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gfanTropicalStartingCone -- a pair of Groebner bases for use with gfanTropicalTraverse



This method compute a pair of Groebner bases as needed for gfanTropicalTraverse. It heuristically finds a cone of the Tropical Variety. Its first output is the Groebner basis of the cone's monomial-free initial ideal. And the second output is the Groebner basis of the original ideal. Note that gfanTropicalStartingCone uses graded reverse lex order.

i1 : QQ[x,y,z]

o1 = QQ[x..z]

o1 : PolynomialRing
i2 : gfanTropicalStartingCone{x+y+z}

o2 = {{{z}, {y + z}}, {{z}, {x + y + z}}}

o2 : List
i3 : QQ[x,y]

o3 = QQ[x..y]

o3 : PolynomialRing
i4 : I=ideal(x+y)

o4 = ideal(x + y)

o4 : Ideal of QQ[x..y]
i5 : gfanTropicalStartingCone(I)

o5 = {{{y}, {x + y}}, {{y}, {x + y}}}

o5 : List

gfan Documentation This program computes a starting pair of marked reduced Groebner bases to be used as input for gfan_tropicaltraverse. The input is a homogeneous ideal whose tropical variety is a pure d-dimensional polyhedral complex.Options:-g: Tell the program that the input is already a reduced Groebner basis.-d: Output dimension information to standard error.--stable: Find starting cone in the stable intersection or, equivalently, pretend that the coefficients are genereric.

See also

Ways to use gfanTropicalStartingCone :

For the programmer

The object gfanTropicalStartingCone is a method function with options.