Algorithms yield upper bounds in differential algebra

doi:10.4153/S0008414X21000560

	Algorithms yield upper bounds in differential algebra
	Li, Wei 1; Ovchinnikov, Alexey 5,6; Pogudin, Gleb 3,4; Scanlon, Thomas 2
刊名	CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
	2021-09-29
页码	23
关键词	delay PDEs elimination of unknowns uniform bounds oracle machine
ISSN号	0008-414X
DOI	10.4153/S0008414X21000560
英文摘要	Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that, if the algorithm is guaranteed to terminate on every input, then there is a computable upper bound for the size of the output of the algorithm in terms of the size of the input. We also generalize this to algorithms working with models of good enough theories (including, for example, difference fields). We then apply this to differential algebraic geometry to show that there exists a computable uniform upper bound for the number of components of any variety defined by a system of polynomial PDEs. We then use this bound to show the existence of a computable uniform upper bound for the elimination problem in systems of polynomial PDEs with delays.
资助项目	NSF[CCF-1564132] ; NSF[CCF-1563942] ; NSF[DMS-1760448] ; NSF[DMS-1760413] ; NSF[DMS-1853650] ; NSF[DMS-1853482] ; NSF[DMS-1800492] ; NSFC[11971029] ; NSFC[12122118] ; NSFC[11688101] ; Youth Innovation Promotion Association of CAS
WOS研究方向	Mathematics
语种	英语
出版者	CAMBRIDGE UNIV PRESS
WOS记录号	WOS:000747373800001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59932]
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Wei
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China 2.Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA 3.Natl Res Univ Higher Sch Econ, Fac Comp Sci, Moscow, Russia 4.Ecole Polytech, LIX, CNRS, Inst Polytech Paris, 1 Rue Honore dEstienne dOrves, F-91120 Palaiseau, France 5.CUNY, Grad Ctr, PhD Programs Math & Comp Sci, 365 Fifth Ave, New York, NY 10016 USA 6.CUNY Queens Coll, Dept Math, 65-30 Kissena Blvd, Queens, NY 11367 USA
推荐引用方式 GB/T 7714	Li, Wei,Ovchinnikov, Alexey,Pogudin, Gleb,et al. Algorithms yield upper bounds in differential algebra[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,2021:23.
APA	Li, Wei,Ovchinnikov, Alexey,Pogudin, Gleb,&Scanlon, Thomas.(2021).Algorithms yield upper bounds in differential algebra.CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,23.
MLA	Li, Wei,et al."Algorithms yield upper bounds in differential algebra".CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES (2021):23.