Academic literature on the topic 'Grobner theory'
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Journal articles on the topic "Grobner theory"
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Jensen, Anders Nedergaard. "A Non-Regular Grobner Fan." Discrete & Computational Geometry 37, no. 3 (2007): 443–53. http://dx.doi.org/10.1007/s00454-006-1289-0.
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Petrovic, Zoran, and Branislav Prvulovic. "New immersion theorems for Grassmann manifolds G3,n." Publications de l'Institut Math?matique (Belgrade) 101, no. 115 (2017): 1–10. http://dx.doi.org/10.2298/pim1715001p.
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A Grobner basis for the ideal determining mod 2 cohomology of Grassmannian G3,n, obtained in a previous paper, is used, along with the method of obstruction theory, to establish some new immersion results for these manifolds.
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Kawasaki, Harushisa, and Toshimi Shimizu. "Symbolic Analysis of Robot Base Parameter Set Using Grobner-Basis." Journal of Robotics and Mechatronics 10, no. 6 (1998): 475–81. http://dx.doi.org/10.20965/jrm.1998.p0475.
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We analyzed base parameters for closed-loop robots using robot symbolic analysis based on the completion procedure in polynomial ideal theory. The robot dynamics regressor is represented as a matrix of multivariate polynomials and reduced to normal form based on Buchberger's algorithm by constructing reduced Grobner basis from kinematic constrained equations. The linear independence of the reduced regressor's column vectors is studied by Gauss-Jordan elimination. Original dynamic parameters are regrouped and some eliminated, depending on results. This omits the need to solve kinematic constrained equations explicitly, deriving all base parameters systematically in theory. An example is shown using robot symbolic analysis system: ROSAM 11.
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Muzika-Dizdarevic, Manuela, and Rade Zivaljevic. "Symmetric polyomino tilings, tribones, ideals, and Gröbner bases." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 1–23. http://dx.doi.org/10.2298/pim1512001m.
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We apply the theory of Grobner bases to the study of signed, symmetric polyomino tilings of planar domains. Complementing the results of Conway and Lagarias we show that the triangular regions TN = T3k?1 and TN = T3k in a hexagonal lattice admit a signed tiling by three-in-line polyominoes (tribones) symmetric with respect to the 120? rotation of the triangle if and only if either N = 27r ? 1 or N = 27r for some integer r > 0. The method applied is quite general and can be adapted to a large class of symmetric tiling problems.
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Saints, K., and C. Heegard. "Algebraic-geometric codes and multidimensional cyclic codes: a unified theory and algorithms for decoding using Grobner bases." IEEE Transactions on Information Theory 41, no. 6 (1995): 1733–51. http://dx.doi.org/10.1109/18.476246.
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Rigby, John. "A simple proof of Lester’s theorem." Mathematical Gazette 87, no. 510 (2003): 444–52. http://dx.doi.org/10.1017/s0025557200173620.
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Lester’s theorem (1997) states that in any scalene triangle the two Fermat points F and F' (to be defined later), the nine-point centre N, and the circumcentre O, are concyclic, and that the pair of points O,F separates the pair N, F'. (In certain geometrical situations a line is regarded as a circle of infinite radius, so that the word ‘concyclic’ includes ‘collinear’ as a special case, but here ‘concyclic’ means ‘lying on a proper circle of finite radius’.) Previous proofs of Lester’s theorem have involved advanced techniques and/or computer algebra; to quote from Ron Shail’s recent article [1],‘Lester’s original computer-assisted discovery and proof make use of her theory of “complex triangle coordinates” and “complex triangle functions”. ... A proof has also been given by Trott ... using the advanced concept of GrObner bases in the reduction of systems of polynomial equations to “diagonal” form. Trott’s work uses the computer algebra system Mathematica as an essential tool.’
