Relevant bibliographies by topics / Application de base de Gröbner

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Academic literature on the topic 'Application de base de Gröbner'

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Published: 25 May 2024

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Journal articles on the topic "Application de base de 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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Xia, Shengxiang, and Gaoxiang Xia. "AN APPLICATION OF GRÖBNER BASES." Mathematics Enthusiast 6, no. 3 (July 1, 2009): 381–94. http://dx.doi.org/10.54870/1551-3440.1159.

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BORISOV, A. V., A. V. BOSOV, and A. V. IVANOV. "APPLICATION OF COMPUTER SIMULATION TO THE ANONYMIZATION OF PERSONAL DATA: STATE-OF-THE-ART AND KEY POINTS." Программирование, no. 4 (July 1, 2023): 58–74. http://dx.doi.org/10.31857/s0132347423040040.

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A new version of GInv (Gröbner Involutive) for computing involutive Gröbner bases is presented as a library in C++11. GInv uses object-oriented memory reallocation for dynamic data structures, such as lists, red-black trees, binary trees, and GMP libraries for arbitrary-precision integer calculations. The interface of the package is designed as a Python3 module.
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Çelik, Ercan, and Mustafa Bayram. "Application of Gröbner basis techniques to enzyme kinetics." Applied Mathematics and Computation 153, no. 1 (May 2004): 97–109. http://dx.doi.org/10.1016/s0096-3003(03)00612-x.

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HASHEMI, AMIR, and PARISA ALVANDI. "APPLYING BUCHBERGER'S CRITERIA FOR COMPUTING GRÖBNER BASES OVER FINITE-CHAIN RINGS." Journal of Algebra and Its Applications 12, no. 07 (May 16, 2013): 1350034. http://dx.doi.org/10.1142/s0219498813500345.

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Norton and Sălăgean [Strong Gröbner bases and cyclic codes over a finite-chain ring, in Proc. Workshop on Coding and Cryptography, Paris, Electronic Notes in Discrete Mathematics, Vol. 6 (Elsevier Science, 2001), pp. 391–401] have presented an algorithm for computing Gröbner bases over finite-chain rings. Byrne and Fitzpatrick [Gröbner bases over Galois rings with an application to decoding alternant codes, J. Symbolic Comput.31 (2001) 565–584] have simultaneously proposed a similar algorithm for computing Gröbner bases over Galois rings (a special kind of finite-chain rings). However, they have not incorporated Buchberger's criteria into their algorithms to avoid unnecessary reductions. In this paper, we propose the adapted version of these criteria for polynomials over finite-chain rings and we show how to apply them on Norton–Sălăgean algorithm. The described algorithm has been implemented in Maple and experimented with a number of examples for the Galois rings.
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Yunus, Gulshadam, Zhenzhen Gao, and Abdukadir Obul. "Gröbner-Shirshov Basis of Quantum Groups." Algebra Colloquium 22, no. 03 (July 14, 2015): 495–516. http://dx.doi.org/10.1142/s1005386715000449.

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In this paper, by using the Ringel-Hall algebra method, we prove that the set of the skew-commutator relations of quantum root vectors forms a minimal Gröbner-Shirshov basis for the quantum groups of Dynkin type. As an application, we give an explicit basis for the types E7 and Dn.
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Kolesnikov, P. S. "Gröbner–Shirshov Bases for Replicated Algebras." Algebra Colloquium 24, no. 04 (November 15, 2017): 563–76. http://dx.doi.org/10.1142/s1005386717000372.

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We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Gröbner–Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras (Lie di-algebras). As another application, we prove an analogue of the Poincaré–Birkhoff–Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD!-algebra).
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Li, Huishi. "The General PBW Property." Algebra Colloquium 14, no. 04 (December 2007): 541–54. http://dx.doi.org/10.1142/s1005386707000508.

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For ungraded quotients of an arbitrary ℤ-graded ring, we define the general PBW property, that covers the classical PBW property and the N-type PBW property studied via the N-Koszulity by several authors (see [2–4]). In view of the noncommutative Gröbner basis theory, we conclude that every ungraded quotient of a path algebra (or a free algebra) has the general PBW property. We remark that an earlier result of Golod [5] concerning Gröbner bases can be used to give a homological characterization of the general PBW property in terms of Shafarevich complex. Examples of application are given.
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Chaharbashloo, Mohammad Saleh, Abdolali Basiri, Sajjad Rahmany, and Saber Zarrinkamar. "An Application of Gröbner Basis in Differential Equations of Physics." Zeitschrift für Naturforschung A 68, no. 10-11 (November 1, 2013): 646–50. http://dx.doi.org/10.5560/zna.2013-0044.

