next | previous | forward | backward | up | index | toc

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

Synopsis

• Usage:
gfanTropicalStartingCone(L)
gfanTropicalStartingCone(I)
• Inputs:
• L, a list, of polynomials, homogeneous with respect to a positive weight vector
• I, an ideal, homogeneous with respect to a positive weight vector
• Optional inputs:
• d
• g
• stable
• Outputs:

Description

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.