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Yabuno, Hiroshi. "Nonlinear Stability Analysis for Summed-Type Combination Resonance under Parametrical Excitation. (Application of Center Manifold Theory and Grobner Basiswith Computer Algebra)." Transactions of the Japan Society of Mechanical Engineers Series C 60, no. 572 (1994): 1151–58. http://dx.doi.org/10.1299/kikaic.60.1151.
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VAMPELJ SUHADOLNIK, Nataša. "Podoba in vloga Matere Zahodnega kraljestva v grobni umetnosti dinastije Han." Asian Studies 3, no. 2 (2015): 197–212. http://dx.doi.org/10.4312/as.2015.3.2.197-212.
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Pričujoči prispevek podrobneje obravnava podobo kitajske starodavne boginje Matere Zahodnega kraljestva, v kitajščini imenovane Xiwangmu 西王母. Xiwangmu je v mitološki tradiciji prikazana kot boginja, ki poseduje eliksir nesmrtnosti in prebiva v Zahodnem raju na magični gori Kunlun 崑崙. Njeno podobo je mogoče opazovati v stenskem slikarstvu, na lakiranih izdelkih, bronastih ogledalih, največkrat pa se pojavi kot reliefna podoba na kamnih ali opekah, ki so sestavljale grobne komore ali posamezne templje na površju grobne zasnove dinastije Han (206 pr. n. št.–220 n. št.). Literarna tradicija razkriva večfunkcionalno vlogo matere s številnim atributi, ki se razvija skladno s spreminjajočimi se vrednotami družbenih mitoloških konceptov. Kakšna je njena podoba in kakšno vlogo prevzema v širšem kozmološkem konceptu v grobni umetnosti dinastije Han, je osrednja problematika pričujočega prispevka.
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Kawasaki, Haruhisa. "Special Issue on Analysis and Simulation Systems for Robotics and Mechatronics." Journal of Robotics and Mechatronics 10, no. 6 (1998): 463. http://dx.doi.org/10.20965/jrm.1998.p0463.
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Superior analysis and simulation systems play an important part in robotics and mechatronics R&D. Developing apparatuses involves repeating planning, trial manufacture, experiments, analysis, and improvement. Simulation and analysis are now executed before trial manufacture, decreasing the number of trial manufacture, shortening development, and cutting development cost. Virtual reality is often applied to simulation, and commercialization without trial manufactures will eventually be possible. Most commercialized simulation software are being improved for general use based on software made by researchers because existing analysis and simulation do not function sufficiently and researchers are often required to develop their own analysis and simulation. Simulation developed for research thus may be used by many technical experts and researchers in the future. This special issue introduces seven reports on basic mechanism analysis developed to survey simulation research. Michisuke Jo et al. developed a mechanism kinetic analysis Motor Drive using FORTRAN and MATLAB. This article, entitled Kinematic Analysis of Mechanisms Using Motor Algebra and Graph Theory, considers kinematic analysis method using the latest drive version. Haruhisa Kawasaki et al. are developing robot analysis ROSAM II using C and Maple V. This article, entitled Symbolic Analysis of Robot Base Parameter Set Using Grobner-Basis, considers base parameter analysis of general robots with closed links. Hajime Morikawa et al. developed a robot simulator kinematically simulated by connecting graphic icons. This article, entitled Network-Based Robot Simulator Using Hierarchical Graphic Icons, considers construction of a robot simulator, kinetic analysis of multiple robot arms, dynamic analysis of forest trimmers, and an example applying remote control to space robots. Shigeki Toyama et al. developed general-use mechanism analysis simulator AI MOTION. This article, entitled Dynamic Autonomous Car Mobile Analysis Simulating Mechanical Systems Analysis, considers an autonomous car travel simulator dynamically modeling tires combined into AI MOTION. The simulator analyzes the connection of tire rigidity, car width, caster radius, and motion performance. Takayoshi Muto et al. developed dynamic behavior simulator BDSP for hydraulic systems. This article, entitled Software Package BDSP Developed to Simulate Hydraulic Systems, considers construction of BDSP that analyzes hydraulic systems using easy block diagrams. The simulator analyzes fluid line, nonlinear elements, and discrete time control. Shinichi Nakajima et al. developed a two-dimensional jaw movement simulator for clarifying the function of muscles in lower jaw motion. This article, entitled Development of 2-D Jaw Movement Simulator(JSN/SI), considers hardware and a control system for chewing food at a required force. Yoshiyuki Sankai et al., in Robot Objective Parallel Calculation and Real-time Control Using a Digital Signal Processor, consider parallel distributed and realtime control by DSP for constructing control in an actual robot. This issue discussed analysis and simulation developed for robotics and mechatronics R&D. Most systems are applicable to general-purpose situations. We hope this issue helps deepen the understanding of the status and applications of simulation research in mechatronics and promotes further development in the field.