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We apply the Gröbner basis to the ansatz method in quantum mechanics to obtain the energy eigenvalues and the wave functions in a very simple manner. There are important physical potentials such as the Cornell interaction which play significant roles in particle physics and can be treated via this technique. As a typical example, the algorithm is applied to the semi-relativistic spinless Salpeter equation under the Cornell interaction. Many other applications of the idea in a wide range of physical fields are listed as well.
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Dissertations / Theses on the topic "Application de base de Gröbner"

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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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Verron, Thibaut. "Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale." Electronic Thesis or Diss., Paris 6, 2016. http://www.theses.fr/2016PA066355.

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La résolution de systèmes polynomiaux est un problème aux multiples applications, et les bases de Gröbner sont un outil important dans ce cadre. Il est connu que de nombreux systèmes issus d'applications présentent une structure supplémentaire par rapport à des systèmes arbitraires, et que ces structures peuvent souvent être exploitées pour faciliter le calcul de bases de Gröbner.Dans cette thèse, on s'intéresse à deux exemples de telles structures, pour différentes applications. Tout d'abord, on étudie les systèmes homogènes avec poids, qui sont homogènes si on calcule le degré en affectant un poids à chaque variable. Cette structure apparaît naturellement dans de nombreuses applications, dont un problème de cryptographie (logarithme discret). On montre comment les algorithmes existants, efficaces pour les polynômes homogènes, peuvent être adaptés au cas avec poids, avec des bornes de complexité générique divisées par un facteur polynomial en le produit des poids.Par ailleurs, on étudie un problème de classification de racines réelles pour des variétés définies par des déterminants. Ce problème a une application directe en théorie du contrôle, pour l'optimisation de contraste de l'imagerie à résonance magnétique. Ce système particulier s'avère insoluble avec les stratégies générales pour la classification. On montre comment ces stratégies peuvent tirer profit de la structure déterminantielle du système, et on illustre ce procédé en apportant des réponses aux questions posées par le problème d'optimisation de contraste
Polynomial system solving is a problem with numerous applications, and Gröbner bases are an important tool in this context. Previous studies have shown that systèmes arising in applications usually exhibit more structure than arbitrary systems, and that these structures can be used to make computing Gröbner bases easier.In this thesis, we consider two examples of such structures. First, we study weighted homogeneous systems, which are homogeneous if we give to each variable an arbitrary degree. This structure appears naturally in many applications, including a cryptographical problem (discrete logarithm). We show how existing algorithms, which are efficient for homogeneous systems, can be adapted to a weighted setting, and generically, we show that their complexity bounds can be divided by a factor polynomial in the product of the weights.Then we consider a real roots classification problem for varieties defined by determinants. This problem has a direct application in control theory, for contrast optimization in magnetic resonance imagery. This specific system appears to be out of reach of existing algorithms. We show how these algorithms can benefit from the determinantal structure of the system, and as an illustration, we answer the questions from the application to contrast optimization
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Verron, Thibaut. "Régularisation du calcul de bases de Gröbner pour des systèmes avec poids et déterminantiels, et application en imagerie médicale." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066355/document.

