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Kernel: Python 2 (SageMath)

Issue 1: Referencing the counter of a loop

This is problematic. Each time the loop is completed the variable reverts to its value as a counter.

In [3]:

for i in range(5):
    print i
    i = 100
    print i

Out[3]:

Issue 2: functions that do not return anything

You can create functions which do not return anything:

In [12]:

def nothing(x):
    if x == 5:
        return 5

In [13]:

nothing(5)

Out[13]:

5

In [14]:

nothing(4)

In [15]:

print nothing(4)

Out[15]:

None

In [19]:

def reverse(L):
    return L.reverse()

In [21]:

print reverse([1, 2])

Out[21]:

None

What happened here?

In [2]:

L = [1, 2]

In [4]:

M = L.reverse()
print L
print M

Out[4]:

[1, 2]
None

The reverse method for lists reverses the list in-place. It does not return any value.

Lists and generators:

A binary list if length n is a list of length n, all of whose elements are 0 or 1. Recursion is a convenient method to generate a list of all such strings:

In [17]:

def list_of_binary_lists(n):
    if n == 0:
        return [[]] # The only binary string of length 0 is the empty string
    else:
        L = []
        for s in list_of_binary_lists(n-1):
            L += [s + [0], s + [1]]
        return L

In [19]:

list_of_binary_lists(3)

Out[19]:

[[0, 0, 0],
 [0, 0, 1],
 [0, 1, 0],
 [0, 1, 1],
 [1, 0, 0],
 [1, 0, 1],
 [1, 1, 0],
 [1, 1, 1]]

We now look at a generator for such lists:

In [24]:

def binary_list_gen(n):
    if n == 0:
        yield []
    else:
        for s in binary_list_gen(n-1):
            yield s + [0]
            yield s + [1]

In [25]:

list(binary_list_gen(4))

Out[25]:

[[0, 0, 0, 0],
 [0, 0, 0, 1],
 [0, 0, 1, 0],
 [0, 0, 1, 1],
 [0, 1, 0, 0],
 [0, 1, 0, 1],
 [0, 1, 1, 0],
 [0, 1, 1, 1],
 [1, 0, 0, 0],
 [1, 0, 0, 1],
 [1, 0, 1, 0],
 [1, 0, 1, 1],
 [1, 1, 0, 0],
 [1, 1, 0, 1],
 [1, 1, 1, 0],
 [1, 1, 1, 1]]

In [35]:

D = dict((i,0) for i in range(21))
for L in binary_list_gen(20):
    D[sum(L)] += 1

In [36]:

Out[36]:

In [37]:

D = dict((i,0) for i in range(21))
for L in list_of_binary_lists(20):
    D[sum(L)] += 1

In [38]:

Out[38]:

Generating all the square numbers

In [47]:

def squares_gen():
    i = 1
    while True:
        yield i^2
        i += 1

Find the smallest square number that is greater than n

In [45]:

def smallest_square_greater_than()

In [46]:

2 + 2

Out[46]:

4

In [ ]:

Issue 1: Referencing the counter of a loop

Issue 2: functions that do not return anything

Lists and generators:

Generating all the square numbers

Find the smallest square number that is greater than n

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