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Ferlus, Michel. "Les Systèmes De Tons Dans Les Langues Viet-Muong." Diachronica 15, no. 1 (1998): 1–27. http://dx.doi.org/10.1075/dia.15.1.02fer.
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SUMMARY The Viet-Muong languages present a wide variety of systems having four to six tones, and reflecting two earlier systems: a six-tone system and a four-tone system in which final -h is preserved. Vietnamese, Muòng and Cuoi are representative of a pure six-tone system in the traditional definition. Sách/ Ruc and Thavung have a four-tone system in which vowel breathiness is preserved in the low tone series. When in such a system breathiness is lost too fast, as in Maleng, the result is a kind of eroded two-tone system. In some languages like Pong and some Vietnamese dialects, final -h was lost without giving contrastive tones, the result being a kind of heterodox four-tone system. The situation of tone systems in Viet-Muong languages is of the highest importance for the theory of tonogenesis. RÉSUMÉ Les langues viet-muong offrent un large éventail de systèmes tonals, de quatre à six tons, provenant tous de deux systèmes antérieurs de base: l'un à six tons et l'autre à quatre tons où le -h final est préservé. Le vietnamien, le muròng et le cuôi sont représentatifs d'un pur système à six tons dans leur définition la plus classique. Le sách/ruc et le thavung ont un système à quatre tons avec des voyelles soufflées sous les tons de la série basse. La chute trop rapide du caractère soufflé, comme en maleng, donne une sorte de système érrodé à deux tons. En pong et dans certains dialectes vietnamiens le -h final est tombé sans entraîner la création de tons supplémentaires, le résultat étant la formation de systèmes tonals hétérodoxes à quatre tons. La variété des systèmes tonals en viet-muong représente un apport important à une théorie de la tonogénèse. ZUSAMMENFASSUNG Die Viet-Muong-Sprachen stellen eine groBe Varietät von Systemen zwi-schen vier und sechs Tonen dar; sie reflektieren zwei frühere Systeme, und zwar ein Sechstonsystem und ein Viertonsystem, in welchen ein finales -h erhalten geblieben ist. Vietnamesisch, Muòng and Cuoi sind repräsentativ fur ein reines Sechstonsystem der herkommlichen Art. Sách/Ruc und Thavung hingegen haben ein Viertonsystem, in welchem eine rauhe Vokalbehauchung in der niederen Tonreihe erhalten geblieben ist. Wenn in einem solchen System die rauhe Behauchung zu schnell verlorengeht, wie im Maleng, ist das Ergebnis eine Art heruntergekommenes Zweitonsystem. In solchen Sprachen wie Pong und einigen vietnamesischen Dialekten war das End-h verlorenge-gangen, ohne jedoch kontrastierende Tone zu erhalten: das Ergebnis war eine Art heterodoxes Viertonsystem. The Situation der Tonsysteme in den Viet-Muong-Sprachen ist von groBter Wichtigkeit fur die Theorie der Tongenese.
Dissertations / Theses on the topic "Grobner theory"
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Chang, Eun R. "Grobner Bases and Ideals of Points." VCU Scholars Compass, 2006. http://scholarscompass.vcu.edu/etd/1214.
