user variable ist not assigned when using function like SUM(), MAX(), AVG()

Hello,

this is may first bug report so I don't really know exactly what and how to
tell ...

The bug appears in all tested versions:
4.0.12-nt/Windows 2000 prof. SP4
4.0.15/Linux/SuSE
4.0.17-nt/Windows XP prof. SP1
4.0.20-nt/Windows 2000 prof. SP4
5.0.00-alpha/Windows XP prof. SP1

User variables are assigned correctly with
    SELECT @var := value;

This fails when one of the the following functions is used
    MIN(), MAX(), SUM(), AVG(), COUNT() ...
    

Screenshot of command line sequence:

--------------------- 8< ---------------------------

mysql> -- MySQL dump 9.11
mysql> --
mysql> -- Host: localhost    Database: test
mysql> -- ------------------------------------------------------
mysql> -- Server version       4.0.20a-nt
mysql>
mysql> --
mysql> -- Table structure for table `test`
mysql> --
mysql>
mysql> CREATE TABLE test (
    ->   a int(11) default NULL
    -> ) TYPE=MyISAM;
Query OK, 0 rows affected (0.05 sec)

mysql> --
mysql> -- Dumping data for table `test`
mysql> --
mysql>
mysql> INSERT INTO test VALUES (1);
Query OK, 1 row affected (0.00 sec)

mysql> INSERT INTO test VALUES (2);
Query OK, 1 row affected (0.00 sec)

mysql> INSERT INTO test VALUES (3);
Query OK, 1 row affected (0.00 sec)

mysql> INSERT INTO test VALUES (4);
Query OK, 1 row affected (0.00 sec)

mysql> INSERT INTO test VALUES (5);
Query OK, 1 row affected (0.00 sec)

mysql> SET @var = "";
Query OK, 0 rows affected (0.00 sec)

mysql> SELECT @var := t.a, @var
    -> FROM test t;
+-------------+------+
| @var := t.a | @var |
+-------------+------+
|           5 | 5    |
|           4 | 4    |
|           3 | 3    |
|           2 | 2    |
|           1 | 1    |
+-------------+------+
5 rows in set (0.02 sec)

mysql> SET @var = "";
Query OK, 0 rows affected (0.00 sec)

mysql> SELECT @var := SUM(t.a), @var
    -> FROM test t
    -> GROUP BY t.a;
+------------------+------+
| @var := SUM(t.a) | @var |
+------------------+------+
|                1 |      |
|                2 |      |
|                3 |      |
|                4 |      |
|                5 |      |
+------------------+------+
5 rows in set (0.05 sec)

mysql> SELECT @var;
+------+
| @var |
+------+
|    5 |
+------+
1 row in set (0.00 sec)

--------------------- >8 ---------------------------

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