Well, it is embarassing but it seems like I forgot what I learned 8 years ago.
http://jsoftware.com/pipermail/programming/2009-July/015308.html It looks like the APL's Binomial and J's Out of have the same behavioral model. On Mon, Apr 27, 2015 at 8:19 PM, June Kim (김창준) <[email protected]> wrote: > Hello > > I am translating Iverson's Notation as a Tool of Thought -- it is too be > published in a book called Great Papers in Computer Science in Korean. > > Reading the paper, I have a question about "binomial"(!). This mailing > list is of course about J, but I find this place very friendly and the > people here widely informed, I post it here. > > First, look at the passage from the paper: > > The symbol ! denotes the binomial coefficient function, and the table >> d∘.!d is seen to contain Pascal’s triangle with its apex at the left; >> if extended to negative arguments (as with d←¯3 ¯2 ¯1 0 1 2 3) it will >> be seen to contain the triangular and higher-order figurate numbers as well. > > > So the author means the outer product of binomial of _3 _2 _1 0 1 2 3 > contains figurate numbers. However, after looking up many manuals for > various versions of APL I couldn't find out clear descriptions for when the > arguments are negative(or one is negative and the other positive). I looked > up J dictionary and it didn't have clear definition for this case, either. > > Could anyone please help me out understanding what d∘.!d do with > d←¯3 ¯2 ¯1 0 1 2 3 ? > > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