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The main point of this thesis is an introduction to the theory of Grobner bases. The concept of Grobner basis and construction of the Grobner basis by Buchberger's Algorithm, in which the notion of S-polynomials is introduced, and a few modified or improved versions of Grobner basis algorithm are reviewed in this paper. In Chapter 1, we have a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division algorithm and its examples. After ascertaining the monomial ordering on multivariate polynomials, we establish a leading term of a polynomial.In Chapter 2, after defining Grobner bases, we study some nice and useful properties of Grobner bases, such as a uniqueness of reduced Grobner basis and existence of a Grobner basis.In Chapter 3, we explore the Buchberger-Moller algorithm to construct Grobner bases and return a set of polynomials whose residue classes form a basis of a quotient of a polynomial ring. Also, we survey a generalized Buchberger-Moller algorithm to determine directly a Grobner basis for the intersection of a finite number of ideals.In Chapter 4, we conclude this paper with some applications of Grobner bases.
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Staib, Frederico Fontes. "Bases de Grobner aplicadas à k-coloração de grafos." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306260.
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Orientador: Patrícia Helena Araújo da Silva Nogueira<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-17T08:03:36Z (GMT). No. of bitstreams: 1
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Previous issue date: 2010<br>Resumo: Neste trabalho, estudamos a teoria das bases de Gröbner e sua aplicação ao problema da k-coloração de grafos, estabelecendo assim uma interessante conexão entre a álgebra abstrata e a matemática discreta. Fazemos também uma abordagem de caráter lúdico, traduzindo o passatempo chamado Sudoku em um problema de 9-coloração e utilizando a teoria apresentada para resolvê-lo através das bases de Gröbner<br>Abstract: In the present work, we study the Gröbner basis theory and its application on the graph k-coloring problem, establishing an interesting relation between abstract algebra and discrete mathematics. We make a ludic approach, translating the puzzle called Sudoku to a 9-coloring problem and using the given theory to solve it by the Gröbner basis<br>Mestrado<br>Algebra<br>Mestre em Matemática
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Mbirika, Abukuse III. "Analysis of symmetric function ideals: towards a combinatorial description of the cohomology ring of Hessenberg varieties." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/708.
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Symmetric functions arise in many areas of mathematics including combinatorics, topology and algebraic geometry. Using ideals of symmetric functions, we tie these three branches together. This thesis generalizes work of Garsia and Procesi in 1992 that gave a quotient ring presentation for the cohomology ring of Springer varieties.
Let R be the polynomial ring Ζ[x1,…,xn]. We present two different ideals in R. Both are parametrized by a Hessenberg function h, namely a nondecreasing function that satisfies h(i) ≥ i for all i. The first ideal, which we call Ih, is generated by modified elementary symmetric functions. The ideal I_h generalizes the work of Tanisaki who gave a combinatorial description of the ideal used in Garsia and Procesi's quotient ring. Like the Tanisaki ideal, the generating set for Ih is redundant. We give a minimal generating set for this ideal. The second ideal, which we call Jh, is generated by modified complete symmetric functions. The generators of this ideal form a Gröbner basis, which is a useful property. Using the Gröbner basis for Jh, we identify a basis for the quotient R/Jh.
We introduce a partial ordering on the Hessenberg functions, and in turn we discover nice nesting properties in both families of ideals. When h>h', we have Ih ⊂ Ih' and Jh ⊂ Jh'. We prove that Ih equals Jh when h is maximal. Since Ih is the ideal generated by the elementary symmetric functions when h is maximal, the generating set for Jh forms a Gröbner basis for the elementary symmetric functions. Moreover, the quotient R/Jh gives another description of the cohomology ring of the full flag variety.
The generators of the ring R/Jh are in bijective correspondence with the Betti numbers of certain Hessenberg varieties. These varieties are a two-parameter generalization of Springer varieties, parametrized by a nilpotent operator X and a Hessenberg function h. These varieties were introduced in 1992 by De Mari, Procesi and Shayman. We provide evidence that as h varies, the quotient R/Jh may be a presentation for the cohomology ring of a subclass of Hessenberg varieties called regular nilpotent varieties.
