import weyl_utils_sage as wus
import weyl_utils as wu

G2 = wus.DistinguishedUnipotentOrbits("G",2)
F4 = wus.DistinguishedUnipotentOrbits("F",4)
E6 = wus.DistinguishedUnipotentOrbits("E",6)
E7 = wus.DistinguishedUnipotentOrbits("E",7)
E8 = wus.DistinguishedUnipotentOrbits("E",8)

G2_dst_rho = wu.distinguished_rho_list("G",2)
F4_dst_rho = wu.distinguished_rho_list("F",4)
E6_dst_rho = wu.distinguished_rho_list("E",6)
E7_dst_rho = wu.distinguished_rho_list("E",7)
E8_dst_rho = wu.distinguished_rho_list("E",8)

print("G2 full summary (root lattice coordinates)")
G2.print_summary(G2_dst_rho, weight_lattice_coord=False)
print()

print("G2 full summary (weight lattice coordinates)")
G2.print_summary(G2_dst_rho, weight_lattice_coord=True)
print()

print("F4 full summary (root lattice coordinates)")
F4.print_summary(F4_dst_rho, weight_lattice_coord=False)
print()

print("F4 full summary (weight lattice coordinates)")
F4.print_summary(F4_dst_rho, weight_lattice_coord=True)
print()

print("E6 full summary (root lattice coordinates)")
E6.print_summary(E6_dst_rho, weight_lattice_coord=False)
print()

print("E6 full summary (weight lattice coordinates)")
E6.print_summary(E6_dst_rho, weight_lattice_coord=True)
print()

print("E7 center information (root lattice coordinates)")
E7.center_is_lattice_point(E7_dst_rho, weight_lattice_coord=False)
print()

print("E7 center information  (weight lattice coordinates)")
E7.center_is_lattice_point(E7_dst_rho, weight_lattice_coord=True)
print()

print("E8 center information (root lattice coordinates)")
E8.center_is_lattice_point(E8_dst_rho, weight_lattice_coord=False)
print()

print("E8 center information  (weight lattice coordinates)")
E8.center_is_lattice_point(E8_dst_rho, weight_lattice_coord=True)
print()