If the option is used, the specified symmetries are used in the calculation of the tropical variety. For an ideal I of a polynomial ring R = KK[x0 .. xN], each symmetry is a permutation encoded in a list {s0, s1, ..., sN}of numbers from 0 to N which records that swapping the variable xj with the variable xsj in R leaves the ideal I fixed. Exploiting symmetries reduces the number of computations needed. The length of each symmetry equals the number of generators of R, otherwise an error is raised.
i1 : QQ[x_0,x_1,x_2]; |
i2 : I=ideal(x_0+x_1+x_2+1); o2 : Ideal of QQ[x , x , x ] 0 1 2 |
i3 : T=tropicalVariety (I,Symmetry=>{{1,0,2}, {2,1,0} }) o3 = T o3 : TropicalCycle |