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# Intersection of Naruki cones with tropicalization of Cross Functions #
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# The following script verifies that the tropicalization of the Cross functions do not produce any subdivision of the Naruki fan.


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# Load all cells of the Naruki fan #
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orig = load("../../ComputeLines/Scripts/Input/0Cell.sobj")
a = load("../../ComputeLines/Scripts/Input/aCell.sobj")
a2 = load("../../ComputeLines/Scripts/Input/a2Cell.sobj")
a3=load("../../ComputeLines/Scripts/Input/a3Cell.sobj")
a4=load("../../ComputeLines/Scripts/Input/a4Cell.sobj")
b = load("../../ComputeLines/Scripts/Input/bCell.sobj")

aa2=load("../../ComputeLines/Scripts/Input/aa2Cell.sobj")
aa3=load("../../ComputeLines/Scripts/Input/aa3Cell.sobj")
aa4=load("../../ComputeLines/Scripts/Input/aa4Cell.sobj")
a2a3=load("../../ComputeLines/Scripts/Input/a2a3Cell.sobj")
a2a4=load("../../ComputeLines/Scripts/Input/a2a4Cell.sobj")
a3a4=load("../../ComputeLines/Scripts/Input/a3a4Cell.sobj")

ab=load("../../ComputeLines/Scripts/Input/abCell.sobj")
a2b=load("../../ComputeLines/Scripts/Input/a2bCell.sobj")
a3b=load("../../ComputeLines/Scripts/Input/a3bCell.sobj")

aa2a3=load("../../ComputeLines/Scripts/Input/aa2a3Cell.sobj")
aa2a4=load("../../ComputeLines/Scripts/Input/aa2a4Cell.sobj")
aa3a4=load("../../ComputeLines/Scripts/Input/aa3a4Cell.sobj")
a2a3a4=load("../../ComputeLines/Scripts/Input/a2a3a4Cell.sobj")

aa2b=load("../../ComputeLines/Scripts/Input/aa2bCell.sobj")
aa3b=load("../../ComputeLines/Scripts/Input/aa3bCell.sobj")
a2a3b=load("../../ComputeLines/Scripts/Input/a2a3bCell.sobj")

aa2a3a4 = load("../../ComputeLines/Scripts/Input/aa2a3a4Cell.sobj")
aa2a3b = load("../../ComputeLines/Scripts/Input/aa2a3bCell.sobj")


# We load the Yoshida and cross functions.
Yoshidas = var(["Yoshida"+str(i) for i in range(0,40)])
Cross_to_yoshidas = load("../../Yoshida/Scripts/Input/cross_to_yoshidas.sobj")
Cross_to_yoshidas = load("../../Yoshida/Scripts/Input/cross_to_yoshidas.sobj")


# The following function computes the slicing of a given cone by the tropicalization of a fixed Cross function given as a difference of two Yoshida functions.

def is_intersection_simplicial(cross, cone):
    # Tropicalize the cross function
    hyperplane = zero_vector(40)

    # Find the variables appearing in cross
    assert len(cross.variables()) == 2
    (y1,y2) = cross.variables()
    hyperplane[Yoshidas.index(y1)] = 1
    hyperplane[Yoshidas.index(y2)] = -1

    # The inequality has constant term = 0
    ieq = (0,) + tuple(hyperplane)
    
    # Construct a new cone by appending the inequality to the old cone.
    newCone = cone.intersection(Polyhedron(ieqs=[ieq]))

    return newCone.dim() < cone.dim() or newCone == cone



def check_all_cones_and_crosses():
    results = {}
    for cone in [a, a2, a3, a4, b, aa2, aa3, aa4, a2a3, a2a4, a3a4, ab, a2b, a3b, aa2a3, aa2a4, aa3a4, a2a3a4, aa2b, aa3b, a2a3b, aa2a3a4, aa2a3b]:
        for k in Cross_to_yoshidas.keys():
            results[(v,cone)] = is_intersection_simplicial(v, cone)
    return results