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La résolution de systèmes polynomiaux est un problème aux multiples applications, et les bases de Gröbner sont un outil important dans ce cadre. Il est connu que de nombreux systèmes issus d'applications présentent une structure supplémentaire par rapport à des systèmes arbitraires, et que ces structures peuvent souvent être exploitées pour faciliter le calcul de bases de Gröbner.Dans cette thèse, on s'intéresse à deux exemples de telles structures, pour différentes applications. Tout d'abord, on étudie les systèmes homogènes avec poids, qui sont homogènes si on calcule le degré en affectant un poids à chaque variable. Cette structure apparaît naturellement dans de nombreuses applications, dont un problème de cryptographie (logarithme discret). On montre comment les algorithmes existants, efficaces pour les polynômes homogènes, peuvent être adaptés au cas avec poids, avec des bornes de complexité générique divisées par un facteur polynomial en le produit des poids.Par ailleurs, on étudie un problème de classification de racines réelles pour des variétés définies par des déterminants. Ce problème a une application directe en théorie du contrôle, pour l'optimisation de contraste de l'imagerie à résonance magnétique. Ce système particulier s'avère insoluble avec les stratégies générales pour la classification. On montre comment ces stratégies peuvent tirer profit de la structure déterminantielle du système, et on illustre ce procédé en apportant des réponses aux questions posées par le problème d'optimisation de contraste
Polynomial system solving is a problem with numerous applications, and Gröbner bases are an important tool in this context. Previous studies have shown that systèmes arising in applications usually exhibit more structure than arbitrary systems, and that these structures can be used to make computing Gröbner bases easier.In this thesis, we consider two examples of such structures. First, we study weighted homogeneous systems, which are homogeneous if we give to each variable an arbitrary degree. This structure appears naturally in many applications, including a cryptographical problem (discrete logarithm). We show how existing algorithms, which are efficient for homogeneous systems, can be adapted to a weighted setting, and generically, we show that their complexity bounds can be divided by a factor polynomial in the product of the weights.Then we consider a real roots classification problem for varieties defined by determinants. This problem has a direct application in control theory, for contrast optimization in magnetic resonance imagery. This specific system appears to be out of reach of existing algorithms. We show how these algorithms can benefit from the determinantal structure of the system, and as an illustration, we answer the questions from the application to contrast optimization
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Ars, Gwénolé. "Applications des bases de Gröbner à la cryptograhie." Rennes 1, 2005. http://www.theses.fr/2005REN1S039.

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Cette thèse est dédiée à la cryptanalyse algébrique par les bases de Gröbner. Nous avons justifié l'usage des bases de Gröbner par une comparaison théorique et expérimentale avec l'algorithme XL utilisé en cryptographie. Cette thèse a aussi pour objet l'étude de deux problèmes: les registres filtrés et l'AES. Pour prédire le résolution de ces systèmes, nous avons généralisé la notion d'Immunité Algébrique à tout corps fini et étudié les propriétés de cette notion (stabilité, bornes, relation avec d'autres critères cryptographiques). Pour les registres filtrés, une nouvelle représentation a explicité les relations linéaires de la mise en équations. Elle a permi d'obtenir une borne de complexité des attaques algébriques qui ont été vérifiées expérimentalement sur des registres de tailles réelles. Enfin, à travers des résolutions expérimentales d'une simplification appropriée de l'AES, nous avons déterminé des facteurs limitants (taille de la Sbox) ou non (nombre de cycles)
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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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Xiu, Xingqiang [Verfasser], and Martin [Akademischer Betreuer] Kreuzer. "Non-commutative Gröbner Bases and Applications / Xingqiang Xiu. Betreuer: Martin Kreuzer." Passau : Universitätsbibliothek der Universität Passau, 2012. http://d-nb.info/1024803708/34.

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Spaenlehauer, Pierre-Jean. "Résolution de systèmes multi-homogènes et déterminantiels algorithmes - complexité - applications." Paris 6, 2012. http://www.theses.fr/2012PA066467.

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De nombreux systèmes polynomiaux multivariés apparaissant en Sciences de l'Ingénieur possèdent une structure algébrique spécifique. En particulier, les structures multi-homogènes, déterminantielles et les systèmes booléens apparaissent dans une variété d'applications. Une méthode classique pour résoudre des systèmes polynomiaux passe par le calcul d'une base de Gröbner de l'idéal associé au système. Cette thèse présente de nouveaux outils pour la résolution de tels systèmes structurés. D'une part, ces outils permettent d'obtenir sousdes hypothèses de généricité des bornes de complexité du calcul debase de Gröbner de plusieurs familles de systèmes polynomiauxstructurés (systèmes bilinéaires, systèmes déterminantiels, systèmesdéfinissant des points critiques, systèmes booléens). Ceci permetd'identifier des familles de systèmes pour lequels la complexité arithmétique de résolution est polynomiale en le nombre de solutions. D'autre part, cette thèse propose de nouveaux algorithmequi exploitent ces structures algébriques pour améliorer l'efficacité du calcul de base de Gröbner et de la résolution (systèmes multi-homogènes, systèmes booléens). Ces résultats sontillustrés par des applications concrètes en cryptologie (cryptanalyse des systèmes MinRank et ASC), en optimisation et en géométrie réelle effective (calcul de points critiques)
Multivariate polynomial systems arising in Engineering Science often carryalgebraic structures related to the problems they stem from. Inparticular, multi-homogeneous, determinantal structures and booleansystems can be met in a wide range of applications. A classical method to solve polynomial systems is to compute a Gröbner basis ofthe ideal associated to the system. This thesis provides new tools forsolving such structured systems in the context of Gröbner basis algorithms. On the one hand, these tools bring forth new bounds on the complexity of thecomputation of Gröbner bases of several families of structured systems(bilinear systems, determinantal systems, critical point systems,boolean systems). In particular, it allows the identification of families ofsystems for which the complexity of the computation is polynomial inthe number of solutions. On the other hand, this thesis provides new algorithms which takeprofit of these algebraic structures for improving the efficiency ofthe Gröbner basis computation and of the whole solving process(multi-homogeneous systems, boolean systems). These results areillustrated by applications in cryptology (cryptanalysis of MinRank),in optimization and in effective real geometry (critical pointsystems)
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Chenavier, Cyrille. "Le treillis des opérateurs de réduction : applications aux bases de Gröbner non commutatives et en algèbre homologique." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC334.

