Quickly Computing Isotopy Type for Exponential Sums over Circuits (Extended Abstract)

Author:

Bihan Frédéric1,Croy Erika2,Deng Weixun3,Phillipson Kaitlyn4,Rennie Robert J.5,Rojas J. Maurice3

Affiliation:

1. Université Savoie Mont Blanc

2. First Interstate Bank

3. Texas A&M University

4. University of Wisconsin, Madison

5. Colorado College

Abstract

Fewnomial Theory [Kho91] has established bounds on the number of connected components (a.k.a. pieces ) of a broad class of real analytic sets as a function of a particular kind of input complexity, e.g., the number of distinct exponent vectors among a generating set for the underlying ideal. Here, we pursue the algorithmic side: We show how to efficiently compute the exact isotopy type of certain (possibly singular) real zero sets, instead of just estimating their number of pieces. While we focus on the circuit case, our results form the foundation for an approach to the general case that we will pursue later.

Publisher

Association for Computing Machinery (ACM)

Subject

Microbiology (medical),Immunology,Immunology and Allergy

Reference11 articles.

1. [Bak77] Alan Baker , " The Theory of Linear Forms in Logarithms ," in Transcendence Theory : Advances and Applications: proceedings of a conference held at the University of Cambridge , Cambridge, Jan .- Feb. , 1976 , Academic Press , London, 1977. [Bak77] Alan Baker, "The Theory of Linear Forms in Logarithms," in Transcendence Theory: Advances and Applications: proceedings of a conference held at the University of Cambridge, Cambridge, Jan.-Feb., 1976, Academic Press, London, 1977.

2. Divide and Conquer Roadmap for Algebraic Sets

3. On the number of homotopy types of fibres of a definable map

4. [Bih11] Frederic Bihan , "Topologie des variétés creuses," Habilitation à Diriger des Recherches , Universitde Savoie , France , 2011 . Downloadable from http://www.lama.univ-savoie.fr/bihan/MyPapers/HDRfinal.pdf [Bih11] Frederic Bihan, "Topologie des variétés creuses," Habilitation à Diriger des Recherches, Universitde Savoie, France, 2011. Downloadable from http://www.lama.univ-savoie.fr/bihan/MyPapers/HDRfinal.pdf

5. [BRS09] Frederic Bihan , J. Maurice Rojas , and Casey E . Stella, "Faster real feasibility via circuit discriminants," proceedings of ISSAC 2009 (July 28--31 , Seoul, Korea ), pp. 39 -- 46 , ACM Press , 2009 . [BRS09] Frederic Bihan, J. Maurice Rojas, and Casey E. Stella, "Faster real feasibility via circuit discriminants," proceedings of ISSAC 2009 (July 28--31, Seoul, Korea), pp. 39--46, ACM Press, 2009.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3