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, y, z] |
i3 : T1 = tropicalVariety(I); |
i4 : J = ideal(x*y+y*z+x*z+1); o4 : Ideal of QQ[x, y, z] |
i5 : T2 = tropicalVariety(J); |
i6 : V = tropicalVariety(I+J); |
i7 : W2 = stableIntersection(T1,T2,Strategy=>"gfan"); |
i8 : V#"Fan" == W2 o8 = true |
The object stableIntersection is a method function with options.