algorithms for mixed systems. We use two prominent tools in nonlinear algebra: sparse resultants and Groebner bases. We work on each theory independently, but we also combine them to introduce new algorithms: we take advantage of the algebraic properties of the systems associated to a non-vanishing resultant to improve the complexity of computing their Groebner bases; for example, we exploit the exactness of some strands of the associated Koszul complex to deduce an early stopping criterion for our Groebner bases algorithms and to avoid every redundant computation (reductions to zero). In addition, we introduce quasi-optimal algorithms to decompose binary forms
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Rahmany, Sajjad. "Utilisation des bases de Gröbner SAGBI pour la résolution des systèmes polynômiaux invariants par symétries." Paris 6, 2009. http://www.theses.fr/2009PA066214.

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Dans cette thèse, nous proposons une méthode efficace pour résoudre des systèmes polynômiaux dont les équations sont invariantes par l'action d'un groupe fini G. L'idée est calculer simultanément une base de Gröbner SAGBI(une génération des bases de Gröbner à des idéaux de sous algèbres de l'anneau des polynômes) et une base de Gröbner dans l'anneau des invariants symétriques. Plus précisément, nous proposons dans cette thèse deux algorithmes: nous explicitions d'abord un algorithme à la F5 pour calculer efficacement une base de Gröbner SAGBI. Le deuxième algorithme est une version légèrement modifiée de l'algorithme FGLM qui permet de convertir une base de Gröbner SAGBI tronquée d'un idéal de dimension zéro en une base de Gröbner tronquée dans l'anneau des invariants symétriques. Enfin, nous montrons comment ces algorithmes peuvent être combinés pour trouver les racines complexes d'un tel système algébrique.
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Rocha, Junior Mauro Rodrigues. "Bases de Gröbner aplicadas a códigos corretores de erros." Universidade Federal de Juiz de Fora (UFJF), 2017. https://repositorio.ufjf.br/jspui/handle/ufjf/5946.

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O principal objetivo desse trabalho é estudar duas aplicações distintas das bases de Gröbner a códigos lineares. Com esse objetivo, estudamos como relacionar códigos a outras estruturas matemáticas, fazendo com que tenhamos novas ferramentas para a realização da codificação. Em especial, estudamos códigos cartesianos afins e os códigos algébrico-geométricos de Goppa.
The main objective of this work is to study two different applications of Gröbner basis to linear codes. With this purpose, we study how to relate codes to other mathematical structures, allowing us to use new tools to do the coding. In particular, we study affine cartesian codes e algebraic-geometric Goppa codes.
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Sénéchaud, Pascale. "Calcul formel et parallélisme : bases de Gröbner booléennes, méthodes de calcul : applications, parallélisation." Grenoble INPG, 1990. http://tel.archives-ouvertes.fr/tel-00337227.

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Nous présentons les bases de Grobner, leur utilisation et la parallélisation des algorithmes qui les calculent dans le cas de polynômes booléens. Une première partie est consacrée à la présentation théorique des bases de Grobner dans le cas général. Cette présentation se veut accessible a des non-spécialistes. Une étude bibliographique de la complexité est faite. Une deuxième partie concerne les applications des bases de Grobner booléennes en calcul propositionnel et en preuve de circuits combinatoires. Nous proposons un algorithme de preuve formelle de circuits combinatoires hiérarchisés. Dans la troisième partie nous adaptons l'algorithme séquentiel au cas booléen et nous étudions plus en détail la normalisation. Nous proposons deux méthodes de parallélisation a granularité différentes. Nous analysons et comparons plusieurs implantations parallèles et présentons des résultats expérimentaux. Les algorithmes sont généralisables au cas des polynômes a coefficients rationnels. Nous soulignons l'influence de la répartition des données sur le temps d'exécution. Nous présentons une methode de répartition des polynômes basée sur la recherche de chemins de longueur donnée dans un graphe oriente. Cette répartition nous permet d'obtenir des résultats interpretables et de conclure sur les différents algorithmes
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García, Fontán Jorge. "Singularity and Stability Analysis of vision-based controllers." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS015.

