SELECT vec_to_string(parse_vec('[1.0, 2.0]'));

+----------------------------------------------+
| vec_to_string(parse_vec(Utf8("[1.0, 2.0]"))) |
+----------------------------------------------+
| [1,2]                                        |
+----------------------------------------------+

SELECT vec_to_string(parse_vec('[1.0, 2.0, 3.0]'));

+---------------------------------------------------+
| vec_to_string(parse_vec(Utf8("[1.0, 2.0, 3.0]"))) |
+---------------------------------------------------+
| [1,2,3]                                           |
+---------------------------------------------------+

SELECT vec_to_string(parse_vec('[]'));

+--------------------------------------+
| vec_to_string(parse_vec(Utf8("[]"))) |
+--------------------------------------+
| []                                   |
+--------------------------------------+

SELECT vec_to_string(vec_add('[1.0, 2.0]', '[3.0, 4.0]'));

+---------------------------------------------------------------+
| vec_to_string(vec_add(Utf8("[1.0, 2.0]"),Utf8("[3.0, 4.0]"))) |
+---------------------------------------------------------------+
| [4,6]                                                         |
+---------------------------------------------------------------+

SELECT vec_to_string(vec_add(parse_vec('[1.0, 2.0]'), '[3.0, 4.0]'));

+--------------------------------------------------------------------------+
| vec_to_string(vec_add(parse_vec(Utf8("[1.0, 2.0]")),Utf8("[3.0, 4.0]"))) |
+--------------------------------------------------------------------------+
| [4,6]                                                                    |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_add('[1.0, 2.0]', parse_vec('[3.0, 4.0]')));

+--------------------------------------------------------------------------+
| vec_to_string(vec_add(Utf8("[1.0, 2.0]"),parse_vec(Utf8("[3.0, 4.0]")))) |
+--------------------------------------------------------------------------+
| [4,6]                                                                    |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_mul('[1.0, 2.0]', '[3.0, 4.0]'));

+---------------------------------------------------------------+
| vec_to_string(vec_mul(Utf8("[1.0, 2.0]"),Utf8("[3.0, 4.0]"))) |
+---------------------------------------------------------------+
| [3,8]                                                         |
+---------------------------------------------------------------+

SELECT vec_to_string(vec_mul(parse_vec('[1.0, 2.0]'), '[3.0, 4.0]'));

+--------------------------------------------------------------------------+
| vec_to_string(vec_mul(parse_vec(Utf8("[1.0, 2.0]")),Utf8("[3.0, 4.0]"))) |
+--------------------------------------------------------------------------+
| [3,8]                                                                    |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_mul('[1.0, 2.0]', parse_vec('[3.0, 4.0]')));

+--------------------------------------------------------------------------+
| vec_to_string(vec_mul(Utf8("[1.0, 2.0]"),parse_vec(Utf8("[3.0, 4.0]")))) |
+--------------------------------------------------------------------------+
| [3,8]                                                                    |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_sub('[1.0, 1.0]', '[1.0, 2.0]'));

+---------------------------------------------------------------+
| vec_to_string(vec_sub(Utf8("[1.0, 1.0]"),Utf8("[1.0, 2.0]"))) |
+---------------------------------------------------------------+
| [0,-1]                                                        |
+---------------------------------------------------------------+

SELECT vec_to_string(vec_sub('[-1.0, -1.0]', '[1.0, 2.0]'));

+-----------------------------------------------------------------+
| vec_to_string(vec_sub(Utf8("[-1.0, -1.0]"),Utf8("[1.0, 2.0]"))) |
+-----------------------------------------------------------------+
| [-2,-3]                                                         |
+-----------------------------------------------------------------+

SELECT vec_to_string(vec_sub('[1.0, 1.0]', parse_vec('[1.0, 2.0]')));

+--------------------------------------------------------------------------+
| vec_to_string(vec_sub(Utf8("[1.0, 1.0]"),parse_vec(Utf8("[1.0, 2.0]")))) |
+--------------------------------------------------------------------------+
| [0,-1]                                                                   |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_sub('[-1.0, -1.0]', parse_vec('[1.0, 2.0]')));

