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