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L’objectif de cette thèse doctoral est d’explorer les cas d’échec de l’asservissement visuel, d’un point de vue mathématique rigoureux et à l’aide d’outils de calcul exact issus de la géométrie algébrique et du calcul formel. Les cas d’échec possibles proviennent de deux sources : les singularités des équations cinématiques, et l’existence de multiples points d’équilibre, ce qui affecte la stabilité asymptotique globale des lois de contrôle. Dans cette thèse, nous avons atteint deux objectifs principaux. Le premier est de calculer les conditions de singularité pour le modèle d’interaction lié à l’observation de plus de trois droites 3D, en étendant les résultats des publications antérieurs pour trois droites. Le deuxième est le calcul des points critiques en IBVS dans l’observation de quatre points de référence, comme première étape vers l’analyse de la stabilité globale des méthodes d’asservissement visuel
The objective of this PhD thesis is to explore the failure cases of Image-Based Visual Servoing (IBVS), a class of Robotics controllers based on computer vision data. The failure cases arise from two sources: the singularities of the governing kinematic equations, and the existance of multiple stable points of equilibrium, which impacts the global asymptotic stability of the control laws. In this thesis, we study these two problems from a rigurous mathematical perspective and with the help of exact computational tools from algebraic geometry and computer algebra. Two main objectives were achieved. The first is to determine the conditions for singularity for the interaction model related to the observation of more than three straight lines in space, which extends the previous existing results for three lines. The second is the computation of the critical points (the equilibrium points) of IBVS in the observation of four reference points, as a first step towards an analysis of the global stability behaviour of visual servoing
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Chakraborty, Olive. "Design and Cryptanalysis of Post-Quantum Cryptosystems." Electronic Thesis or Diss., Sorbonne université, 2020. http://www.theses.fr/2020SORUS283.

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La résolution de systèmes polynomiaux est l’un des problèmes les plus anciens et des plus importants en Calcul Formel et a de nombreuses applications. C’est un problème intrinsèquement difficile avec une complexité, en générale, au moins exponentielle en le nombre de variables. Dans cette thèse, nous nous concentrons sur des schémas cryptographiques basés sur la difficulté de ce problème. Cependant, les systèmes polynomiaux provenant d’applications telles que la cryptographie multivariée, ont souvent une structure additionnelle cachée. En particulier, nous donnons la première cryptanalyse connue du crypto-système « Extension Field Cancellation ». Nous travaillons sur le schéma à partir de deux aspects, d’abord nous montrons que les paramètres de challenge ne satisfont pas les 80bits de sécurité revendiqués en utilisant les techniques de base Gröbner pour résoudre le système algébrique sous-jacent. Deuxièmement, en utilisant la structure des clés publiques, nous développons une nouvelle technique pour montrer que même en modifiant les paramètres du schéma, le schéma reste vulnérable aux attaques permettant de retrouver le secret. Nous montrons que la variante avec erreurs du problème de résolution d’un système d’équations est encore difficile à résoudre. Enfin, en utilisant ce nouveau problème pour concevoir un nouveau schéma multivarié d’échange de clés nous présentons un candidat qui a été soumis à la compétition Post-Quantique du NIST
Polynomial system solving is one of the oldest and most important problems incomputational mathematics and has many applications in computer science. Itis intrinsically a hard problem with complexity at least single exponential in the number of variables. In this thesis, we focus on cryptographic schemes based on the hardness of this problem. In particular, we give the first known cryptanalysis of the Extension Field Cancellation cryptosystem. We work on the scheme from two aspects, first we show that the challenge parameters don’t satisfy the 80 bits of security claimed by using Gröbner basis techniques to solve the underlying algebraic system. Secondly, using the structure of the public keys, we develop a new technique to show that even altering the parameters of the scheme still keeps the scheme vulnerable to attacks for recovering the hidden secret. We show that noisy variant of the problem of solving a system of equations is still hard to solve. Finally, using this new problem to design a new multivariate key-exchange scheme as a candidate for NIST Post Quantum Cryptographic Standards
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Thomas, Gabriel. "Contributions théoriques et algorithmiques à l'étude des équations différencielles-algébriques : Approche par le calcul formel." Grenoble INPG, 1997. http://www.theses.fr/1997INPG0095.