+----------------------------------------------------------------------------+
| vec_to_string(vec_sub(Utf8("[-1.0, -1.0]"),parse_vec(Utf8("[1.0, 2.0]")))) |
+----------------------------------------------------------------------------+
| [-2,-3]                                                                    |
+----------------------------------------------------------------------------+

SELECT vec_to_string(vec_sub(parse_vec('[1.0, 1.0]'), '[1.0, 2.0]'));

+--------------------------------------------------------------------------+
| vec_to_string(vec_sub(parse_vec(Utf8("[1.0, 1.0]")),Utf8("[1.0, 2.0]"))) |
+--------------------------------------------------------------------------+
| [0,-1]                                                                   |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_sub(parse_vec('[-1.0, -1.0]'), '[1.0, 2.0]'));

+----------------------------------------------------------------------------+
| vec_to_string(vec_sub(parse_vec(Utf8("[-1.0, -1.0]")),Utf8("[1.0, 2.0]"))) |
+----------------------------------------------------------------------------+
| [-2,-3]                                                                    |
+----------------------------------------------------------------------------+

SELECT vec_elem_sum('[1.0, 2.0, 3.0]');

+---------------------------------------+
| vec_elem_sum(Utf8("[1.0, 2.0, 3.0]")) |
+---------------------------------------+
| 6.0                                   |
+---------------------------------------+

SELECT vec_elem_sum('[-1.0, -2.0, -3.0]');

+------------------------------------------+
| vec_elem_sum(Utf8("[-1.0, -2.0, -3.0]")) |
+------------------------------------------+
| -6.0                                     |
+------------------------------------------+

SELECT vec_elem_sum(parse_vec('[1.0, 2.0, 3.0]'));

+--------------------------------------------------+
| vec_elem_sum(parse_vec(Utf8("[1.0, 2.0, 3.0]"))) |
+--------------------------------------------------+
| 6.0                                              |
+--------------------------------------------------+

SELECT vec_elem_sum(parse_vec('[-1.0, -2.0, -3.0]'));

+-----------------------------------------------------+
| vec_elem_sum(parse_vec(Utf8("[-1.0, -2.0, -3.0]"))) |
+-----------------------------------------------------+
| -6.0                                                |
+-----------------------------------------------------+

SELECT vec_to_string(vec_div('[1.0, 2.0]', '[3.0, 4.0]'));

+---------------------------------------------------------------+
| vec_to_string(vec_div(Utf8("[1.0, 2.0]"),Utf8("[3.0, 4.0]"))) |
+---------------------------------------------------------------+
| [0.33333334,0.5]                                              |
+---------------------------------------------------------------+

SELECT vec_to_string(vec_div(parse_vec('[1.0, 2.0]'), '[3.0, 4.0]'));

+--------------------------------------------------------------------------+
| vec_to_string(vec_div(parse_vec(Utf8("[1.0, 2.0]")),Utf8("[3.0, 4.0]"))) |
+--------------------------------------------------------------------------+
| [0.33333334,0.5]                                                         |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_div('[1.0, 2.0]', parse_vec('[3.0, 4.0]')));

+--------------------------------------------------------------------------+
| vec_to_string(vec_div(Utf8("[1.0, 2.0]"),parse_vec(Utf8("[3.0, 4.0]")))) |
+--------------------------------------------------------------------------+
| [0.33333334,0.5]                                                         |
+--------------------------------------------------------------------------+

SELECT vec_to_string(vec_div('[1.0, -2.0]', parse_vec('[0.0, 0.0]')));

+---------------------------------------------------------------------------+
| vec_to_string(vec_div(Utf8("[1.0, -2.0]"),parse_vec(Utf8("[0.0, 0.0]")))) |
+---------------------------------------------------------------------------+
| [inf,-inf]                                                                |
+---------------------------------------------------------------------------+