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Shokrieh, Farbod. "Divisors on graphs, binomial and monomial ideals, and cellular resolutions." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52176.
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We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs.
We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their Z-graded Betti tables coincide.
As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results related to the theory of chip-firing games on graphs also follow from our general techniques and results.
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Johnston, Ann. "Markov Bases for Noncommutative Harmonic Analysis of Partially Ranked Data." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/4.
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Given the result $v_0$ of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe $v_0$. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic. Their approach involves the computation of a Markov basis, followed by the use of a Markov process with stationary hypergeometric distribution to generate a sample.This technique for data analysis has become an accepted tool of algebraic statistics, particularly for the study of fully ranked data. In this thesis, we explore the extension of this technique for data analysis to the study of partially ranked data, focusing on data from surveys in which participants are asked to identify their top $k$ choices of $n$ items. Before we move on to our own data analysis, though, we present a thorough discussion of the Diaconis–Sturmfels algorithm and its use in data analysis. In this discussion, we attempt to collect together all of the background on Markov bases, Markov proceses, Gröbner bases, implicitization theory, and elimination theory, that is necessary for a full understanding of this approach to data analysis.
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Grobler, Magdalena Johanna. "Using topological information in opportunistic network coding / by Magdalena Johanna (Leenta) Grobler." Thesis, North-West University, 2008. http://hdl.handle.net/10394/2639.
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Chou, Chun-yu, and 周純玉. "Grobner Bases and Invariant Theory." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/35955911799684289985.
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碩士<br>淡江大學<br>數學學系<br>90<br>We want to know that both the division algorithm and the Euclidean algorithm can be extended to polynomials in several variables. Even though these results are elementary, they were discovered only recently, in 1965,by B.Buchberger. Buchberger's main contribution is a finite algorithm for transforming an arbitrary generating set of an ideal into a Groebner basis for that ideal,the basic algorithms are implemented in many computer algebra systems, e.g.,MAPLE, MATHEMATICA, COCOA.Classical invariant theory was a hot topic in the 19th centry and in the beginining of the 20th century. We study polynomials which remain invariant under the action of finite matrix group GÎGL(n,k). The result is a collection ofalgorithms for finding a finite set {I1,I2,×××,Im} of fundamental invariants which generate the invariant subring k[x1,×××,xn] G. These algorithms make use of the Molienseries for the ring of invariant and its Cohen-Macaulay property. Since the algebra of invariants is Cohen-Macaulay, which implies that they admit a very nice decomposition. In other words, it can be presented by a set of primary invariants p1,×××,pn (which are algebraically independent) and a set of secondary invariants which form a basis of the algebra as a free k[p1,×××,pn]-module. The Molien formula for the Hilbert series of the algebra of invariants and analgorithm for computing the primary and secondary invariants are given in this case. We give some examples and discuss the invariant subring in this paper.
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Sen, Aritra. "Module Grobner Bases Over Fields With Valuation." Thesis, 2015. http://etd.iisc.ernet.in/handle/2005/2644.
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Tropical geometry is an area of mathematics that interfaces algebraic geometry and combinatorics. The main object of study in tropical geometry is the tropical variety, which is the combinatorial counterpart of a classical variety. A classical variety is converted into a tropical variety by a process called tropicalization, thus reducing the problems of algebraic geometry to problems of combinatorics. This new tropical variety encodes several useful information about the original variety, for example an algebraic variety and its tropical counterpart have the same dimension.
