d = {0: [1,4,5], 1: [2,6], 2: [3,7], 3: [4,8], 4: [9], 5: [7, 8], 6: [8,9], 7: [9]}
G = Graph(d)
plot(G)
show(G)
G=Graph(d)
G
 
|
show(G)
|
CollatzTree={}
for i in srange(1,27):
a=i
while a>1:
if is_even(a):
#if a<50:
CollatzTree.update({a:[a/2]})
a=a/2
else:
#if a<50:
CollatzTree.update({a:[3*a+1]})
a=3*a+1
T=Graph(CollatzTree)
show(T)
x=T.graphplot(layout='tree', tree_root=1,tree_orientation='up')
x.show(figsize=[25,20])
 
|
print(CollatzTree)
{2: [1], 3: [10], 4: [2], 5: [16], 6: [3], 7: [22], 8: [4], 9: [28], 10:
[5], 11: [34], 12: [6], 13: [40], 14: [7], 15: [46], 16: [8], 17: [52],
18: [9], 19: [58], 20: [10], 21: [64], 22: [11], 23: [70], 24: [12], 25:
[76], 26: [13], 28: [14], 29: [88], 32: [16], 34: [17], 35: [106], 38:
[19], 40: [20], 44: [22], 46: [23], 52: [26], 53: [160], 58: [29], 64:
[32], 160: [80], 70: [35], 76: [38], 80: [40], 88: [44], 106: [53]}
{2: [1], 3: [10], 4: [2], 5: [16], 6: [3], 7: [22], 8: [4], 9: [28], 10: [5], 11: [34], 12: [6], 13: [40], 14: [7], 15: [46], 16: [8], 17: [52], 18: [9], 19: [58], 20: [10], 21: [64], 22: [11], 23: [70], 24: [12], 25: [76], 26: [13], 28: [14], 29: [88], 32: [16], 34: [17], 35: [106], 38: [19], 40: [20], 44: [22], 46: [23], 52: [26], 53: [160], 58: [29], 64: [32], 160: [80], 70: [35], 76: [38], 80: [40], 88: [44], 106: [53]}
|
|
|
How can we used these tree graphs to display factor trees?
What issues will we face?
1. Need to label vertices with the *same* label!
2. Need to position the vertices left or right appropriately.
Need to use Binary Trees!
T=BinaryTree([None, BinaryTree([None, None])])
|
|
T.show()
|
G=T.to_ordered_tree_left_branch()
|
|
type(G)
<class 'sage.combinat.ordered_tree.OrderedTrees_all_with_category.element_class\ '> <class 'sage.combinat.ordered_tree.OrderedTrees_all_with_category.element_class'> |
show(G)
|
|
collatz_tree = {1:[2], 2:[4], 4:[8]}
|
|