Does Python have a pool of all strings and are they (strings) singletons there?

More precise, in the following code, are one or two strings created in memory?

a = str(num)
b = str(num)

Strings are immutable in Python, so the implementation can decide whether to intern (that's a term often associated with C#, meaning that some strings are stored in a pool) strings or not.

In your example, you're dynamically creating strings. CPython does not always look into the pool to detect whether the string is already there - it also doesn't make sense because you first have to reserve memory in order to create the string, and then compare it to the pool content (inefficient for long strings).

But for strings of length 1, CPython does look into the pool (cf. "stringobject.c"):

static PyStringObject *characters[UCHAR_MAX + 1];

...

PyObject *
PyString_FromStringAndSize(const char *str, Py_ssize_t size)
{

...

    if (size == 1 && str != NULL &&
    (op = characters[*str & UCHAR_MAX]) != NULL)
    {
        #ifdef COUNT_ALLOCS
            one_strings++;
        #endif

        Py_INCREF(op);
        return (PyObject *)op;
    }

...

So:

a = str(num)
b = str(num)
print a is b # <-- this will print False in most cases (but try str(1) is str(1))

But when using constant strings directly in your code, CPython uses the same string instance:

a = "text"
b = "text"
print a is b # <-- this will print True

In general, strings are not interned in Python, but they do sometimes seem to be:

>>> str(5) is str(5)
True
>>> str(50) is str(50)
False

This isn't uncommon in Python, where common objects might be optimized in ways that unusual ones are not:

>>> int(5+0) is int(5+0)
True
>>> int(50+0) is int(50+0)
True
>>> int(500+0) is int(500+0)
False

And keep in mind, all of these sorts of details will differ between implementations of Python, and even between versions of the same implementation.