QUERY: CREATE TABLE CIRCLE_TBL (f1 circle);
QUERY: INSERT INTO CIRCLE_TBL VALUES ('<(0,0),3>');
QUERY: INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');
QUERY: INSERT INTO CIRCLE_TBL VALUES ('1,3,5');
QUERY: INSERT INTO CIRCLE_TBL VALUES ('((1,2),3)');
QUERY: INSERT INTO CIRCLE_TBL VALUES ('<(100,200),10>');
QUERY: INSERT INTO CIRCLE_TBL VALUES ('<(100,0),100>');
QUERY: INSERT INTO CIRCLE_TBL VALUES ('<(-100,0),-100>');
WARN:Bad circle external representation '<(-100,0),-100>'
QUERY: INSERT INTO CIRCLE_TBL VALUES ('1abc,3,5');
WARN:Bad circle external representation '1abc,3,5'
QUERY: INSERT INTO CIRCLE_TBL VALUES ('(3,(1,2),3)');
WARN:Bad circle external representation '(3,(1,2),3)'
QUERY: SELECT * FROM CIRCLE_TBL;
f1            
--------------
<(0,0),3>     
<(1,2),100>   
<(1,3),5>     
<(1,2),3>     
<(100,200),10>
<(100,0),100> 
(6 rows)

QUERY: SELECT '' AS six, center(f1) AS center
  FROM CIRCLE_TBL;
six|center   
---+---------
   |(0,0)    
   |(1,2)    
   |(1,3)    
   |(1,2)    
   |(100,200)
   |(100,0)  
(6 rows)

QUERY: SELECT '' AS six, radius(f1) AS radius
  FROM CIRCLE_TBL;
six|radius
---+------
   |     3
   |   100
   |     5
   |     3
   |    10
   |   100
(6 rows)

QUERY: SELECT '' AS six, diameter(f1) AS diameter
  FROM CIRCLE_TBL;
six|diameter
---+--------
   |       6
   |     200
   |      10
   |       6
   |      20
   |     200
(6 rows)

QUERY: SELECT '' AS two, f1 FROM CIRCLE_TBL WHERE radius(f1) < 5;
two|f1       
---+---------
   |<(0,0),3>
   |<(1,2),3>
(2 rows)

QUERY: SELECT '' AS four, f1 FROM CIRCLE_TBL WHERE diameter(f1) >= 10;
four|f1            
----+--------------
    |<(1,2),100>   
    |<(1,3),5>     
    |<(100,200),10>
    |<(100,0),100> 
(4 rows)

QUERY: SELECT '' as five, c1.f1 AS one, c2.f1 AS two, (c1.f1 <===> c2.f1) AS distance
  FROM CIRCLE_TBL c1, CIRCLE_TBL c2
  WHERE (c1.f1 < c2.f1) AND ((c1.f1 <===> c2.f1) > 0)
  ORDER BY distance, one, two;
five|one           |two           |        distance
----+--------------+--------------+----------------
    |<(100,200),10>|<(100,0),100> |              90
    |<(100,200),10>|<(1,2),100>   |111.370729772479
    |<(1,3),5>     |<(100,200),10>|205.476756144497
    |<(1,2),3>     |<(100,200),10>|208.370729772479
    |<(0,0),3>     |<(100,200),10>|210.606797749979
(5 rows)