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Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science最新文献

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Enumerative Real Algebraic Geometry 枚举实代数几何
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 2001-07-24 DOI: 10.1090/dimacs/060/11
F. Sottile
{"title":"Enumerative Real Algebraic Geometry","authors":"F. Sottile","doi":"10.1090/dimacs/060/11","DOIUrl":"https://doi.org/10.1090/dimacs/060/11","url":null,"abstract":"Two well-defined classes of structured polynomial systems have been studied from this point of view—sparse systems, where the structure is encoded by the monomials in the polynomials fi—and geometric systems, where the structure comes from geometry. This second class consists of polynomial formulations of enumerative geometric problems, and in this case Question 1.1 is the motivating question of enumerative real algebraic geometry, the subject of this survey. Treating both sparse polynomial systems and enumerative geometry together in the context of Question 1.1 gives useful insight.","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"189 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116343981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 39
How to Show a Set is not Algebraic 如何证明一个集合不是代数的
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 2001-06-11 DOI: 10.1090/dimacs/060/07
C. McCrory
{"title":"How to Show a Set is not Algebraic","authors":"C. McCrory","doi":"10.1090/dimacs/060/07","DOIUrl":"https://doi.org/10.1090/dimacs/060/07","url":null,"abstract":"We revisit Akbulut and King's first example of a compact semialgebraic set which satisfies Sullivan's local Euler characteristic condition, but which is not homeomorphic to an algebraic set. A nontrivial obstruction is computed using the link operator on the ring of constructible functions.","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123694371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Patterns of Dependence Among Powers of Polynomials 多项式幂之间的依赖模式
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 2001-06-01 DOI: 10.1090/dimacs/060/09
B. Reznick
{"title":"Patterns of Dependence Among Powers of Polynomials","authors":"B. Reznick","doi":"10.1090/dimacs/060/09","DOIUrl":"https://doi.org/10.1090/dimacs/060/09","url":null,"abstract":"Let F = {f_1,...,f_r} be a family of polynomials and let the ticket of F, T(F), denote the set of integers m so that ${f_j^m}$ is linearly dependent. We show that |T(F)| le (r-1)(r-2)/2 and present many concrete examples, including one with r=6 and T(F) = {1,2,3,4,8,14}.","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"455 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123030863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Minimizing Polynomial Functions 最小化多项式函数
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 2001-03-26 DOI: 10.1090/dimacs/060/08
P. Parrilo, B. Sturmfels
{"title":"Minimizing Polynomial Functions","authors":"P. Parrilo, B. Sturmfels","doi":"10.1090/dimacs/060/08","DOIUrl":"https://doi.org/10.1090/dimacs/060/08","url":null,"abstract":"We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gr\"obner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation technique, due to N.Z. Shor and the first author, which involves sums of squares and semidefinite programming. This opens up the possibility of using semidefinite programming relaxations arising from the Positivstellensatz for a wide range of computational problems in real algebraic geometry. \u0000This paper was presented at the Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, held at DIMACS, Rutgers University, March 12-16, 2001.","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116603062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 366
Combinatorial Characterizations of Algebraic Sets 代数集的组合刻画
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 1900-01-01 DOI: 10.1090/dimacs/060/03
Isabelle Bonnard
{"title":"Combinatorial Characterizations of Algebraic Sets","authors":"Isabelle Bonnard","doi":"10.1090/dimacs/060/03","DOIUrl":"https://doi.org/10.1090/dimacs/060/03","url":null,"abstract":"","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124435033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Constructive Approaches to Representation Theorems in Finitely Generated Real Algebras 有限生成实代数中表示定理的构造方法
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 1900-01-01 DOI: 10.1090/dimacs/060/02
D. Bailey, V. Powers
{"title":"Constructive Approaches to Representation Theorems in Finitely Generated Real Algebras","authors":"D. Bailey, V. Powers","doi":"10.1090/dimacs/060/02","DOIUrl":"https://doi.org/10.1090/dimacs/060/02","url":null,"abstract":"","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129456038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient Algorithms Based on Critical Points Method 基于临界点法的高效算法
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 1900-01-01 DOI: 10.1090/dimacs/060/10
F. Rouillier
{"title":"Efficient Algorithms Based on Critical Points Method","authors":"F. Rouillier","doi":"10.1090/dimacs/060/10","DOIUrl":"https://doi.org/10.1090/dimacs/060/10","url":null,"abstract":"","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129536890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Combinatorial Roadmaps in Configuration Spaces of Simple Planar Polygons 平面简单多边形位形空间中的组合路线图
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 1900-01-01 DOI: 10.1090/dimacs/060/12
I. Streinu
{"title":"Combinatorial Roadmaps in Configuration Spaces of Simple Planar Polygons","authors":"I. Streinu","doi":"10.1090/dimacs/060/12","DOIUrl":"https://doi.org/10.1090/dimacs/060/12","url":null,"abstract":"One-degree-of-freedom mechanisms induced by minimum pseudotriangulations with one convex hull edge removed have been recently introduced by the author to solve a family of non-colliding motion planning problems for planar robot arms (open or closed polygonal chains). They induce canonical roadmaps in configuration spaces of simple planar polygons with","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133297948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Lower Bounds and Real Algebraic Geometry 下界与实代数几何
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 1900-01-01 DOI: 10.1090/dimacs/060/04
Peter Bürgisser
{"title":"Lower Bounds and Real Algebraic Geometry","authors":"Peter Bürgisser","doi":"10.1090/dimacs/060/04","DOIUrl":"https://doi.org/10.1090/dimacs/060/04","url":null,"abstract":"","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128579404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
The Viro Method Applied with Quadratic Transforms 二次变换的Viro方法
Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science Pub Date : 1900-01-01 DOI: 10.1090/dimacs/060/05
B. Chevallier
{"title":"The Viro Method Applied with Quadratic Transforms","authors":"B. Chevallier","doi":"10.1090/dimacs/060/05","DOIUrl":"https://doi.org/10.1090/dimacs/060/05","url":null,"abstract":"","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117001242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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