{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:46:01Z","timestamp":1776725161186,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"233","license":[{"start":{"date-parts":[[2001,7,21]],"date-time":"2001-07-21T00:00:00Z","timestamp":995673600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.<\/p>","DOI":"10.1090\/s0025-5718-00-01295-3","type":"journal-article","created":{"date-parts":[[2005,7,11]],"date-time":"2005-07-11T17:02:26Z","timestamp":1121101346000},"page":"395-417","source":"Crossref","is-referenced-by-count":10,"title":["Classification of quintic eutactic forms"],"prefix":"10.1090","volume":"70","author":[{"given":"Christian","family":"Batut","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,7,21]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"1040","DOI":"10.4153\/CJM-1977-101-2","article-title":"On eutactic forms","volume":"29","author":"Ash, Avner","year":"1977","journal-title":"Canadian J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0008-414X","issn-type":"print"},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1112\/blms\/12.3.192","article-title":"On the existence of eutactic forms","volume":"12","author":"Ash, Avner","year":"1980","journal-title":"Bull. London Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6093","issn-type":"print"},{"key":"3","unstructured":"[Ba] J.-L. Baril, Autour de l\u2019algorithme de Voronoi: constructions de r\u00e9seaux euclidiens, Th\u00e8se Bordeaux (1996)."},{"key":"4","unstructured":"[Bv] C. Bavard, Une formule d\u2019Euler pour les classes minimales de r\u00e9seaux, preprint."},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1112\/jlms\/53.3.417","article-title":"Sur la classification des r\u00e9seaux eutactiques","volume":"53","author":"Berg\u00e9, Anne-Marie","year":"1996","journal-title":"J. London Math. Soc. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6107","issn-type":"print"},{"key":"6","series-title":"Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2016-7","volume-title":"Sphere packings, lattices and groups","volume":"290","author":"Conway, J. H.","year":"1988","ISBN":"https:\/\/id.crossref.org\/isbn\/038796617X"},{"issue":"1854","key":"7","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1098\/rspa.1988.0073","article-title":"Low-dimensional lattices. III. Perfect forms","volume":"418","author":"Conway, J. H.","year":"1988","journal-title":"Proc. Roy. Soc. London Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0962-8444","issn-type":"print"},{"key":"8","doi-asserted-by":"crossref","unstructured":"[KZ3] A. Korkine, G. Zolotareff, Sur les formes quadratiques positives, Math. 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Vorono\u00ef, Nouvelles applications des param\u00e8tres continus \u00e0 la th\u00e9orie des formes quadratiques : 1 Sur quelques propri\u00e9t\u00e9s des formes quadratiques positives parfaites, J. Reine Angew. Math 133 (1908), 97\u2013178.","DOI":"10.1515\/crll.1908.133.97"},{"key":"13","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1112\/S0025579300008378","article-title":"On the minimum points of a postive quadratic form","volume":"18","author":"Watson, G. 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