Symmetry -- option to declare if the input ideal has symmetries

Synopsis

Usage:

tropicalVariety(I,Symmetry=>{{..},{..}})

Description

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[x_0 .. x_N], each symmetry is a permutation encoded in a list \{s_0, s_1, ..., s_N\} of numbers from 0 to N which records that swapping the variable x_j with the variable x_{s_j} 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 ]
                  0   2

i3 : T=tropicalVariety (I,Symmetry=>{{1,0,2}, {2,1,0} })

o3 = T

o3 : TropicalCycle

Functions with optional argument named Symmetry :

tropicalVariety(...,Symmetry=>...) -- see tropicalVariety -- the tropical variety associated to an ideal

For the programmer

The object Symmetry is a symbol.