Littérature scientifique sur le sujet « Gröbner bases application »
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Articles de revues sur le sujet "Gröbner bases application"
Xia, Shengxiang, et Gaoxiang Xia. « AN APPLICATION OF GRÖBNER BASES ». Mathematics Enthusiast 6, no 3 (1 juillet 2009) : 381–94. http://dx.doi.org/10.54870/1551-3440.1159.
Texte intégralHASHEMI, AMIR, et PARISA ALVANDI. « APPLYING BUCHBERGER'S CRITERIA FOR COMPUTING GRÖBNER BASES OVER FINITE-CHAIN RINGS ». Journal of Algebra and Its Applications 12, no 07 (16 mai 2013) : 1350034. http://dx.doi.org/10.1142/s0219498813500345.
Texte intégralKolesnikov, P. S. « Gröbner–Shirshov Bases for Replicated Algebras ». Algebra Colloquium 24, no 04 (15 novembre 2017) : 563–76. http://dx.doi.org/10.1142/s1005386717000372.
Texte intégralBORISOV, A. V., A. V. BOSOV et A. V. IVANOV. « APPLICATION OF COMPUTER SIMULATION TO THE ANONYMIZATION OF PERSONAL DATA : STATE-OF-THE-ART AND KEY POINTS ». Программирование, no 4 (1 juillet 2023) : 58–74. http://dx.doi.org/10.31857/s0132347423040040.
Texte intégralOhsugi, Hidefumi, et Takayuki Hibi. « Prestable ideals and Sagbi bases ». MATHEMATICA SCANDINAVICA 96, no 1 (1 mars 2005) : 22. http://dx.doi.org/10.7146/math.scand.a-14942.
Texte intégralQiu, Jianjun, et Yuqun Chen. « Free Lie differential Rota–Baxter algebras and Gröbner–Shirshov bases ». International Journal of Algebra and Computation 27, no 08 (décembre 2017) : 1041–60. http://dx.doi.org/10.1142/s0218196717500485.
Texte intégralConca, A., E. De Negri et E. Gorla. « Universal Gröbner Bases and Cartwright–Sturmfels Ideals ». International Mathematics Research Notices 2020, no 7 (25 avril 2018) : 1979–91. http://dx.doi.org/10.1093/imrn/rny075.
Texte intégralGao, Xing, et Tianjie Zhang. « Averaging algebras, rewriting systems and Gröbner–Shirshov bases ». Journal of Algebra and Its Applications 17, no 07 (13 juin 2018) : 1850130. http://dx.doi.org/10.1142/s021949881850130x.
Texte intégralMatsuda, Kazunori, Hidefumi Ohsugi et Kazuki Shibata. « Toric Rings and Ideals of Stable Set Polytopes ». Mathematics 7, no 7 (10 juillet 2019) : 613. http://dx.doi.org/10.3390/math7070613.
Texte intégralBOKUT, L. A., et A. A. KLEIN. « SERRE RELATIONS AND GRÖBNER-SHIRSHOV BASES FOR SIMPLE LIE ALGEBRAS II ». International Journal of Algebra and Computation 06, no 04 (août 1996) : 401–12. http://dx.doi.org/10.1142/s0218196796000234.
Texte intégralThèses sur le sujet "Gröbner bases application"
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.
Texte intégralPolynomial 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
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.
Texte intégralPolynomial 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
García, Fontán Jorge. « Singularity and Stability Analysis of vision-based controllers ». Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS015.
Texte intégralThe 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
Ars, Gwénolé. « Applications des bases de Gröbner à la cryptograhie ». Rennes 1, 2005. http://www.theses.fr/2005REN1S039.
Texte intégralXiu, Xingqiang [Verfasser], et 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.
Texte intégralSpaenlehauer, Pierre-Jean. « Résolution de systèmes multi-homogènes et déterminantiels algorithmes - complexité - applications ». Paris 6, 2012. http://www.theses.fr/2012PA066467.
Texte intégralMultivariate 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)
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.
Texte intégralIn 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
Al-Kaabi, Mahdi Jasim Hasan. « Bases de monômes dans les algèbres pré-Lie libres et applications ». Thesis, Clermont-Ferrand 2, 2015. http://www.theses.fr/2015CLF22599/document.