In this thesis, we look at the some of the computational aspects of tropical algebraic geometry. We study a generalization of Grobner basis theory of modules which unlike the standard Grobner basis also takes the valuation of coefficients into account. This was rst introduced in (Maclagan & Sturmfels, 2009) in the settings of polynomial rings and its computational aspects were first studied in (Chan & Maclagan, 2013) for the polynomial ring case. The motivation for this comes from tropical geometry as it can be used to compute tropicalization of varieties. We further generalize this to the case of modules. But apart from that it has many other computational advantages. For example, in the standard case the size of the initial submodule generally grows with the increase in degree of the generators. But in this case, we give an example of a family of submodules where the size of the initial submodule remains constant. We also develop an algorithm for computation of Grobner basis of submodules of modules over Z=p`Z[x1; : : : ; xn] that works for any weight vector.
We also look at some of the important applications of this new theory. We show how this can be useful in efficiently solving the submodule membership problem. We also study the computation of Hilbert polynomials, syzygies and free resolutions.
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Francis, Maria. "Grobuer Basis Algorithms for Polynomial Ideal Theory over Noetherian Commutative Rings." Thesis, 2017. http://etd.iisc.ernet.in/2005/3543.
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One of the fundamental problems in commutative algebra and algebraic geometry is to understand the nature of the solution space of a system of multivariate polynomial equations over a field k, such as real or complex numbers. An important algorithmic tool in this study is the notion of Groebner bases (Buchberger (1965)). Given a system of polynomial equations, f1= 0,..., fm = 0, Groebner basis is a “canonical" generating set of the ideal generated by f1,...., fm, that can answer, constructively, many questions in computational ideal theory. It generalizes several concepts of univariate polynomials like resultants to the multivariate case, and answers decisively the ideal membership problem. The dimension of the solution set of an ideal I called the affine variety, an important concept in algebraic geometry, is equal to the Krull dimension of the corresponding coordinate ring, k[x1,...,xn]/I. Groebner bases were first introduced to compute k-vector space bases of k[x1,....,xn]/I and use that to characterize zero-dimensional solution sets. Since then, Groebner basis techniques have provided a generic algorithmic framework for computations in control theory, cryptography,
formal verification, robotics, etc, that involve multivariate polynomials over fields.
The main aim of this thesis is to study problems related to computational ideal theory over Noetherian commutative rings (e.g: the ring of integers, Z, the polynomial ring over a field, k[y1,…., ym], etc) using the theory of Groebner bases. These problems surface in many domains including lattice based cryptography, control systems, system-on-chip design, etc.
Although, formal and standard techniques are available for polynomial rings over fields, the presence of zero divisors and non units make developing similar techniques for polynomial rings over rings challenging.
Given a polynomial ring over a Noetherian commutative ring, A and an ideal I in A[x1,..., xn], the first fundamental problem that we study is whether the residue class polynomial ring, A[x1,..., xn]/I is a free A-module or not. Note that when A=k, the answer is always ‘yes’ and the k-vector space basis of k[x1,..., xn]/I plays an important role in computational ideal theory over fields. In our work, we give a Groebner basis characterization for A[x1,...,xn]/I to have a free A-module representation w.r.t. a monomial ordering. For such A-algebras, we give an algorithm to compute its A-module basis. This extends the Macaulay-Buchberger basis theorem to polynomial rings over Noetherian commutative rings. These results help us develop a theory of border bases in A[x1,...,xn] when the residue class polynomial ring is
finitely generated. The theory of border bases is handled as two separate cases: (i) A[x1,...,xn]/I is free and (ii) A[x1,...,xn]/I has torsion submodules.
For the special case of A = Z, we show how short reduced Groebner bases and the characterization for a free A-module representation help identify the cases
when Z[x1,...,xn]/I is isomorphic to ZN for some positive integer N. Ideals in such Z-algebras are called ideal lattices. These structures are interesting since this means we can use the algebraic structure, Z[x1,...,xn]/I as a representation for point lattices and extend all the computationally hard problems in point lattice theory to Z[x1,...,xn]/I . Univariate ideal lattices are widely used in lattice based cryptography for they are a more compact representation for lattices than matrices. In this thesis, we give a characterization for multivariate ideal lattices and construct collision resistant hash functions based on them using Groebner basis techniques. For the construction of hash functions, we define a worst case problem,
shortest substitution problem w.r.t. an ideal in Z[x1,...,xn], and establish hardness results for this problem.