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Cette thèse de Calcul Formel présente une étude des Equations Différentielles-Algébriques (ou avec contraintes), de type polynomiales et quasilinéaires. Il faut en général dériver ces équations pour pouvoir décider de l'existence de solutions. Ce nombre de dérivations est appelé indice par les numériciens. La première partie précise la définition de l'indice, par une approche algébrique du problème, qui est ensuite comparée aux travaux récents en algèbre différentielle, théorie créée par J. F. Ritt vers 1940. Nous montrons que l'indice ne dépend que des composantes irréductibles de la variété des contraintes. L'utilisation d'idéaux premiers rend ces résultats peu effectifs. En deuxième partie nous remédions à ce problème en utilisant un algorithme dû à D. Lazard, qui décompose les EDA en systèmes triangulaires. Les variétés sont représentées par des idéaux radicaux équidimensionnels. L'algorithme est implémenté dans les systèmes Maple V et GB, pour les calculs de bases de Gröbner. Il s'agit du premier algorithme entièrement formel calculant indice et ensemble des contraintes d'une EDA. La dernière partie étudie localement les points-impasse des EDO implicites, singularités génériques des EDA quasi-linéaires. En nous plaçant dans l'espace complexe, nous montrons simplement que ces points ne sont autres que des points de branchement algébriques des solutions. L'exposant des séries de Puiseux solutions en ces points est obtenu en considérant leur multiplicité dans le déterminant du système, ce qui généralise un résultat de Briot et Bouquet
In this Computer Algebra thesis we develop the thoery of quasi-linear Differential-Algebraic Equations (DAEs) with polynomial coefficients. The existence of solutions to these systems is answered after differentiating the equations ; the minimal number of differentiations to get an integrable form is called the differential index by numerical analysts. In the first part, we make precise the definition of the differential index. By use of algebraic geometry and commutative algebra (modules over quotient rings) we show that the index depends on the irreducible components of the constraints variety of the original DAEs. The second part is devoted to algorithmic issues : we give an original and effective method of decomposing a quasi-linear polynomial DAEs into ODEs on equidimensional algebraic sets. For each subsystem, the index is computed, while both algebraic and differential parts are obtained without using the factorization of polynomials. This algorithm has been implemented with Maple and GB software. The other part of the thesis deals with the local study of so-called impasse points of non linear Differential Equations. These points are the standard singularities of quasi-linear DAEs. Taking a complex viewpoint, we show by simple calculations that impasse points are actually algebraic branch points of the soluions. Getting the multiplicity of these branch points from the determinant of the differential part, we show how to express the solution as a Puiseux expansion near a given impasse point
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Books on the topic "Base du Gröbner"

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Hibi, Takayuki, ed. Gröbner Bases. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3.

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Becker, Thomas, and Volker Weispfenning. Gröbner Bases. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0913-3.

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Sala, Massimiliano, Shojiro Sakata, Teo Mora, Carlo Traverso, and Ludovic Perret, eds. Gröbner Bases, Coding, and Cryptography. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-93806-4.

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Bruns, Winfried, Aldo Conca, Claudiu Raicu, and Matteo Varbaro. Determinants, Gröbner Bases and Cohomology. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-05480-8.

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service), SpringerLink (Online, ed. Gröbner bases, coding, and cryptography. Berlin: Springer, 2009.

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Radon Institute for Computational and Applied Mathematics and Special Semester on Gröbner Bases and Related Methods (2006 : Linz, Austria), eds. Gröbner bases in symbolic analysis. Berlin: Walter De Gruyter, 2007.

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1947-, Herzog Jürgen, ed. Gröbner bases in commutative algebra. Providence, R.I: American Mathematical Society, 2012.

