Gröbner fan
From HandWiki
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 was 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] Macaulay2,[6] and CoCoA.[7]
See also
References
- ↑ Mora, Teo; Robbiano, Lorenzo (1988). "The Gröbner fan of an ideal" (in en). Journal of Symbolic Computation 6 (2–3): 183–208. doi:10.1016/S0747-7171(88)80042-7.
- ↑ Bayer, David; Morrison, Ian (1988). "Standard bases and geometric invariant theory I. Initial ideals and state polytopes" (in en). Journal of Symbolic Computation 6 (2–3): 209–217. doi:10.1016/S0747-7171(88)80043-9.
- ↑ "Gfan". http://home.math.au.dk/jensen/software/gfan/gfan.html.
- ↑ Fukuda, Komei; Jensen, Anders N.; Thomas, Rekha R. (2007). "Computing Gröbner fans". Mathematics of Computation 76 (260): 2189–2212. doi:10.1090/S0025-5718-07-01986-2.
- ↑ "Online Manual - groebnerFan". https://www.singular.uni-kl.de/Manual/4-3-0/sing_2606.htm.
- ↑ "gfan -- all reduced Groebner bases of a polynomial ideal". https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2-1.19.1/share/doc/Macaulay2/gfanInterface/html/_gfan.html.
- ↑ "GroebnerFanReducedGBases". http://cocoa.dima.unige.it/download/CoCoAManual/html/cmdGroebnerFanReducedGBases.html.
 |  |