Finally, we develop an approach to compute the Krull dimension of A[x1,...,xn]/I using Groebner bases, when A is a Noetherian integral domain. When A is a field, the Krull dimension of A[x1,...,xn]/I has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetherian rings. We introduce the notion of combinatorial dimension of A[x1,...,xn]/I and give a Groebner basis method to compute it for residue class polynomial rings that have a free A-module representation w.r.t. a lexicographic ordering. For such A-algebras, we derive a relation between Krull dimension and combinatorial dimension of A[x1,...,xn]/I. For A-algebras that have a free A-module representation w.r.t. degree compatible monomial orderings, we introduce the concepts of Hilbert function, Hilbert series and Hilbert polynomials and show that Groebner basis methods can be used to compute these quantities. We then proceed to show that the combinatorial dimension of such A-algebras is equal to the degree of the Hilbert polynomial. This enables us to extend the relation between Krull dimension and combinatorial dimension to A-algebras with a free A-module representation w.r.t. a degree compatible ordering as well.
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Norouzizadeh, Behnam. "Some Aspects on Coarse Homotopy Theory." Doctoral thesis, 2009. http://hdl.handle.net/11858/00-1735-0000-000D-F174-0.
Full textBooks on the topic "Grobner theory"
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Saito, Mutsumi. Gröbner deformations of hypergeometric differential equations. Springer, 2000.
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Hibi, Takayuki. Harmony of Grobner Bases and the Modern Industrial Society - the Second Crest-Sbm International Conference. World Scientific Publishing Co Pte Ltd, 2012.
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Saito, Mutsumi, Nobuki Takayama, and Bernd Sturmfels. Groebner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6. Springer, 2000.
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Böschen, Stefan, Armin Grunwald, Bettina-Johanna Krings, and Christine Rösch, eds. Technikfolgenabschätzung. Nomos Verlagsgesellschaft mbH & Co. KG, 2021. http://dx.doi.org/10.5771/9783748901990.
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The complexity of socio-technological challenges and the uncertainty of decisions are both increasing. Therefore, there is a need for knowledge-based and option-oriented assessment and advice. Technology assessment (TA) can offer alternative approaches to and perspectives on current decision-making processes. This handbook provides guidance in developing new answers to the problems under investigation. It pursues three objectives. Firstly, it reflects on TA by looking at developments in TA. Secondly, it serves as a compass for orientation by providing heuristics for the systematic contextualisation of TA knowledge. Thirdly and finally, it reveals the prospects for the future development of TA. With contributions by Suzana Alpsancar, Manuel Baumann, Richard Beecroft, Alexander Bogner, Stefan Böschen, Helmut Breitmeier, Andrés Checa, Kerstin Cuhls, Bert Droste-Franke, Elisabeth Ehrensperger, Torsten Fleischer, Antje Grobe, Armin Grunwald, Reinhard Grünwald, Martina Haase, Julia Hahn, Christiane Hauser, Roger Häußling, Leonhard Hennen, Nils Heyen, Regine Kollek, Kornelia Konrad, Jürgen Kopfmüller, Bettina-Johanna Krings, Miltos Ladikas, Roh Pin Lee, Annette Leßmöllmann, Peter Letmathe, Ralf Lindner, Andreas Lösch, Jacob Manderbach, Martin Meister, Linda Nierling, Maren Paegert, Oliver Parodi, Walter Peissl, Witold-Roger Poganietz, Christine Rösch, Maximilian Roßmann, Martin Sand, Jens Schippl, Jan C. Schmidt, Christoph Schneider, Jan-Felix Schrape, Ingo Schulz-Schaeffer, Sandra Schwindenhammer, Hans-Jörg Sigwart, Mahshid Sotoudeh, Magdalena Tanzer, Helge Torgesen, Peter Wehling, Christina Wulf, Petra Zapp and Silke Zimmer-Merkle.