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Adams, William W. An introduction to Gröbner bases. Providence, R.I: American Mathematical Society, 1994.

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Saito, Mutsumi. Gröbner deformations of hypergeometric differential equations. Berlin: Springer, 2000.

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Klin, Mikhail, Gareth A. Jones, Aleksandar Jurišić, Mikhail Muzychuk, and Ilia Ponomarenko, eds. Algorithmic Algebraic Combinatorics and Gröbner Bases. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01960-9.

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Book chapters on the topic "Base du Gröbner"

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Collart, Stéphane, and Daniel Mall. "The ideal structure of Gröbner base computations." In Integrating Symbolic Mathematical Computation and Artificial Intelligence, 156–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60156-2_12.

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Koppenhagen, Ulla, and Ernst W. Mayr. "Optimal gröbner base algorithms for binomial ideals." In Automata, Languages and Programming, 244–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61440-0_132.

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Hibi, Takayuki. "A Quick Introduction to Gröbner Bases." In Gröbner Bases, 1–54. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_1.

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Hamada, Tatsuyoshi. "Warm-Up Drills and Tips for Mathematical Software." In Gröbner Bases, 55–106. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_2.

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Noro, Masayuki. "Computation of Gröbner Bases." In Gröbner Bases, 107–63. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_3.

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Aoki, Satoshi, and Akimichi Takemura. "Markov Bases and Designed Experiments." In Gröbner Bases, 165–221. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_4.

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Ohsugi, Hidefumi. "Convex Polytopes and Gröbner Bases." In Gröbner Bases, 223–78. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_5.

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Takayama, Nobuki. "Gröbner Basis for Rings of Differential Operators and Applications." In Gröbner Bases, 279–344. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_6.

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Nakayama, Hiromasa, and Kenta Nishiyama. "Examples and Exercises." In Gröbner Bases, 345–466. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_7.

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Becker, Thomas, and Volker Weispfenning. "Basics." In Gröbner Bases, 1–13. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0913-3_1.

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Conference papers on the topic "Base du Gröbner"

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Hu, Jing, Yuheng Lin, and Xiwei Zhang. "Reversible Logic Synthesis Using Gröbner Base." In 2019 IEEE 2nd International Conference on Electronics Technology (ICET). IEEE, 2019. http://dx.doi.org/10.1109/eltech.2019.8839444.

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Sartayev, Bauyrzhan, and Abdibek Ydyrys. "Free products of operads and Gröbner base of some operads." In 2023 17th International Conference on Electronics Computer and Computation (ICECCO). IEEE, 2023. http://dx.doi.org/10.1109/icecco58239.2023.10147149.

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Kong, Xianwen. "Classification of 3-DOF 3-UPU Translational Parallel Mechanisms Based on Constraint Singularity Loci Using Gröbner Cover." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-70059.

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Abstract A 3-UPU translational parallel mechanism (TPM) is one of typical TPMs. Several types of 3-UPU TPMs have been proposed in the literature. Despite comprehensive studies on 3-UPU TPMs in which the joint axes on the base and the moving platform are coplanar, only a few 3-UPU TPMs with a skewed base and moving platform have been proposed. However, the impact of link parameters on singularity loci of such TPMs has not been systematically investigated. The advances in computing CGS (comprehensive Gröbner system) or Gröbner cover of parametric polynomial systems provide an efficient tool for solving this problem. This paper presents a systematic classification of 3-UPU TPMs, especially those with a skewed base and moving platform, based on constraint singularity loci. First, the constraint singularity equation of a 3-UPU TPM is derived. To simplify this equation, the coordinate frame on the base (or moving platform) is set up such that the centers of three U joints are located on different coordinate axes. Using Gröbner Cover, the 3-UPU TPMs are classified into 20 types based on the constraint singularity loci. Finally, a novel 3-UPU TPM is proposed. Unlike most of existing 3-UPU TPMs which can transit to two or more 3-DOF operation modes at a constraint singular configuration, the proposed 3-UPU TPM can only transit to one general 3-DOF operation mode in a constraint singular configuration. The singularity locus divides the workspace of this 3-UPU TPM into two constraint singularity-free regions. This work provides a solid foundation for the design of 3-UPU TPMs and a starting point for the classification of a general 3-UPU parallel mechanism.
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Kong, Xianwen. "Classification of a Class of 3-RER Parallel Manipulators Using Gröbner Cover and Primary Decomposition of Ideals." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98057.