SELECT vec_elem_product('[1.0, 2.0, 3.0, 4.0]');

+------------------------------------------------+
| vec_elem_product(Utf8("[1.0, 2.0, 3.0, 4.0]")) |
+------------------------------------------------+
| 24.0                                           |
+------------------------------------------------+

SELECT vec_elem_product('[-1.0, -2.0, -3.0, 4.0]');

+---------------------------------------------------+
| vec_elem_product(Utf8("[-1.0, -2.0, -3.0, 4.0]")) |
+---------------------------------------------------+
| -24.0                                             |
+---------------------------------------------------+

SELECT vec_elem_product(parse_vec('[1.0, 2.0, 3.0, 4.0]'));

+-----------------------------------------------------------+
| vec_elem_product(parse_vec(Utf8("[1.0, 2.0, 3.0, 4.0]"))) |
+-----------------------------------------------------------+
| 24.0                                                      |
+-----------------------------------------------------------+

SELECT vec_elem_product(parse_vec('[-1.0, -2.0, -3.0, 4.0]'));

+--------------------------------------------------------------+
| vec_elem_product(parse_vec(Utf8("[-1.0, -2.0, -3.0, 4.0]"))) |
+--------------------------------------------------------------+
| -24.0                                                        |
+--------------------------------------------------------------+

SELECT vec_to_string(vec_norm('[0.0, 2.0, 3.0]'));

+--------------------------------------------------+
| vec_to_string(vec_norm(Utf8("[0.0, 2.0, 3.0]"))) |
+--------------------------------------------------+
| [0,0.5547002,0.8320503]                          |
+--------------------------------------------------+

SELECT vec_to_string(vec_norm('[1.0, 2.0, 3.0]'));

+--------------------------------------------------+
| vec_to_string(vec_norm(Utf8("[1.0, 2.0, 3.0]"))) |
+--------------------------------------------------+
| [0.26726124,0.5345225,0.8017837]                 |
+--------------------------------------------------+

SELECT vec_to_string(vec_norm('[7.0, 8.0, 9.0]'));

+--------------------------------------------------+
| vec_to_string(vec_norm(Utf8("[7.0, 8.0, 9.0]"))) |
+--------------------------------------------------+
| [0.5025707,0.5743665,0.64616233]                 |
+--------------------------------------------------+

SELECT vec_to_string(vec_norm('[7.0, -8.0, 9.0]'));

+---------------------------------------------------+
| vec_to_string(vec_norm(Utf8("[7.0, -8.0, 9.0]"))) |
+---------------------------------------------------+
| [0.5025707,-0.5743665,0.64616233]                 |
+---------------------------------------------------+

SELECT vec_to_string(vec_norm(parse_vec('[7.0, -8.0, 9.0]')));

+--------------------------------------------------------------+
| vec_to_string(vec_norm(parse_vec(Utf8("[7.0, -8.0, 9.0]")))) |
+--------------------------------------------------------------+
| [0.5025707,-0.5743665,0.64616233]                            |
+--------------------------------------------------------------+

SELECT vec_to_string(vec_sum(v))
FROM (
    SELECT '[1.0, 2.0, 3.0]' AS v
    UNION ALL
    SELECT '[-1.0, -2.0, -3.0]' AS v
    UNION ALL
    SELECT '[4.0, 5.0, 6.0]' AS v
);

+---------------------------+
| vec_to_string(vec_sum(v)) |
+---------------------------+
| [4,5,6]                   |
+---------------------------+

SELECT vec_to_string(vec_product(v))
FROM (
    SELECT '[1.0, 2.0, 3.0]' AS v
    UNION ALL
    SELECT '[-1.0, -2.0, -3.0]' AS v
    UNION ALL
    SELECT '[4.0, 5.0, 6.0]' AS v
);

+-------------------------------+
| vec_to_string(vec_product(v)) |
+-------------------------------+
| [-4,-20,-54]                  |
+-------------------------------+

SELECT vec_dim('[7.0, 8.0, 9.0, 10.0]');

