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. "The Gröbner fan of an ideal". Journal of Symbolic Computation. 6: 183–208. doi:10.1016/S0747-7171(88)80042-7. Retrieved 2017-03-29.
  2. ↑ Bayer, David. "Standard bases and geometric invariant theory I. Initial ideals and state polytopes". Journal of Symbolic Computation. 6: 209–217. doi:10.1016/S0747-7171(88)80043-9. Retrieved 2017-03-29.
  3. ↑ "Gfan". home.math.au.dk. Retrieved 2017-04-03.
  4. ↑ KOMEI FUKUDA, ANDERS N. JENSEN, AND REKHA R. THOMAS (2007). "Computing Gröbner Fan" (PDF). Mathematics of Computation. 76: 2189–2212. doi:10.1090/s0025-5718-07-01986-2.
  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.
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