The input data is as follows:

FlagVariety

An increasing list of integers defining the flag variety. The last integer in the list is the dimension of the ambient vector space.

EnumerativeProblem

A list of sequences of integers. Each sequence represents a permutation corresponding to a Schubert variety. The first sequence in the list defines an open Schubert cell which is used to choose local coordinates on the flag variety, and the remaining sequences give equations for the remaining Schubert varieties in these local coordinates.

Time

The elapsed time of the computation. This is the sum of the elapsed time of the Gröbner basis computation (in Singular), called GroebnerTime, and the real root computation (in Maple), called RealTime.

coeffHeight

A measure of the number of digits needed to store the eliminant.

NumberOfSoultions

The number of complex points in the intersection of Schubert varieties encoded in EnumerativeProblem.

Necklaces

A list of sequences of integers (permutations) which encode how to select points on the rational normal curve at which to pick osculating flags. Once N points on the rational normal curve are chosen, a necklace S = [S₁,...,S_N ] determines that the osculating flag at the S_i^th point on the rational normal curve is used to define the i ^th Schubert condition.

Points

A list of points [x,y] on the real projective line with x>0. A random list is selected from Points, converted to a list of real numbers by assigning y/x to [x,y]. This list is then sorted from smallest to largest and used to define Schubert conditions on the flag variety as described above.

Table

This records the observed frequencies of real solutions for each necklaces.

NumberOfIterations

The number of instances of the enumerative problem to be computed

Instance

Record the current number of instances of the enumerative problem computed. When the computation is completed, this equals NumberOfIterations.

Machine

Identifies the machine on which the computations were performed.