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Dans cette thèse, on étudie les algèbres associatives unitaires par des méthodes de réécriture. La théorie des bases de \G\ non commutatives permet de résoudre des problèmes de décidabilité ou de calculer des invariants homologiques par de telles méthodes. Motivé par des questions d'algèbre homologique, Berger caractérise les bases de \G\ quadratiques en termes de treillis. Cette caractérisation a pour base les opérateurs de réduction. Ceux-ci sont des projecteurs particuliers d'un espace vectoriel admettant une base totalement ordonnée. Berger montre que, dans le cas où cet espace vectoriel est de dimension finie, l'ensemble des opérateurs de réduction admet une structure de treillis. Il en déduit une formulation de la confluence en termes de treillis lui permettant de caractériser les bases de \G\ quadratiques. Dans ce travail, on étend l'approche par les opérateurs de réduction en l'appliquant au cas des algèbres non nécessairement quadratiques. Pour cela, on montre qu'en dimension quelconque l'ensemble des opérateurs de réduction admet également une structure de treillis. En dimension finie, celle-ci coïncide avec celle exhibée par Berger. On en déduit une formulation de la confluence en termes de treillis généralisant celle de Berger. En outre, on donne une interprétation de la complétion en termes de treillis.La formulation algébrique de la confluence permet en particulier des caractériser les bases de \G\ non commutatives en termes de treillis. De plus, la formulation algébrique de la complétion, nous permet de montrer que celle-ci peut être obtenue via une construction dans le treillis des opérateurs de réduction. On en déduit une méthode pour construire des bases de \G\ non commutatives.On construit également une homotopie contractante du complexe de Koszul en termes d'opérateurs de réduction. La formulation de la confluence en termes de treillis nous permet de caractériser celle-ci par des équations. Ces équations induisent des représentations d'une famille d'algèbres que sont les algèbres de confluence. L'homotopie contractante est construite à partir de ces représentations
In this thesis, we study associative unitary algebras with rewriting methods. \G\ bases theory enables us to solve decision problems and to compute homological invariants with such methods. In order to study homological problems, Berger characterises quadratic \G\ bases in a lattice way. This characterisationis obtained using reduction operators. The latter ones are specific projectors of a vector space equipped with a wellfounded basis. When this vector space is finite-dimensional, Berger proves that the associated set of reduction operators admits a lattice structure. Using it, he deduces the lattice characterisation of quadratic \G\ bases. In this thesis, we extend the approach in terms of reduction operators applying it to not necessarily quadratic algebras.For that, we show that the set of reduction operators relative to a not necessarily finite-dimensional vector space admitsa lattice structure. In the finite-dimensional case, we obtain the same lattice structure than Berger's one. We provide a lattice formulation of confluence generalizing Berger's one. Moreover, we provide a lattice characterisation of completion.We use the lattice formulation of confluence to characterise non commutative \G\ bases. Moreover, we deduce from the lattice formulation of confluence a procedure to construct non commutative \G\ bases.We also construct a contracting homotopt for the Koszul complex using reduction operators. The lattice formulation of confluence enables us to characterise it with algebraic equations. These equations induce representations of a family of algebras called confluence algebras. Our contracting homotopy is built using these representations
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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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Books on the topic "Application de base de Gröbner"

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Bruno, Buchberger, and Winkler Franz 1955-, eds. Gröbner bases and applications. Cambridge, U.K: Cambridge University Press, 1998.

