Sturmfels, Bernd 1962Overview
Publication Timeline
Most widely held works by
Bernd Sturmfels
Algorithms in invariant theory
by Bernd Sturmfels
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26 editions published between 1993 and 2008 in 3 languages and held by 831 WorldCat member libraries worldwide Serves as a textbook for invariant theory and a research monograph that introduces a different approach to the algorithmic side of invariant theory. This title includes several research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems
Combinatorial commutative algebra
by Ezra Miller
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25 editions published between 2004 and 2007 in English and held by 786 WorldCat member libraries worldwide "Recent developments are covered; Contains over 100 figures and 250 exercises; Includes complete proofs."Publisher's website
Lectures on algebraic statistics
by Mathias Drton
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17 editions published in 2009 in English and held by 514 WorldCat member libraries worldwide
Computational synthetic geometry
by Jürgen Bokowski
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17 editions published between 1988 and 1989 in English and held by 463 WorldCat member libraries worldwide Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research
Theory of algebraic invariants
by David Hilbert
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6 editions published between 1993 and 2006 in English and held by 430 WorldCat member libraries worldwide
Gröbner bases and convex polytopes
by Bernd Sturmfels
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8 editions published between 1996 and 1997 in English and held by 340 WorldCat member libraries worldwide
Solving systems of polynomial equations
by Bernd Sturmfels
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10 editions published in 2002 in English and held by 300 WorldCat member libraries worldwide
Applications of computational algebraic geometry : American Mathematical Society short course, January 67, 1997, San Diego, California
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6 editions published in 1998 in English and held by 297 WorldCat member libraries worldwide
Algebraic statistics for computational biology
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11 editions published in 2005 in English and held by 284 WorldCat member libraries worldwide "The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms can be applied to biological problems such as aligning genomes, finding genes, and constructing phylogenies."BOOK JACKET
Gröbner deformations of hypergeometric differential equations
by Mutsumi Saito
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11 editions published between 1999 and 2011 in English and held by 265 WorldCat member libraries worldwide In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gröbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gröbner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric partial differentiel equations introduced by Gel'fand, Kapranov and Zelevinsky. The Gröbner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and thus leads to an unexpected interplay between analysis and combinatorics. This book contains a number of original research results on holonomic systems and hypergeometric functions, and it raises many open problems for future research in this rapidly growing area of computational mathematics '
Geometric combinatorics
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8 editions published between 2007 and 2008 in English and held by 192 WorldCat member libraries worldwide Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry
Applied geometry and discrete mathematics : the Victor Klee festschrift
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7 editions published in 1991 in English and held by 155 WorldCat member libraries worldwide
Solving polynomial equations foundations, algorithms, and applications
by Manuel Bronstein
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4 editions published in 2005 in English and held by 28 WorldCat member libraries worldwide "This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the stateoftheart in several symbolic, numeric, and symbolicnumeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision." "Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications."Jacket
Oriented Matroids and combinatorial convex geometry
by Bernd Sturmfels
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5 editions published in 1987 in English and held by 22 WorldCat member libraries worldwide
Minkowski addition of polytopes : computational complexity and applications to Gröbner bases
by Peter Gritzmann
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6 editions published between 1990 and 1992 in English and German and held by 20 WorldCat member libraries worldwide Using the Minkowski addition of Newton polytopes, we show that the following problem can be solved in polynomial time for any finite set of polynomials [formula], where d is fixed: Does there exist a term order [tau] such that [Tau] is a Gröbner basis for its ideal with respect to [tau]? If not, find an optimal term order for [Tau] with respect to a natural Hilbert function criterion."
Solving systems of polynomial equations : [... ten lectures given by the author at the CBMS Conference at Texas A & M University, College Station, during the week of May 2024, 2002]
by Bernd Sturmfels
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2 editions published in 2002 in English and held by 17 WorldCat member libraries worldwide
Structural Gröbner basis detection
by Bernd Sturmfels
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3 editions published in 1996 in English and held by 16 WorldCat member libraries worldwide
Oriented matroids
by Anders Björner
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4 editions published between 1993 and 1999 in English and held by 13 WorldCat member libraries worldwide First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
Computability of Julia sets
by Mark Braverman
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1 edition published in 2009 in English and held by 13 WorldCat member libraries worldwide Among all computergenerated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. This book summarizes the knowledge about the computational properties of Julia sets in a selfcontained way. It is suitable for experts and students with interest in theoretical computer science or dynamical systems
Applications of computational algebraic geometry : American Mathematical Society short course, January 67, 1997
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Book
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2 editions published between 1997 and 1998 in English and held by 13 WorldCat member libraries worldwide more
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Associated Subjects
Algebra AlgebraData processing Algorithms Artificial intelligence Biometry Combinatorial analysis Combinatorial geometry Commutative algebra Computational complexity Computer science Computer software Convex polytopes Differential equationsAsymptotic theory Distribution (Probability theory) EquationsNumerical solutions Geometry Geometry, Algebraic Geometry, AlgebraicData processing Geometry, Projective GeometryData processing Global analysis (Mathematics) Gröbner bases Hypergeometric functions Information theory Invariants Klee, Victor Linear programming Logic, Symbolic and mathematical Mathematical statistics Mathematics Matroids Oriented matroids Polynomials Statistics Vector spaces

Alternative Names
Sturmfels, B. (Bernd), 1962
Sturmfels, Bernd
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