Quickly Computing Isotopy Type for Exponential Sums over Circuits (Extended Abstract)-Reference-Cited by-同舟云学术

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

Published:2023-09 Issue:3 Volume:57 Page:152-155
ISSN:1932-2240
Container-title:ACM Communications in Computer Algebra
language:en
Short-container-title:ACM Commun. Comput. Algebra

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

Link

https://dl.acm.org/doi/pdf/10.1145/3637529.3637538

Reference11 articles.

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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.