Exercising on tacit verbs I succeed to define
the Mobius function.
Explicit version:
mobiusX=: 3 : 0
ms=.{:__ q: y
if. 0=+/1<ms do. _1^+/ms else. 0 end.
)
mobiusX"0 [1+i.16
1 _1 _1 0 _1 1 _1 0 0 1 _1 0 _1 1 1 0
Tacit version
mobiusT=: [: 0: ` (_1^#) @. (0= [:+/1<]) [: {: __ q: ]
For the value of mobius N = (-1)^r in case N is the product
of r different primes, one may use (_1^#) or (_1^+/) because
in this case they are equivalent:
- determining the length of the list of exponents
- summing the one's of the exponents.
It's also very convenient that they both handle the special
case for mobius 1 = 1.
In case mobius N is not square free the result has to be 0,
so I have to use the constant function 0:.
mobiusT"0 [1+i.16
1 _1 _1 0 _1 1 _1 0 0 1 _1 0 _1 1 1 0
a.{~q:9991
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