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D.13.5.2 irrRealizationDim
Procedure from library realizationMatroids.lib (see realizationMatroids_lib).
- Usage:
- irrRealizationDim(I,C); where I is a homogeneous linear ideal defining the projective plane Y = V(I) and C is a list of intvectors such that each intvector represents a one-dimensional cone in the tropical fan curve whose irreducible relative realizability should be checked. This representation is done in the following way: a one-dimensional cone K is represented by a vector w whose equivalence class [w] in R^n/<1> can be written as [w] = m*[v] where [v] is the primitive generator of K and m is the weight of K.
- Returns:
- the dimension of the irreducible relative realization space of C with respect to Y, and -1 if the irreducible realization space is empty.
Example:
| | LIB "realizationMatroids.lib";
ring r = 0,(x(1..4)),dp;
ideal I = x(1)+x(2)+x(3)+x(4);
list C = list(intvec(2,2,0,0),intvec(0,0,2,2));
//C represents the tropical fan curve which consists of the cones
//cone([(1,1,0,0)]) and cone([(1,1,0,0)]), both with weight 2
realizationDim(I,C);
==> 0
irrRealizationDim(I,C);
==> -1
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