##############################################
# Computation of all cells in the Naruki fan #
##############################################

# The following script computes the Naruki fan as the union of the images of maximal cells in the Bergman fan under the Yoshida matrix. We only consider those maximal cones in the Bergman fan whose images are top dimensional.


#load(“subdivision.sage”)

load("BergmanCones.sage")

# We load the Yoshida matrix:
Yoshida_matrix = load("../../Yoshida/Output/Yoshida_matrix.sobj")

RootSystemE6 = load("../../General/L6.sobj")

L6 = RootSystem('E6').root_lattice()

positive_roots = load("../../General/posRootsE6.sobj")

G6 = L6.weyl_group()

###############################################
# Data associated to the Bergman fan Berg(E6) #
###############################################

# This data was computed in the folder BergmanFan and in Yoshida.

E6_1_Numbers =  load("../../BergmanFan/Scripts/Input/E6_1_Numbers.sobj")
E6_2_Numbers =  load("../../BergmanFan/Scripts/Input/E6_2_Numbers.sobj")
E6_4_Numbers =  load("../../BergmanFan/Scripts/Input/E6_4_Numbers.sobj")
E6_7_Numbers =  load("../../BergmanFan/Scripts/Input/E6_7_Numbers.sobj")
E6_8_Numbers =  load("../../BergmanFan/Scripts/Input/E6_8_Numbers.sobj")
E6_12_Numbers =  load("../../BergmanFan/Scripts/Input/E6_12_Numbers.sobj")
E6_13_Numbers =  load("../../BergmanFan/Scripts/Input/E6_13_Numbers.sobj")







vertexIndexListE6 = E6_1_Numbers[1] + E6_2_Numbers[1]+E6_4_Numbers[1]+E6_7_Numbers[1]+E6_8_Numbers[1]+E6_12_Numbers[1]+E6_13_Numbers[1]

BergmanFan =  load("BergmanFanOfE6TruncatedFVectorAndOrbitsPerDimension.sobj")


# We generate the potential vertices of the Naruki fan. 
# Naruki_vertex = {i:vector(Yoshida_map([i]).rays()[0]) for i in range(0,750) if Yoshida_map([i]) != Polyhedron()}
#v = Naruki_vertex
#save(v,"Input/NarukiVertices.sobj")
#print len(v)
# 678

# # We save the list of all vertices as plain text file (one vector per line)
# f = file("../Output/NarukiVertices.txt",'w')
# for i in v.keys():
#     f.write(str(i) + ':' + str(v[i]) + '\n')
# f.close()

v = load("../../NarukiFan/Scripts/Input/NarukiVertices.sobj")

# We use the knowledge of the Naruki fan to compute each cell type as polyhedrons (using the baricentric subdivision described in [RSS]. Our choice of representatives is compatible with inclusions of polyhedra (e.g. aCell is a face of aa2Cell)


# os.chdir('../../ComputeLines/Scripts/')
# orig = Polyhedron(vertices=[vector(QQ, {35:0})])
# save(orig, "Input/0Cell.sobj")
# a = Polyhedron(rays=[v[0]])
# save(a, "Input/aCell.sobj")
# a2= Polyhedron(rays=[v[0]+v[1]])
# save(a2, "Input/a2Cell.sobj")
# a3 = Polyhedron(rays=[v[0]+v[1]+v[4]])
# save(a3, "Input/a3Cell.sobj")
# a4 = Polyhedron(rays=[v[0]+v[1]+v[4]+v[29]])
# save(a4, "Input/a4Cell.sobj")
# b = Polyhedron(rays=[v[36]])
# save(b, "Input/bCell.sobj")

# aa2 = Polyhedron(rays=[v[0],v[0]+v[1]])
# save(aa2, "Input/aa2Cell.sobj")

# aa3 = Polyhedron(rays=[v[0],v[0]+v[1]+v[4]])
# save(aa3, "Input/aa3Cell.sobj")
# aa4 = Polyhedron(rays=[v[0],v[0]+v[1]+v[4]+v[29]])
# save(aa4, "Input/aa4Cell.sobj")
# a2a3 = Polyhedron(rays=[v[0]+v[1], v[0]+v[1]+v[4]])
# save(a2a3, "Input/a2a3Cell.sobj")
# a2a4 = Polyhedron(rays=[v[0]+v[1], v[0]+v[1]+v[4]+v[29]])
# save(a2a4, "Input/a2a4Cell.sobj")
# a3a4 = Polyhedron(rays=[v[0]+v[1]+v[4], v[0]+v[1]+v[4]+v[29]])
# save(a3a4, "Input/a3a4Cell.sobj")
# ab = Polyhedron(rays=[v[0], v[36]])
# save(ab, "Input/abCell.sobj")
# a2b = Polyhedron(rays=[v[0]+v[1], v[36]])
# save(a2b, "Input/a2bCell.sobj")
# a3b = Polyhedron(rays=[v[0]+v[1]+v[4], v[36]])
# save(a3b, "Input/a3bCell.sobj")

