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:
- P, a list, a pair of MarkedPolynomialLists

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.

Ways to use gfanTropicalStartingCone :

gfanTropicalStartingCone(Ideal)
gfanTropicalStartingCone(List)

For the programmer

The object gfanTropicalStartingCone is a method function with options.

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

Synopsis

Description

See also

Ways to use gfanTropicalStartingCone :

For the programmer