I was trying to put myself to sleep last night by
working out (tacit) ways to list the distinct factors
of positive integers. Is there a better way than
simply sieving through all the candidates less
than or equal to the square root of the number ?
But my sleeplessness was prolonged by the thought
that the fit conjunction could be used on q: to give
a variety of integer decompositions and allow
efficient implementation. The following usage for
right operands of fit sprang to my mind before
I dropped off to sleep.
* Positives: decomposition
* Others: distinct factors
* 0 : list of distinct factors
* 1 : as is, that is, prime decomposition
* 2 : semiprime decomposition
* 3 : decomposition into products of three primes
* 4 : " " " 4 " . . .
I would think the semiprime decomposition would
most interestingly pair successively pair the head
and tail of the prime list, leaving the centre of an
odd number of primes as prime to complete the
decomposition. !.4 could take pairs from the head
and tail, and !.3 and !.5 could take the extra prime
from the centre of the list. This approach should
give a more interesting list than most other
approaches.
As for the negatives, maybe
* _1 : distinct prime factors (nub of !.1)
* _2 : distinct semiprime factors (not nub of !.2)
* _3 : distinct tri-prime factors . . .
An interesting question is whether ^:_1 on these
would usefully return the least integer with these
distinct factors.
An even wilder speculation, just before I got to
sleep, was whether complex operands for fit
mightn't be interesting, for example to reveal that
2 is 1j1*1j_1, i.e., not prime in the complex domain.
Is this the right forum for a suggestion or
speculation of this kind ?
Neville Holmes, P.O.Box 404, Mowbray 7248, Tasmania
Normal e-mail: [EMAIL PROTECTED]
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