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

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Basilio, C. I. Application of the acid-base theory to flotation systems. S.l: s.n, 1991.

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Michel, Izygon, and United States. National Aeronautics and Space Administration., eds. Advanced software development workstation: Knowledge base design : design of knowledge base for flight planning application. [Houston, Tex.]: Research Institute for Computing and Information Systems, University of Houston-Clear Lake, 1992.

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United States. National Aeronautics and Space Administration., ed. Partial gravity habitat study with application to lunar base design. [Houston, Tex.]: Sasakawa International Center for Space Architecture, University of Houston, College of Architecture, 1989.

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Bullock, Keith. An Application of high angle conveying in base metal mines. Sudbury, Ont: Laurentian University, School of Engineering, 1986.

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1964-, Kraft George, ed. Building applications with the Linux standard base. Upper Saddle River, NJ: IBM Press, 2005.

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Donnelly, Dennis M. Selecting stands for the forest planning data base: Sampling background and application. Fort Collins, Colo: U.S. Dept. of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station, 1995.

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Furuorasu kemisutorī no kiso to ōyō: Base and application of fluorous chemistry. Tōkyō: Shīemshī Shuppan, 2010.

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Purasuchikku saishigenka no kiso to ōyō: Base and application of plastic recycling. Tōkyō: Shīemushī Shuppan, 2012.

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Book chapters on the topic "Application de base de Gröbner"

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Borges-Quintana, M., M. A. Borges-Trenard, and E. Martínez-Moro. "An Application of Möller’s Algorithm to Coding Theory." In Gröbner Bases, Coding, and Cryptography, 379–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-93806-4_24.

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Bahloul, Rouchdi. "Gröbner Bases in D-Modules: Application to Bernstein-Sato Polynomials." In Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers, 75–93. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-26454-3_2.

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Becker, Thomas, and Volker Weispfenning. "First Applications of Gröbner Bases." In Gröbner Bases, 243–92. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0913-3_7.

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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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Adams, William, and Philippe Loustaunau. "Applications of Gröbner bases." In An Introduction to Gröbner Bases, 53–112. Providence, Rhode Island: American Mathematical Society, 1994. http://dx.doi.org/10.1090/gsm/003/02.

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Göbel, Manfred. "Symideal Gröbner bases." In Rewriting Techniques and Applications, 48–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61464-8_42.

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Robertz, Daniel. "Janet Bases and Applications." In Gröbner Bases in Symbolic Analysis, edited by Markus Rosenkranz and Dongming Wang, 139–68. Berlin, Boston: DE GRUYTER, 2007. http://dx.doi.org/10.1515/9783110922752.139.

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Fajardo, William, Claudia Gallego, Oswaldo Lezama, Armando Reyes, Héctor Suárez, and Helbert Venegas. "Gröbner Bases of Modules." In Algebra and Applications, 261–86. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53378-6_14.

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Monfroy, Eric. "Gröbner bases: Strategies and applications." In Artificial Intelligence and Symbolic Mathematical Computing, 133–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/3-540-57322-4_9.

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Fajardo, William, Claudia Gallego, Oswaldo Lezama, Armando Reyes, Héctor Suárez, and Helbert Venegas. "Matrix Computations Using Gröbner Bases." In Algebra and Applications, 335–53. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53378-6_17.

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Conference papers on the topic "Application de base de Gröbner"

1

Ohsugi, Hidefumi. "Gröbner bases of toric ideals and their application." In the 39th International Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2608628.2627495.

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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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Arikawa, Keisuke. "Improving the Method for Kinematic Analysis of Mechanisms That Was Based on Parametric Polynomial System With Gröbner Cover." 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/detc2019-97679.

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Abstract A polynomial system that contains parameters is termed a parametric polynomial system (PPS). We had previously proposed a method of kinematic analysis of mechanisms based on PPS with Gröbner cover, where the parameters are used to express link lengths, displacements of active joints, and so on. Calculating Gröbner cover of PPS that expresses kinematic constraints, and interpreting the segments of the parameter space that are generated by Gröbner cover, it is possible to gain an insight for comprehensively understanding kinematic properties of mechanisms characterized by the parameters. In this study, certain improvements to the method were made to enhance its practical application. The validity check of the segments in the real domain using quantifier elimination provides an automatic reliable check even for a large number of segments. The evaluation of the solution spaces in the segments using primary decomposition facilitates the kinematic interpretation of the complex solution spaces. The active joint selection based on the variable order in Gröbner cover enables the analyses without explicitly specifying active joints. Moreover, the alternative algebraic formulation of kinematic problems based on a homogeneous transformation matrix provides further insight regarding the mechanisms containing zero-length links. The effectiveness of these improvements was verified by the analyses of the configurations of 3RPR mechanism and five-bar linkage.
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Wang, Hai, Lei Zhang, Qiong Wang, and Shi Yan. "The Gröbner Bases Algorithm and its Application in Polynomial Ideal Theory." In 2019 Chinese Control And Decision Conference (CCDC). IEEE, 2019. http://dx.doi.org/10.1109/ccdc.2019.8833013.

