Postgresql: Insert the cartesian product of two or more sets

Question

as definition: The cartesian product of two sets is the set of all possible pairs of these sets, so {A,B} x {a,b} = {(A,a),(A,b),(B,a),(B,b)}.

Now i want to insert such a cartesian product into a database table (each pair as a row). It is intended to fill the table with default values for each pair, so the data, i.e. the two sets, are not present in the database at this point.

Any idea how to achieve this with postgresql?

EDIT :

With the help of Grzegorz Szpetkowski's answer I was able to produce a query that does what I want to achieve, but it really isn't the prettiest one. Suppose I want to insert the cartesian product of the sets {1,2,3} and {'A','B','C'}.

INSERT INTO "Test"
SELECT * FROM
(SELECT 1 UNION SELECT 2 UNION SELECT 3) P
CROSS JOIN
(SELECT 'A' UNION SELECT 'B' UNION SELECT 'C') Q

Is there any better way to do this?

EDIT2 : Accepted answer is fine, but i found another version which might be appropriate if it gets more complex:

CREATE TEMP TABLE "Numbers" (ID integer) ON COMMIT DROP;
CREATE TEMP TABLE "Chars" (Char character varying) ON COMMIT DROP;
INSERT INTO "Numbers" (ID) VALUES (1),(2),(3);
INSERT INTO "Chars" (Char) VALUES ('A'),('B'),('C');
INSERT INTO "Test"
SELECT * FROM
"Numbers"
CROSS JOIN
"Chars";

Answer 1

I am not sure if this really answers your question, but in PostgreSQL there is CROSS JOIN defined as:

For every possible combination of rows from T1 and T2 (i.e., a Cartesian product), the joined table will contain a row consisting of all columns in T1 followed by all columns in T2. If the tables have N and M rows respectively, the joined table will have N * M rows.

FROM T1 CROSS JOIN T2 is equivalent to FROM T1, T2. It is also equivalent to FROM T1 INNER JOIN T2 ON TRUE (see below).

EDIT:

One way is to use VALUES Lists (note that in fact you have no order, use ORDER BY clause to get some ordering):

SELECT N AS number, L AS letter FROM
    (VALUES (1), (2), (3)) a(N)
CROSS JOIN
    (VALUES ('A'), ('B'), ('C')) b(L);

Result:

 number | letter
--------+--------
      1 | A
      1 | B
      1 | C
      2 | A
      2 | B
      2 | C
      3 | A
      3 | B
      3 | C
(9 rows)

BTW:

For more numbers I believe it's handle to use generate_series function, e.g.:

SELECT n AS number, chr(ascii('A') + L - 1) AS letter
FROM
    generate_series(1, 5) N
CROSS JOIN
    generate_series(1, 5) L
ORDER BY N, L;

Result:

 number | letter
--------+--------
      1 | A
      1 | B
      1 | C
      1 | D
      1 | E
      2 | A
      2 | B
      2 | C
      2 | D
      2 | E
      3 | A
      3 | B
      3 | C
      3 | D
      3 | E
      4 | A
      4 | B
      4 | C
      4 | D
      4 | E
      5 | A
      5 | B
      5 | C
      5 | D
      5 | E
(25 rows)