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Dear All, 

Happy New Year

I´m back to a lot of work with sets, subsets and supersets and I have an idea/suggestion:

 

When evaluating this

(pcs-super-sets 7 (pcs '3-1) :forte)

I get this result

(7-1 7-2 7-2b 7-3 7-3b 7-4 7-4b 7-5 7-5b 7-6 7-6b 7-7 7-7b 7-8 7-9 7-9b 7-10 7-10b 7-11 7-11b 7-z12 7-13 7-13b 7-14 7-14b 7-15 7-16 7-16b 7-z17 7-z18 7-z18b 7-19 7-19b 7-20 7-20b 7-21 7-21b 7-22 7-23 7-23b 7-24 7-24b 7-25 7-25b 7-26 7-26b 7-27 7-27b 7-28 7-28b 7-29 7-29b 7-30 7-30b 7-33 7-z36 7-z36b 7-z37 7-z38 7-z38b)

These are all the supersets of cardinality 7 of the 3-1 set.

Would be very nice in this context to have a keyword to invert the result, i.e., actually showing the excluded sets, like all the sets that ARE NOT supersets of the 3-1 set.

Like inverting, like a (pcs-non-super-sets) function. I think that maybe it´s not so difficult, because the algorythm of the function already give the result, the only thing necessary is that the function return exactly the opposite result.

 

Best,

Julio

 

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A more specific example

(pcs-super-sets 4 (pcs '3-1) :forte)
;; (4-1 4-2 4-2b 4-4 4-4b 4-5 4-5b 4-6)

(pcs-super-sets 4 (pcs '3-1) :forte :complementary)
;; (all other 4 note sets, except 4-1 4-2 4-2b 4-4 4-4b 4-5 4-5b 4-6)

Best,

Julio

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(let ((out (pcs-cardinal 4 :forte)))
  (loop for i in (pcs-super-sets 4 (pcs '3-1) :forte)
    do (setf out (remove i out))
    finally (return out)))
(let ((rem (pcs-cardinal 7 :forte))
      (super (pcs-super-sets 7 (pcs '3-1) :forte)))
  (loop for i in super
    do (setf rem (remove i rem))
    finally (return rem)))
=> (7-31 7-31b 7-32 7-32b 7-34 7-35)

here it is.

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