{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:20:57Z","timestamp":1777994457840,"version":"3.51.4"},"reference-count":31,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[1991,11,1]],"date-time":"1991-11-01T00:00:00Z","timestamp":688953600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":7929,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Applied Mathematics"],"published-print":{"date-parts":[[1991,11]]},"DOI":"10.1016\/0166-218x(91)90109-a","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T23:43:01Z","timestamp":1027640581000},"page":"73-94","source":"Crossref","is-referenced-by-count":57,"title":["The membership problem for unmixed polynomial ideals is solvable in single exponential time"],"prefix":"10.1016","volume":"33","author":[{"given":"Alicia","family":"Dickenstein","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noa\u00ef","family":"Fitchas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc","family":"Giusti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carmen","family":"Sessa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/0166-218X(91)90109-A_bib1","series-title":"Introduction to Commutative Algebra","author":"Atiyah","year":"1969"},{"key":"10.1016\/0166-218X(91)90109-A_bib2","series-title":"Bounds for the degrees in the division problem","author":"Berenstein","year":"1988"},{"key":"10.1016\/0166-218X(91)90109-A_bib3","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0020-0190(84)90018-8","article-title":"On computing the determinant in small parallel time using a small number of processors","volume":"18","author":"Berkowitz","year":"1984","journal-title":"Inform. Process. Lett."},{"issue":"2","key":"10.1016\/0166-218X(91)90109-A_bib4","doi-asserted-by":"crossref","first-page":"577","DOI":"10.2307\/1971361","article-title":"Bounds for the degree in the Nullstellensatz","volume":"126","author":"Brownawell","year":"1987","journal-title":"Ann. of math."},{"key":"10.1016\/0166-218X(91)90109-A_bib5","series-title":"Ph.D. Thesis","article-title":"An algorithm for finding a basis for the residue class ring of a zero dimensional polynomial ideal","author":"Buchberger","year":"1965"},{"key":"10.1016\/0166-218X(91)90109-A_bib6","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/BF01844169","article-title":"Ein algorithmisches Kriterium f\u00fcr die L\u00f6sbarkeit eines algebraischen Gleichungssystems","volume":"4","author":"Buchberger","year":"1970","journal-title":"Aequationes math."},{"key":"10.1016\/0166-218X(91)90109-A_bib7","series-title":"Multidimensional System Theory","first-page":"184","article-title":"Gr\u00f6bner-Bases: An algorithmic method in polynomial ideal theory","author":"Buchberger","year":"1985"},{"key":"10.1016\/0166-218X(91)90109-A_bib8","series-title":"Ph.D. Thesis","article-title":"Complejidad de algoritmos en Geometr\u00eda Computacional","author":"Caniglia","year":"1989"},{"key":"10.1016\/0166-218X(91)90109-A_bib9","series-title":"Proceedings 6th International Conference","first-page":"131","article-title":"Some new effectivity bounds in computational geometry","volume":"357","author":"Caniglia","year":"1989"},{"key":"10.1016\/0166-218X(91)90109-A_bib10","first-page":"255","article-title":"Borne simple exponentielle pour les degr\u00e9s dans le th\u00e9or\u00e8mes des z\u00e9ros sur un corps de caract\u00e9ristique quelconque","volume":"307","author":"Caniglia","year":"1988","journal-title":"C.R. Acad. Sci. Paris S\u00e9r. 1"},{"key":"10.1016\/0166-218X(91)90109-A_bib11","article-title":"Subexponential time solving systems of algebraic equations","author":"Chistov","year":"1983","journal-title":"LOMI Preprints E-9-83, E-10-83"},{"key":"10.1016\/0166-218X(91)90109-A_bib12","author":"Dickenstein","year":"1988","journal-title":"An effective residual criterion for the membership problem in C[z1,...,zn]"},{"key":"10.1016\/0166-218X(91)90109-A_bib13","unstructured":"J.C. Frang\u00e8re, P. Gianni, D. Lazard and T. Mora, Efficient computation of zero dimensional Gr\u00f6bner bases by change of ardering, J. Symbolic Comput., to appear."