Computing constraint sets for differential fields

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• 作者：Russell Miller^a ; ^b ; ¹ ; ^{Russell.Miller@qc.cuny.edu" class="auth_mail} ; Alexey Ovchinnikov^a ; ^c ; ² ; ^{aovchinnikov@qc.cuny.edu" class="auth_mail} ; Dmitry Trushin^d ; ^{trushindima@yandex.ru" class="auth_mail}
• 关键词：primary ; 12H05 ; secondary ; 03D25 ; 13N10 ; 34M15
• 刊名：Journal of Algebra
• 出版年：1 June 2014
• 年：2014
• 卷：407
• 期：Complete
• 页码：316-357
• 全文大小：476 K

文摘

Kronecker's Theorem and Rabin's Theorem are fundamental results about computable fields F and the decidability of the set of irreducible polynomials over F. We adapt these theorems to the setting of differential fields K, with constrained pairs of differential polynomials over K assuming the role of the irreducible polynomials. We prove that two of the three basic aspects of Kronecker's Theorem remain true here, and that the reducibility in one direction (but not the other) from Rabin's Theorem also continues to hold.