Texte intégralIn this thesis, we study the concept of free pre-Lie algebra generated by a (non-empty) set. We review the construction by A. Agrachev and R. Gamkrelidze of monomial bases in free pre-Lie algebras. We describe the matrix of the monomial basis vectors in terms of the rooted trees basis exhibited by F. Chapoton and M. Livernet. Also, we show that this matrix is unipotent and we find an explicit expression for its coefficients, adapting a procedure implemented for the free magmatic algebra by K. Ebrahimi-Fard and D. Manchon. We construct a pre-Lie structure on the free Lie algebra $\mathcal{L}$(E) generated by a set E, giving an explicit presentation of $\mathcal{L}$(E) as the quotient of the free pre-Lie algebra $\mathcal{T}$^E, generated by the (non-planar) E-decorated rooted trees, by some ideal I. We study the Gröbner bases for free Lie algebras in tree version. We split the basis of E- decorated planar rooted trees into two parts O(J) and $\mathcal{T}$(J), where J is the ideal defining $\mathcal{L}$(E) as a quotient of the free magmatic algebra generated by E. Here $\mathcal{T}$(J) is the set of maximal terms of elements of J, and its complement O(J) then defines a basis of $\mathcal{L}$(E). We get one of the important results in this thesis (Theorem 3.12), on the description of the set O(J) in terms of trees. We describe monomial bases for the pre-Lie (respectively free Lie) algebra $\mathcal{L}$(E), using the procedure of Gröbner bases and the monomial basis for the free pre-Lie algebra obtained in Chapter 2. Finally, we study the so-called classical and pre-Lie Magnus expansions, discussing how we can find a recursion for the pre-Lie case which already incorporates the pre-Lie identity. We give a combinatorial vision of a numerical method proposed by S. Blanes, F. Casas, and J. Ros, on a writing of the classical Magnus expansion in $\mathcal{L}$(E), using the pre-Lie structure
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.
Texte intégralMou, Chenqi. « Solving polynomial systems over finite fields : Algorithms, Implementations and applications ». Paris 6, 2013. http://www.theses.fr/2013PA066805.
Texte intégralPolynomial system solving over finite fields is of particular interest because of its applications in Cryptography, Coding Theory, and other areas of information science and technologies. In this thesis we study several important theoretical and computational aspects for solving polynomial systems over finite fields, in particular on the two widely used tools Gröbner bases and triangular sets. We propose efficient algorithms for change of ordering of Gröbner bases of zero-dimensional ideals by using the sparsity of multiplication matrices and evaluate such sparsity for generic polynomial systems. Original algorithms are presented for decomposing polynomial sets into simple triangular sets over finite fields. We also define squarefree decomposition and factorization of polynomials over unmixed products of field extensions and propose algorithms for computing them. The effectiveness and efficiency of these algorithms have been verified by experiments with our implementations. Methods for polynomial system solving over finite fields are also applied to solve practical problems arising from Biology and Coding Theory
Livres sur le sujet "Gröbner bases application"
Bruno, Buchberger, et Winkler Franz 1955-, dir. Gröbner bases and applications. Cambridge, U.K : Cambridge University Press, 1998.
Trouver le texte intégral1947-, Herzog Jürgen, dir. Gröbner bases in commutative algebra. Providence, R.I : American Mathematical Society, 2012.
Trouver le texte intégral1962-, Sturmfels Bernd, dir. Introduction to tropical geometry. Providence, Rhode Island : American Mathematical Society, 2015.
Trouver le texte intégralBuchberger, Bruno, et Franz Winkler, dir. Gröbner Bases and Applications. Cambridge University Press, 1998. http://dx.doi.org/10.1017/cbo9780511565847.
Texte intégralBuchberger, Bruno, et Franz Winkler. Gröbner Bases and Applications. Cambridge University Press, 2012.
Trouver le texte intégralBuchberger, Bruno, et Franz Winkler. Gröbner Bases and Applications. Cambridge University Press, 1998.
Trouver le texte intégralBuchberger, Bruno, et Franz Winkler. Gröbner Bases and Applications. Cambridge University Press, 2011.
Trouver le texte intégralElkadi, Mohamed, et Bernard Mourrain. Introduction à la résolution des systèmes polynomiaux (Mathématiques et Applications). Springer, 2007.
Trouver le texte intégralAlgebraic Statistics. American Mathematical Society, 2018.
Trouver le texte intégralChapitres de livres sur le sujet "Gröbner bases application"
Borges-Quintana, M., M. A. Borges-Trenard et E. Martínez-Moro. « An Application of Möller’s Algorithm to Coding Theory ». Dans 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.
Texte intégralBahloul, Rouchdi. « Gröbner Bases in D-Modules : Application to Bernstein-Sato Polynomials ». Dans 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.
