tropicalPrevariety -- the intersection of the tropical hypersurfaces

Synopsis

Usage:

tropicalPrevariety(L)

tropicalPrevariaty(L,LS)

tropicalPrevariety(L,Strategy=>S)

tropicalPrevariety(L,LS,Strategy=>S)
Inputs:
- L, a list, of polynomials
- LS, a list, of Symmetries (optional)
Optional inputs:
- Strategy => a string, default value "gfan", Strategy (currently only "gfan")
Outputs:
- F, an instance of the type Fan, the intersection of the tropical hypersurfaces of polynomials in L

Description

This method intersects the tropical hypersurfaces coming from the tropicalizations of the polynomials in the list L. If there are symmetries that leave the specified polynomials fixed, they can be specified by passing a list with the symmetries as second argument, with the same format as the option Symmetry.

i1 : QQ[x_1,x_2,x_3,x_4]

o1 = QQ[x ..x ]
         1   4

o1 : PolynomialRing

i2 : L={x_1+x_2+x_3+x_4,x_1*x_2+x_2*x_3+x_3*x_4+x_4*x_1,x_1*x_2*x_3+x_2*x_3*x_4+x_3*x_4*x_1+x_4*x_1*x_2,x_1*x_2*x_3*x_4-1}

o2 = {x  + x  + x  + x , x x  + x x  + x x  + x x , x x x  + x x x  + x x x 
       1    2    3    4   1 2    2 3    1 4    3 4   1 2 3    1 2 4    1 3 4
     ------------------------------------------------------------------------
     + x x x , x x x x  - 1}
        2 3 4   1 2 3 4

o2 : List

i3 : tropicalPrevariety L

o3 = Fan{...1...}

o3 : Fan

i4 : QQ[x_0,x_1]

o4 = QQ[x ..x ]
         0   1

o4 : PolynomialRing

i5 : tropicalPrevariety({x_0+x_1+1}, {{1,0}})

o5 = Fan{...1...}

o5 : Fan

i6 : QQ[x_0,x_1]

o6 = QQ[x ..x ]
         0   1

o6 : PolynomialRing

i7 : tropicalPrevariety({x_0+x_1+1,x_0+x_1},Strategy => "gfan")

o7 = Fan{...1...}

o7 : Fan

Ways to use tropicalPrevariety :

tropicalPrevariety(List)
tropicalPrevariety(List,List)

For the programmer

The object tropicalPrevariety is a method function with options.