Unifying small and great divide
Looking at the small and great divide in DTATRM with the modification on page 181 to switch the per and the operands, I believe that they can be unified to one operation.
- Small divide to find the suppliers that supply all purple parts:
WITH ( P WHERE COLOR = COLOR('Purple') )AS PP:
SP { S#, P# } DIVIDEBY PP { P# } PER ( S { S# } )
which can be implemented as
WITH ( P WHERE COLOR = COLOR('Purple') )AS PP,
( S { S# } JOIN PP { P# } )AS QQ,
( QQ MINUS SP { S#, P# } )AS RR: //(a)
S { S# } MINUS RR { S# }
2. Great divide to find the suppliers that supply all red parts for a project
WITH ( PJ JOIN ( P WHERE COLOR = COLOR('Red') ) AS RPJ:
SP { S#, P# } DIVIDEBY RPJ { P#, J# } PER ( S { S# } , J { J# } )
which can be implemented as:
( S { S# } JOIN J { J# } )MINUS ( ( S { S# } JOIN RPJ { P#, J# } )MINUS ( SP { S#, P# }JOIN RPJ { P#, J# } ) ) { S#, J# }
which can be rewritten as:
WITH ( S { S# } JOIN J { J# } ) AS SJ,
( S { S# } JOIN RPJ { P#, J# } ) AS QQ, //(b)
(QQ MINUS ( SP { S#, P# }JOIN RPJ { P#, J# } )) AS RR,
SJ {S#, J#} MINUS RR{S#, J#}
Now I observe that in the small divide:
( QQ MINUS SP { S#, P# } )AS RR: //(a)
can just as well be written:
( QQ MINUS (SP { S#, P# } JOIN PP{P#} )AS RR: //(a)
and in the great divide
( S { S# } JOIN RPJ { P#, J# } ) AS QQ, //(b)
can just as well be written:
( SJ { S#, J# } JOIN RPJ { P#, J# } ) AS QQ, //(b)
So, we have it complete that
A DIVIDEBY B PER C
is implemented as
WITH ( C JOIN B ) AS QQ,
( QQ MINUS (A JOIN B) )AS RR:
C MINUS RR
Where for the small divide example A = SP, B=PP and C=S
and for the great divide example A = SP, B=RPJ and C=SJ
Is that correct?