Gröbner fan

In computer algebra, the Gröbner fan of an ideal in the ring of polynomials is a concept in the theory of Gröbner bases. It is defined to be a fan consisting of cones that correspond to different monomial orders on that ideal. The concept has been introduced by Mora and Robbiano in 1988.[1] The result is a weaker version of the result presented in the same issue of the journal by Bayer and Morrison.[2] Gröbner fan is a base for the nowadays active field of tropical geometry. One implementation of the Gröbner fan is called Gfan,[3] based on an article of Fukuda, et. al.[4] which is included in some computer algebra systems such as Singular[5] and Macaulay2.[6]

See also

References
  1. Mora, Teo; Robbiano, Lorenzo (1988). "The Gröbner fan of an ideal". Journal of Symbolic Computation. 6 (2–3): 183–208. doi:10.1016/S0747-7171(88)80042-7.
  2. Bayer, David; Morrison, Ian (1988). "Standard bases and geometric invariant theory I. Initial ideals and state polytopes". Journal of Symbolic Computation. 6 (2–3): 209–217. doi:10.1016/S0747-7171(88)80043-9.
  3. "Gfan". home.math.au.dk. Retrieved 2017-04-03.
  4. KOMEI FUKUDA, ANDERS N. JENSEN, AND REKHA R. THOMAS (2007). "Computing Gröbner fans" (PDF). Mathematics of Computation. 76 (260): 2189–2212. doi:10.1090/s0025-5718-07-01986-2.CS1 maint: multiple names: authors list (link)
  5. "Singular Manual: groebnerFan". www.singular.uni-kl.de. Retrieved 2017-03-29.
  6. "groebnerFan – the fan of all groebner bases of an ideal". www.math.uiuc.edu. Retrieved 2017-03-29.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.