2014_SciPy.sagews

a = 5
type(a)

<type 'sage.rings.integer.Integer'>

a/3

5/3

a.parent()

Integer Ring

a = 5464512
a.factor()

2^6 * 3^2 * 53 * 179

bt = BinaryTree([[None,[]],[[],[[[],[]],[None,[]]]]])
latex.eval(latex(bt))

''

BT = BinaryTrees()

Binary trees

BT.cardinality()

+Infinity

BT2 = BinaryTrees(2)
BT2

Binary trees of size 2

BT2.cardinality()

2

latex.eval(latex(BT2[0]))

''

latex.eval(latex(BT2[1]))

''

for bt in BT3:
    latex.eval(latex(bt))

''

''

''

''

''

[BinaryTrees(i).cardinality() for i in xrange(10)]

[1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]

[1/(n+1) * binomial(2*n, n) for n in xrange(10)]

[1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862]

︠c37e2cae-2793-42b5-b804-3b4c5b8391b4︠