You can create a list of `m`

iterators and then call `cartesian_product_iterator()`

on it:

```
sage: multicart = lambda m,q : cartesian_product_iterator([xrange(q+1) for i in range(m)])
sage: list(multicart(3,2))
[(0, 0, 0),
(0, 0, 1),
(0, 0, 2),
(0, 1, 0),
(0, 1, 1),
(0, 1, 2),
(0, 2, 0),
(0, 2, 1),
(0, 2, 2),
(1, 0, 0),
(1, 0, 1),
(1, 0, 2),
(1, 1, 0),
(1, 1, 1),
(1, 1, 2),
(1, 2, 0),
(1, 2, 1),
(1, 2, 2),
(2, 0, 0),
(2, 0, 1),
(2, 0, 2),
(2, 1, 0),
(2, 1, 1),
(2, 1, 2),
(2, 2, 0),
(2, 2, 1),
(2, 2, 2)]
```

You can see this very similar question.

Now, if you want true vectors instead of tuples, you can do:

```
sage: import itertools
sage: multicartvect = lambda m,q : itertools.imap(vector, cartesian_product_iterator([xrange(q+1) for i in range(m)]))
```