Book chapters on the topic "Grobner theory"
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"A Missionary for History: Essays in Honor of Simon Dubnow." In Polin: Studies in Polish Jewry Volume 16, edited by Kristi Groberg and Avraham Greenbaum. Liverpool University Press, 2003. http://dx.doi.org/10.3828/liverpool/9781874774730.003.0032.
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This chapter reviews A Missionary for History: Essays in Honor of Simon Dubnow, which was edited by Kristi Groberg and Avraham Greenbaum. The most useful cluster of essays in this volume is the trio on Dubnow and the pogroms. Michael Hamm, Shlomo Lambroza, and John Klier show that there is little evidence to support Dubnow's view that the pogroms of the late imperial period were carefully prepared and centrally directed, in part to discredit and intimidate liberals and revolutionaries, and in part to divert peasant discontent. Most importantly, they explain how Dubnow's understanding of the pogroms, which still enjoys enormous influence and informs many synthetic accounts of modern Jewish history, derived from his lack of access to important sources as well as to his lack of distance from the events and his own involvement in Russian Jewry's political struggles. Stimulating as well is Israel Bartal's essay on how Dubnow's diaspora nationalism influenced his view of medieval Jewish autonomy, leading him to reverse the Haskalah's negative attitude towards communal autonomy and, at the same time, to describe this autonomy in thoroughly anachronistic terms.
Conference papers on the topic "Grobner theory"
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Jia-Ping Chen and Chung-Chin Lu. "A serial-in-serial-out hardware architecture for systematic encoding of hermitian codes via grobner bases." In IEEE International Symposium on Information Theory, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isit.2003.1228345.
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Augot, D., M. Bardet, and J. C. Faugere. "Efficient decoding of (binary) cyclic codes above the correction capacity of the code using grobner bases." In IEEE International Symposium on Information Theory, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isit.2003.1228378.
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Ruiz, O. E., and P. M. Ferreira. "Geometric Reasoning in the Analysis of Assemblies and Mechanisms." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0233.
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Abstract Geometric Reasoning ability is central to many applications in CAD / CAM / CAPP environments. An increasing demand exists for Geometric Reasoning systems which evaluate the feasibility of virtual scenes specified by geometric relations. Thus, the Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) problem consists of a basic scenario containing geometric entities, whose context is used to propose constraining relations among still undefined entities. If the constraint specification is consistent, the answer of the problem is one of finitely or infinitely many solution scenarios satisfying the prescribed constraints. Otherwise, a diagnostic of inconsistency is expected. The three main approaches used for this problem are numerical, procedural or operational and mathematical. Numerical and procedural approaches answer only part of the problem, and are not complete in the sense that a failure to provide an answer does not preclude the existence of one. The mathematical approach previously presented by the authors describes the problem using a set of polynomial equations. The common roots to this set of polynomials characterizes the solution space for such a problem. That work presents the use of Grobner basis techniques for verifying the consistency of the constraints. It also integrates subgroups of the Special Euclidean Group of Displacements SE(3) in the problem formulation to exploit the structure implied by geometric relations. Although theoretically sound, these techniques require large amounts of computing resources. This work proposes Divide-and-Conquer techniques applied to local GCS/SF subproblems to identify strongly constrained clusters of geometric entities. The identification and preprocessing of these clusters generally reduces the effort required in solving the overall problem. Cluster identification can be related to identifying short cycles in the Spatial Constraint graph for the GCS/SF problem. Their preprocessing uses the aforementioned Algebraic Geometry and Group theoretical techniques on the local GCS/SF problems that correspond to these cycles. Besides improving the efficiency of the solution approach, the Divide-and-Conquer techniques capture the physical essence of the problem. This is illustrated by applying the discussed techniques to the analysis of the degrees of freedom of mechanisms.