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Pethö, Attila. "Application of Gröbner bases to the resolution of systems of norm equations." In the 1991 international symposium. New York, New York, USA: ACM Press, 1991. http://dx.doi.org/10.1145/120694.120713.

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zhao, zhiqin, and xuewei xiong. "Gröbner bases method for solving N-path in finite graph and its application." In International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), edited by Zhen Wang and Dunhui Xiao. SPIE, 2023. http://dx.doi.org/10.1117/12.2679167.

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Levandovskyy, Viktor, Grischa Studzinski, and Benjamin Schnitzler. "Enhanced computations of gröbner bases in free algebras as a new application of the letterplace paradigm." In the 38th international symposium. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2465506.2465948.

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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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KURIKI, Satoshi, Tetsuhisa MIWA, and Anthony J. HAYTER. "Abstract Tubes Associated with Perturbed Polyhedra with Applications to Multidimensional Normal Probability Computations." In Harmony of Gröbner Bases and the Modern Industrial Society - The Second CREST-CSBM International Conference. Singapore: World Scientific Publishing Co. Pte. Ltd., 2012. http://dx.doi.org/10.1142/9789814383462_0010.

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Reports on the topic "Application de base de Gröbner"

1

R.J. Garrett. Nuclear Safety Design Base for License Application. Office of Scientific and Technical Information (OSTI), September 2005. http://dx.doi.org/10.2172/895368.

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Adve, R., P. Antonik, W. Baldygo, C. Capraro, and G. Capraro. Knowledge-Base Application to Ground Moving Target Detection. Fort Belvoir, VA: Defense Technical Information Center, September 2001. http://dx.doi.org/10.21236/ada388934.

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Yazawa, Keisuke. AlN Base Material Development for High Temperature Application. Office of Scientific and Technical Information (OSTI), August 2023. http://dx.doi.org/10.2172/1994804.

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Lubell, Joshua. The application protocol information base world wide web gateway. Gaithersburg, MD: National Institute of Standards and Technology, 1996. http://dx.doi.org/10.6028/nist.ir.5868.

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Decker, Robert K. Viscous Drag Measurement and Its Application to Base Drag Reduction. Fort Belvoir, VA: Defense Technical Information Center, May 2002. http://dx.doi.org/10.21236/ada403228.

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J.H. Zhu, M.P. Brady, and H.U. Anderson. Tailoring Fe-Base Alloys for Intermediate Temperature SOFC Interconnect Application. Office of Scientific and Technical Information (OSTI), December 2007. http://dx.doi.org/10.2172/932217.

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Binder, Michael J., Franklin H. Holcomb, and William R. Taylor. Site Evaluation for Application of Fuel Cell Technology, Barksdale Air Force Base, LA. Fort Belvoir, VA: Defense Technical Information Center, March 2001. http://dx.doi.org/10.21236/ada387497.

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Binder, Michael J., Franklin H. Holcomb, and William R. Taylor. Site Evaluation for Application of Fuel Cell Technology, Westover Air Reserve Base, MA. Fort Belvoir, VA: Defense Technical Information Center, February 2001. http://dx.doi.org/10.21236/ada387572.

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Binder, Michael J., Franklin H. Holcomb, and William R. Taylor. Site Evaluation for Application of Fuel Cell Technology, Laughlin Air Force Base, TX. Fort Belvoir, VA: Defense Technical Information Center, April 2001. http://dx.doi.org/10.21236/ada387648.

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Binder, Michael J., Franklin H. Holcomb, and William R. Taylor. Site Evaluation for Application of Fuel Cell Technology, Nellis Air Force Base, NV. Fort Belvoir, VA: Defense Technical Information Center, March 2001. http://dx.doi.org/10.21236/ada385549.

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