Algorithms yield upper bounds in differential algebra
文献类型：期刊论文
| 作者 | Li, Wei1; Ovchinnikov, Alexey2,3; Pogudin, Gleb4,5; Scanlon, Thomas6 |
| 刊名 | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000747373800001 |
| 出版者 | CAMBRIDGE UNIV PRESS |
| 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.CUNY Queens Coll, Dept Math, 65-30 Kissena Blvd, Queens, NY 11367 USA 3.CUNY, Grad Ctr, PhD Programs Math & Comp Sci, 365 Fifth Ave, New York, NY 10016 USA 4.Ecole Polytech, LIX, CNRS, Inst Polytech Paris, 1 Rue Honore dEstienne dOrves, F-91120 Palaiseau, France 5.Natl Res Univ Higher Sch Econ, Fac Comp Sci, Moscow, Russia 6.Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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