# aa2a3 = Polyhedron(rays=[v[0], v[0]+v[1], v[0]+v[1]+v[4]])
# save(aa2a3, "Input/aa2a3Cell.sobj")
# aa2a4 = Polyhedron(rays=[v[0], v[0]+v[1], v[0]+v[1]+v[4]+v[29]])
# save(aa2a4, "Input/aa2a4Cell.sobj")
# aa3a4 = Polyhedron(rays=[v[0], v[0]+v[1]+v[4], v[0]+v[1]+v[4]+v[29]])
# save(aa3a4, "Input/aa3a4Cell.sobj")
# a2a3a4 = Polyhedron(rays=[v[0]+v[1], v[0]+v[1]+v[4], v[0]+v[1]+v[4]+v[29]])
# save(a2a3a4, "Input/a2a3a4Cell.sobj")
# aa2b = Polyhedron(rays=[v[0], v[0]+v[1], v[36]])
# save(aa2b, "Input/aa2bCell.sobj")
# aa3b = Polyhedron(rays=[v[0], v[0]+v[1]+v[4], v[36]])
# save(aa3b, "Input/aa3bCell.sobj")
# a2a3b = Polyhedron(rays=[v[0]+v[1], v[0]+v[1]+v[4], v[36]])
# save(a2a3b, "Input/a2a3bCell.sobj")

#aa2a3a4 = Polyhedron(rays=[v[0], v[0]+v[1], v[0]+v[1]+v[4], v[0]+v[1]+v[4]+v[29]])
# save(aa2a3a4, "Input/aa2a3a4Cell.sobj")
#aa2a3b = Polyhedron(rays=[v[0], v[0]+v[1], v[0]+v[1]+v[4], v[36]])
# save(aa2a3b, "Input/aa2a3bCell.sobj")

#We save all these sobj files on "../../ComputeLines/Scripts/Input"

######################
# Plain text outputs #
######################

# os.chdir("../../ComputeLines/Scripts/Input")

orig = load("0Cell.sobj")
a = load("aCell.sobj")
a2 = load("a2Cell.sobj")
a3=load("a3Cell.sobj")
a4=load("a4Cell.sobj")
b = load("bCell.sobj")

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

ab=load("abCell.sobj")
a2b=load("a2bCell.sobj")
a3b=load("a3bCell.sobj")

aa2a3=load("aa2a3Cell.sobj")
aa2a4=load("aa2a4Cell.sobj")
aa3a4=load("aa3a4Cell.sobj")
a2a3a4=load("a2a3a4Cell.sobj")

aa2b=load("aa2bCell.sobj")
aa3b=load("aa3bCell.sobj")
a2a3b=load("a2a3bCell.sobj")

aa2a3a4 = load("aa2a3a4Cell.sobj")
aa2a3b = load("aa2a3bCell.sobj")


os.chdir("../../../NarukiFan/Output")

# We save the rays of each cell as a sobj and a plain text file. 

#################
# 1-dimensional #
#################

rays = a.rays()
save(rays,'aCell_rays.sobj')
f = file("aCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = a2.rays()
save(rays,'a2Cell_rays.sobj')
f = file("a2Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = a3.rays()
save(rays,'a3Cell_rays.sobj')
f = file("a3Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = a4.rays()
save(rays,'a4Cell_rays.sobj')
f = file("a4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = b.rays()
save(rays,'bCell_rays.sobj')
f = file("bCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


#################
# 2-dimensional #
#################

rays = aa2.rays()
save(rays,'aa2Cell_rays.sobj')
f = file("aa2Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = aa3.rays()
save(rays,'aa3Cell_rays.sobj')
f = file("aa3Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = aa4.rays()
save(rays,'aa4Cell_rays.sobj')
f = file("aa4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = a2a3.rays()
save(rays,'a2a3Cell_rays.sobj')
f = file("a2a3Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = a2a4.rays()
save(rays,'a2a4Cell_rays.sobj')
f = file("a2a4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = a3a4.rays()
save(rays,'a3a4Cell_rays.sobj')
f = file("a3a4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = ab.rays()
save(rays,'abCell_rays.sobj')
f = file("abCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = a2b.rays()
save(rays,'a2bCell_rays.sobj')
f = file("a2bCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = a3b.rays()
save(rays,'a3bCell_rays.sobj')
f = file("a3bCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


#################
# 3-dimensional #
#################

rays = aa2a3.rays()
save(rays,'aa2a3Cell_rays.sobj')
f = file("aa2a3Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = aa2a4.rays()
save(rays,'aa2a4Cell_rays.sobj')
f = file("aa2a4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = aa3a4.rays()
save(rays,'aa3a4Cell_rays.sobj')
f = file("aa3a4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


rays = a2a3a4.rays()
save(rays,'a2a3a4Cell_rays.sobj')
f = file("a2a3a4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = aa2b.rays()
save(rays,'aa2bCell_rays.sobj')
f = file("aa2bCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = aa3b.rays()
save(rays,'aa3bCell_rays.sobj')
f = file("aa3bCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = a2a3b.rays()
save(rays,'a2a3bCell_rays.sobj')
f = file("a2a3bCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()


#################
# 4-dimensional #
#################

rays = aa2a3a4.rays()
save(rays,'aa2a3a4Cell_rays.sobj')
f = file("aa2a3a4Cell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()

rays = aa2a3b.rays()
save(rays,'aa2a3bCell_rays.sobj')
f = file("aa2a3bCell_rays.txt",'w')
for i in range(0, len(rays)):
    f.write(str(rays[i]) + '\n')
f.close()