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Abstract Recent studies have revealed that the type/number of operation modes of a parallel manipulator (PM) may vary with the link parameters of the PM. However, current research on the impact of link parameters on the type/number of operation modes of a PM is usually based on intuition. This paper deals with the systematic classification of a 3-RER PM. The 3-RER PM is composed of a base and a moving platform connected by three RER legs, each of which is a serial kinematic chain composed of a revolute (R) joint, a planar (E) joint and an R joint in sequence. The axes of the R joints on the base (or moving platform) are all parallel. At first, a set of constraint equations of the 3-RER PM is first derived. Then using a method called Gröbner cover to calculate the comprehensive Gröbner system of parametric polynomial systems, the 3-RER PM is classified into 21 types. The operation modes of all the types of 3-RER PMs are determined using primary decomposition of ideals. Besides the two 4-DOF (degree-of-freedom) 3T1R operation modes, different types of 3-RER PMs may have up to two more 3-DOF or other types of 4-DOF operation modes. This work is the first systematic study on the impact of link parameters on the operation modes of the 3-RER PM and will contribute to the design and control of 3-RER PMs and research on multi-mode (or reconfigurable) PMs.
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Cox, David A. "Gröbner bases." In the 2007 international symposium. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1277548.1277601.

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Castro-Jiménez, Francisco J., and M. Angeles Moreno-Frías. "Gröbner δ-bases and Gröbner bases for differential operators." In Differential Galois Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc58-0-4.

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Dhingra, A. K., A. N. Almadi, and D. Kohli. "Displacement Analysis of Multi-Loop Mechanisms Using Gröbner Bases." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5906.

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Abstract The displacement analysis problem for planar mechanisms can be written as a system of algebraic equations, in particular as a system of multivariate polynomial equations. Elimination theory based on resultants and polynomial continuation are some of the methods which have been used to solve this problem. This paper explores an alternate approach, based on Gröbner bases, to solve the displacement analysis problem for planar mechanisms. It is shown that the reduced set of generators obtained using the Buchberger’s algorithm for Gröbner bases not only yields the input-output polynomial for the mechanism, but also provides comprehensive information on the number of closures and the relationships between various links of the mechanism. Numerical examples illustrating the applicability of Gröbner bases to displacement analysis of 10 and 12-link mechanisms and determination of coupler curve equation for 8-link mechanisms are presented.
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Arikawa, Keisuke. "Kinematic Analysis of Mechanisms Based on Parametric Polynomial System." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85347.

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Many kinematic problems of mechanisms can be expressed in the form of polynomial systems. Gröbner Bases computation is effective for algebraically analyzing such systems. In this research, we discuss the cases in which the parameters are included in the polynomial systems. The parameters are used to express the link lengths, the displacements of active joints, hand positions, and so on. By calculating Gröbner Cover of the parametric polynomial system that expresses kinematic constraints, we obtain segmentation of the parameter space and valid Gröbner Bases for each segment. In the application examples, we use planar linkages to interpret the meanings of the algebraic equations that define the segments and the Gröbner Bases. Using these interpretations, we confirmed that it was possible to enumerate the assembly and working modes and to identify the geometrical conditions that enable overconstrained motions.
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Faugère, Jean-Charles, Pierre-Jean Spaenlehauer, and Jules Svartz. "Sparse Gröbner bases." In the 39th International Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2608628.2608663.

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Kapur, Deepak, Yao Sun, and Dingkang Wang. "Computing comprehensive Gröbner systems and comprehensive Gröbner bases simultaneously." In the 36th international symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993918.

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