# Import the class Group from the file groups.py from groups import Group # Create an instance of the group (5,+)x(9,x) print("Create a group (5,+)x(9,x)") G = Group(["add", "mult"], [5, 9]) # print the group components Gg = G.g("show") g3 = G.g(3) print("Element 3 = ", G.g(3)) print("Inverse of element 3 = ", G.inv(g3)) g7 = G.g(7) g6 = G.g(6) print("Element 7 = ", g7) print("Element 6 = ", g6) print("Multiplication of element 7 and element 6 = ", G.op(g7, g6)) print("Element 7 to the power of 3 = ", G.pow(g7, 3)) print("Group orders:") Gg = G.g() Ggo = G.go() for (g, go) in zip(Gg, Ggo): print("Element ", g, " has order ", go)
# Import the class Group from the file groups.py from groups import Group # Create an instance of the group (32,x) G = Group("mult", 32) G.g("show") Gg = G.g() Ggo = G.go() print("(32,x) sorted element orders = ", sorted(Ggo), "\n") # Creating candidate groups G1 = Group("add", 16) G2 = Group(["add", "add"], [8, 2]) G3 = Group(["add", "add", "add"], [4, 2, 2]) G4 = Group(["add", "add", "add", "add"], [2, 2, 2, 2]) print("Candidate groups:") G1go = G1.go() print("(16,+) sorted element orders = ", sorted(G1go)) G2go = G2.go() print("(8,+)x(2,+) sorted element orders = ", sorted(G2go)) G3go = G3.go() print("(4,+)x(2,+)x(2,+) sorted element orders = ", sorted(G3go)) G4go = G4.go() print("(2,+)x(2,+)x(2,+)x(2,+) sorted element orders = ", sorted(G4go), "\n") print("Conclusion:")
from groups import Group # Create an instance of the group (10,+) print("Creating a group (10,+)") G = Group("add", 10) # print the group components G.g("show") print("Inverse of element 3 = ", G.inv(3)) print("Multiplication of 7 and 6 = ", G.op(7, 6)) print("7 to the power 3 = ", G.pow(7, 3)) Gg = G.g() Ggo = G.go() GgoDict = dict(zip(Gg, Ggo)) for g in GgoDict: print("Element: ", g, " has order: ", GgoDict[g]) # Create an instance of the group (15,x) print("\nCreating a group (15,x)") H = Group("mult", 15) # print the group components Hh = H.g("show") print("Inverse of element 2 = ", H.inv(2)) print("Multiplication of 2 and 10 = ", H.op(2, 10)) print("2 to the power 10 = ", H.pow(2, 10))
# Importing require modules from groups import Group # Creating group and subgroup print("Create (6,+)x(9,x) group") G = Group(["add", "mult"], [6, 9]) G.g("show") print("Print order of [0,1] is: ", G.go([0, 1])) print("Create sub group with elements 2 and 22") g2 = G.g(2) g22 = G.g(22) GS = G.sub([g2, g22]) GSg = GS.g("show") g2 = GS.g(2) print("Element 2 = ", g2) print("Inverse of element 2 = ", GS.inv(g2)) g4 = GS.g(4) g5 = GS.g(5) print("Element 4 = ", g4) print("Element 5 = ", g5) print("Multiplication of element 4 and element 5 = ", GS.op(g4, g5)) print("Element 4 to the power of 3 = ", GS.pow(g4, 3)) print("Group orders:") GSg = GS.g() GSgo = GS.go() print(GSgo)