First thing to do, when suspecting a typo, is to try it out with example data.
So, I defined a couple words in J and translated his sentences: I=:1 + i. N=:5 +/I N 15 +/|.I N 15 ((+/I N)+(+/|.I N))%2 15 (+/(I N)+(|.I N))%2 15 (+/((N+1)$N))%2 15 ((N+1)*N)%2 15 So I'm not seeing any obvious signs that there were any typos here. Also, if we expand the I N parts, it looks like this: +/1 2 3 4 5 15 +/5 4 3 2 1 15 ((+/1 2 3 4 5)+(+/5 4 3 2 1))%2 15 (+/(1 2 3 4 5)+(5 4 3 2 1))%2 15 (+/((5+1)$5))%2 15 ((5+1)*5)%2 15 And, expressed this way, I guess I might like to see between the fourth and fifth statement something like this: +/(6 6 6 6 6)%2 15 +/(5 5 5 5 5 5)%2 15 The first of that pair uses the result of (1 2 3 4 5)+(5 4 3 2 1) The second of that pair uses an expansion of ((5+1)$5) But I'd worry, also, that by taking such small steps that I might bore and lose the reader. So I am undecided about the best approach here. Still, perhaps, instead of ((N+1)$N) that sub-expression in the fifth statement should instead be (N$(N+1)) - and perhaps the possibility of this more direct form is what you were referring to when you asked about a typo? Thanks, -- Raul On Mon, Jul 27, 2015 at 9:20 AM, June Kim (김창준) <[email protected]> wrote: > Hello > > I am still translating Iverson's paper. It really takes time. One more > question: > > <quote> > +/⍳n+/⌽⍳n+ is associative and commutative((+/⍳n)+(+/⌽⍳n))÷2(x+x)÷2←→x > (+/(⍳n)+(⌽⍳n))÷2+ is associative and commutative(+/((n+1)⍴n))÷2Lemma > ((n+1)×n)÷2Definition of × > > The fourth annotation above concerns an identity which, after observation > of the pattern in the special case (⍳5)+(⌽⍳5) , might be considered obvious > or might be considered worthy of formal proof in a separate lemma. > > http://www.jsoftware.com/papers/tot.htm > > </quote> > > In the above, I think more natural way of thinking is, the fifth line > should've been instead (+/(n⍴n+1))÷2,since (⍳n)+(⌽⍳n) is identical to n⍴n+1. > > Do you also think this was a typo? Or is there any other thing that I am > missing? > > June > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