Texte intégralBecker, Thomas, et Volker Weispfenning. « First Applications of Gröbner Bases ». Dans Gröbner Bases, 243–92. New York, NY : Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0913-3_7.
Texte intégralTakayama, Nobuki. « Gröbner Basis for Rings of Differential Operators and Applications ». Dans Gröbner Bases, 279–344. Tokyo : Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54574-3_6.
Texte intégralAdams, William, et Philippe Loustaunau. « Applications of Gröbner bases ». Dans An Introduction to Gröbner Bases, 53–112. Providence, Rhode Island : American Mathematical Society, 1994. http://dx.doi.org/10.1090/gsm/003/02.
Texte intégralGöbel, Manfred. « Symideal Gröbner bases ». Dans Rewriting Techniques and Applications, 48–62. Berlin, Heidelberg : Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61464-8_42.
Texte intégralRobertz, Daniel. « Janet Bases and Applications ». Dans Gröbner Bases in Symbolic Analysis, sous la direction de Markus Rosenkranz et Dongming Wang, 139–68. Berlin, Boston : DE GRUYTER, 2007. http://dx.doi.org/10.1515/9783110922752.139.
Texte intégralFajardo, William, Claudia Gallego, Oswaldo Lezama, Armando Reyes, Héctor Suárez et Helbert Venegas. « Gröbner Bases of Modules ». Dans Algebra and Applications, 261–86. Cham : Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53378-6_14.
Texte intégralMonfroy, Eric. « Gröbner bases : Strategies and applications ». Dans 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.
Texte intégralPommaret, Jean-François. « Gröbner Bases in Algebraic Analysis : New Perspectives for Applications ». Dans Gröbner Bases in Symbolic Analysis, sous la direction de Markus Rosenkranz et Dongming Wang, 1–22. Berlin, Boston : DE GRUYTER, 2007. http://dx.doi.org/10.1515/9783110922752.1.
Texte intégralActes de conférences sur le sujet "Gröbner bases application"
Ohsugi, Hidefumi. « Gröbner bases of toric ideals and their application ». Dans the 39th International Symposium. New York, New York, USA : ACM Press, 2014. http://dx.doi.org/10.1145/2608628.2627495.
Texte intégralArikawa, Keisuke. « Kinematic Analysis of Mechanisms Based on Parametric Polynomial System ». Dans 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.
Texte intégralWang, Hai, Lei Zhang, Qiong Wang et Shi Yan. « The Gröbner Bases Algorithm and its Application in Polynomial Ideal Theory ». Dans 2019 Chinese Control And Decision Conference (CCDC). IEEE, 2019. http://dx.doi.org/10.1109/ccdc.2019.8833013.
Texte intégralPethö, Attila. « Application of Gröbner bases to the resolution of systems of norm equations ». Dans the 1991 international symposium. New York, New York, USA : ACM Press, 1991. http://dx.doi.org/10.1145/120694.120713.
Texte intégralzhao, zhiqin, et xuewei xiong. « Gröbner bases method for solving N-path in finite graph and its application ». Dans International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), sous la direction de Zhen Wang et Dunhui Xiao. SPIE, 2023. http://dx.doi.org/10.1117/12.2679167.
Texte intégralLevandovskyy, Viktor, Grischa Studzinski et Benjamin Schnitzler. « Enhanced computations of gröbner bases in free algebras as a new application of the letterplace paradigm ». Dans the 38th international symposium. New York, New York, USA : ACM Press, 2013. http://dx.doi.org/10.1145/2465506.2465948.
Texte intégralArikawa, Keisuke. « Improving the Method for Kinematic Analysis of Mechanisms That Was Based on Parametric Polynomial System With Gröbner Cover ». Dans 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.
Texte intégralKURIKI, Satoshi, Tetsuhisa MIWA et Anthony J. HAYTER. « Abstract Tubes Associated with Perturbed Polyhedra with Applications to Multidimensional Normal Probability Computations ». Dans 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.
Texte intégralSATO, Y., et A. SUZUKI. « GRÖBNER BASES IN POLYNOMIAL RINGS OVER VON NEUMANN REGULAR RINGS — THEIR APPLICATIONS ». Dans Proceedings of the Fourth Asian Symposium (ASCM 2000). WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812791962_0007.
Texte intégralSulandra, I. Made, et Gamal Abdul Aziz. « Efficiency strong Gröbner bases computation over principal ideal ring ». Dans THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS (ICOMATHAPP) 2022 : The Latest Trends and Opportunities of Research on Mathematics and Mathematics Education. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0193640.
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