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refineMultiplicity -- Compute the multiplicities of a refinement of a tropical variety

Synopsis

Description

This function calculate the multiplicities of a refinement of a tropical variety T. The output is a list of integers indexed by orbits(X,n-k), where k = dim T, n = dim X and X is the normal toric variety of the refinement.

i1 : X = toricProjectiveSpace 3;
i2 : R = QQ[x_1 .. x_3];
i3 : f = x_1*x_2*x_3 + x_1*x_2 + x_1*x_3 + x_2*x_3;
i4 : T = tropicalVariety(ideal f);
i5 : F = gfanFanCommonRefinement(fan X, fan T);
i6 : X' = makeSimplicial (normalToricVariety F);
i7 : multiplicities T

o7 = {1, 1, 1, 1, 1, 1}

o7 : List
i8 : refineMultiplicity(T,X')

o8 = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

o8 : List

Ways to use refineMultiplicity :

For the programmer

The object refineMultiplicity is a method function.