stableIntersection -- computes the stable intersection of two tropical varieties

Synopsis

Usage:

stableIntersection(F,G)

stableIntersection(L,Strategy=>S)
Inputs:
- F, a tropical cycle, a tropical cycle
- G, a tropical cycle, another tropical cycle
Optional inputs:
- Strategy => a string, default value "gfan", Strategy ("atint" (polymake) or "gfan")
Outputs:
- T, a tropical cycle, a tropical cycle

Description

This computes the stable intersection of two tropical cycles. For details on the definition of stable intersection, see, for example, Section 3.6 of TROPICALBOOK. If a recent enough version of polymake is installed, the Strategy "atint" is default. Otherwise "gfan" will be used, which only computes the fan of the stable intersection without multiplicities.

i1 : QQ[x,y,z];

i2 : I = ideal(x^2+y^2+z^2-1);

o2 : Ideal of QQ[x..z]

i3 : T1 = tropicalVariety(I);

i4 : J = ideal(x*y+y*z+x*z+1);

o4 : Ideal of QQ[x..z]

i5 : T2 = tropicalVariety(J);

i6 : V = tropicalVariety(I+J);

i7 : W2 =  stableIntersection(T1,T2,Strategy=>"gfan");

i8 : V#"Fan" == W2

o8 = true

Ways to use stableIntersection :

stableIntersection(TropicalCycle,TropicalCycle)

For the programmer

The object stableIntersection is a method function with options.