+----------------------------------------+
| vec_dim(Utf8("[7.0, 8.0, 9.0, 10.0]")) |
+----------------------------------------+
| 4                                      |
+----------------------------------------+

SELECT v, vec_dim(v)
FROM (
         SELECT '[1.0, 2.0, 3.0]' AS v
         UNION ALL
         SELECT '[-1.0]' AS v
         UNION ALL
         SELECT '[4.0, 5.0, 6.0]' AS v
     ) Order By vec_dim(v) ASC;

+-----------------+------------+
| v               | vec_dim(v) |
+-----------------+------------+
| [-1.0]          | 1          |
| [1.0, 2.0, 3.0] | 3          |
| [4.0, 5.0, 6.0] | 3          |
+-----------------+------------+

SELECT v, vec_dim(v)
FROM (
         SELECT '[1.0, 2.0, 3.0]' AS v
         UNION ALL
         SELECT '[-1.0]' AS v
         UNION ALL
         SELECT '[7.0, 8.0, 9.0, 10.0]' AS v
     ) Order By vec_dim(v) ASC;

+-----------------------+------------+
| v                     | vec_dim(v) |
+-----------------------+------------+
| [-1.0]                | 1          |
| [1.0, 2.0, 3.0]       | 3          |
| [7.0, 8.0, 9.0, 10.0] | 4          |
+-----------------------+------------+

SELECT vec_to_string(vec_subvector('[1.0,2.0,3.0,4.0,5.0]', 0, 3));

+-------------------------------------------------------------------------------+
| vec_to_string(vec_subvector(Utf8("[1.0,2.0,3.0,4.0,5.0]"),Int64(0),Int64(3))) |
+-------------------------------------------------------------------------------+
| [1,2,3]                                                                       |
+-------------------------------------------------------------------------------+

SELECT vec_to_string(vec_subvector('[1.0,2.0,3.0,4.0,5.0]', 5, 5));

+-------------------------------------------------------------------------------+
| vec_to_string(vec_subvector(Utf8("[1.0,2.0,3.0,4.0,5.0]"),Int64(5),Int64(5))) |
+-------------------------------------------------------------------------------+
| []                                                                            |
+-------------------------------------------------------------------------------+

SELECT v, vec_to_string(vec_subvector(v, 3, 5))
FROM (
     SELECT '[1.0, 2.0, 3.0, 4.0, 5.0]' AS v
     UNION ALL
     SELECT '[-1.0, -2.0, -3.0, -4.0, -5.0, -6.0]' AS v
     UNION ALL
     SELECT '[4.0, 5.0, 6.0, 10, -8, 100]' AS v
) ORDER BY v;

+--------------------------------------+---------------------------------------------------+
| v                                    | vec_to_string(vec_subvector(v,Int64(3),Int64(5))) |
+--------------------------------------+---------------------------------------------------+
| [-1.0, -2.0, -3.0, -4.0, -5.0, -6.0] | [-4,-5]                                           |
| [1.0, 2.0, 3.0, 4.0, 5.0]            | [4,5]                                             |
| [4.0, 5.0, 6.0, 10, -8, 100]         | [10,-8]                                           |
+--------------------------------------+---------------------------------------------------+

SELECT vec_to_string(vec_subvector(v, 0, 5))
FROM (
     SELECT '[1.1, 2.2, 3.3, 4.4, 5.5]' AS v
     UNION ALL
     SELECT '[-1.1, -2.1, -3.1, -4.1, -5.1, -6.1]' AS v
     UNION ALL
     SELECT '[4.0, 5.0, 6.0, 10, -8, 100]' AS v
) ORDER BY v;

+---------------------------------------------------+
| vec_to_string(vec_subvector(v,Int64(0),Int64(5))) |
+---------------------------------------------------+
| [-1.1,-2.1,-3.1,-4.1,-5.1]                        |
| [1.1,2.2,3.3,4.4,5.5]                             |
| [4,5,6,10,-8]                                     |
+---------------------------------------------------+