},{"key":"10.1016\/0166-218X(91)90109-A_bib14","doi-asserted-by":"crossref","unstructured":"N. Fitchas and A. Galligo, Nullstellensatz effectif et Conjecture de Serre (Th\u00e9or\u00e8me de Quillen-Suslin) pour le Calcul Formel, Math. Nachr., to appear.","DOI":"10.1002\/mana.19901490118"},{"key":"10.1016\/0166-218X(91)90109-A_bib15","series-title":"Algorithmes de construction de bases standards","author":"Galligo","year":"1985"},{"key":"10.1016\/0166-218X(91)90109-A_bib16","series-title":"Proceedings 13th Symposium MFCS 1986","first-page":"93","article-title":"Parallel arithmetic computations. A survey","volume":"233","author":"von zur Gathen","year":"1986"},{"key":"10.1016\/0166-218X(91)90109-A_bib17","series-title":"Proceedings 5th International Conference","first-page":"247","article-title":"Algebraic solution of polynomial equations using Groebner Bases","volume":"356","author":"Gianni","year":"1989"},{"key":"10.1016\/0166-218X(91)90109-A_bib18","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0747-7171(88)80046-4","article-title":"Combinatorial dimension theory of algebraic varieties","volume":"6","author":"Giusti","year":"1988","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/0166-218X(91)90109-A_bib19","series-title":"EUROCAL '87","first-page":"333","article-title":"Complexity of standard bases in projective dimension zero","volume":"378","author":"Giusti","year":"1989"},{"key":"10.1016\/0166-218X(91)90109-A_bib20_1","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/0304-3975(83)90002-6","article-title":"Definability and fast quantifier elimination over algebraically closed fields","volume":"24","author":"Heintz","year":"1983","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0166-218X(91)90109-A_bib20_2","first-page":"113","article-title":"Kybernet. Sb.","volume":"22","author":"Heintz","year":"1985","journal-title":"Novaja Ser. Vyp."},{"key":"10.1016\/0166-218X(91)90109-A_bib21","doi-asserted-by":"crossref","first-page":"963","DOI":"10.2307\/1990996","article-title":"Sharp effective Nullstellensatz","volume":"1","author":"Koll\u00e1r","year":"1988","journal-title":"J. Amer. Math. Soc."},{"key":"10.1016\/0166-218X(91)90109-A_bib22","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0747-7171(88)80045-2","article-title":"Computing dimension and independent sets of polynomial ideals","volume":"6","author":"Kredel","year":"1988","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/0166-218X(91)90109-A_bib23","doi-asserted-by":"crossref","first-page":"165","DOI":"10.24033\/bsmf.1848","article-title":"Alg\u00e8bre lin\u00e9aire sur K[Xl,...,Xn] et\u00e9limination","volume":"105","author":"Lazard","year":"1977","journal-title":"Bull. Soc. Math. France"},{"key":"10.1016\/0166-218X(91)90109-A_bib24","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0304-3975(81)90064-5","article-title":"R\u00e9solution des syst\u00e8mes d'\u00e9quations alg\u00e9briques","volume":"15","author":"Lazard","year":"1981","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0166-218X(91)90109-A_bib25","series-title":"Cours de D.E.A.","article-title":"Effectivit\u00e9de Calculs Polynomiaux","author":"Lejeune-Jalabert","year":"1985"},{"key":"10.1016\/0166-218X(91)90109-A_bib26","series-title":"Proceedings 6th International Conference","first-page":"259","article-title":"A computational proof of the Noether's Normalization Lemma","volume":"357","author":"Logar","year":"1989"},{"key":"10.1016\/0166-218X(91)90109-A_bib27","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0001-8708(82)90048-2","article-title":"The complexity of the word problem for commutative semigroups and polynomial ideals","volume":"46","author":"Mayr","year":"1982","journal-title":"Adv. in Math."},{"key":"10.1016\/0166-218X(91)90109-A_bib28","first-page":"338","article-title":"A fast parallel algorithm to compute the rank of a matrix over an arbitrary field","author":"Mulmuley","year":"1986","journal-title":"Proceedings 18th Annual ACM Symposium Theory of Computing"},{"key":"10.1016\/0166-218X(91)90109-A_bib29","article-title":"Th\u00e9or\u00e8me des z\u00e9ros effectif d'apr\u00e8s J. Koll\u00e1r","author":"Philippon","year":"1988","journal-title":"S\u00e9minaire I.H.P."},{"key":"10.1016\/0166-218X(91)90109-A_bib30","series-title":"Algebraic Geometry","author":"Shafarevich","year":"1974"}],"container-title":["Discrete Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0166218X9190109A?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0166218X9190109A?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T02:21:33Z","timestamp":1555122093000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0166218X9190109A"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,11]]},"references-count":31,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1991,11]]}},"alternative-id":["0166218X9190109A"],"URL":"https:\/\/doi.org\/10.1016\/0166-218x(91)90109-a","relation":{},"ISSN":["0166-218X"],"issn-type":[{"value":"0166-218X","type":"print"}],"subject":[],"published":{"date-parts":[[1991,11]]}}}