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
