On Jun 29, 2006, at 7:07 PM, John Randall wrote:
Henry Rich wrote:
The interpreter thinks
11&o. b. _1
_11&o.
but it ain't so. Circle functions 9-12 have no inverse that
I can see. Circle functions _9-_12 do, but they're not
the functions 9-12&o. that the interpreter uses.
Let f be the restriction of 11&o. to the reals. Then y-:_11&o. f y .
Similar restrictions to principal domains are presumably made in the
others.
Best wishes,
John
The table in the J Dictionary for circle is dear to me because I
invented it -- those from + and - 1 through 7. I was working in the
IBM Mohansic Lab when I showed it in 1968 to Ken and Adin and Larry
they accepted it immediately -- Adin was a tad reluctant, and Al Rose
was dubious, too.
It solved the sine, cosine et al. problem they had been wrestling
with: the design they had before I showed up used the monads of the
relationals for them. I pointed out that in my table the parity of
the number was odd or even as the function was odd or even -- and as
a consequence of this they offered me a job in their group at IBM
Research. You can read "The Story of O" in APL Quote Quad 8.2,
December 1977. This gives all the gory details.
If you look up Story of O on Wikipedia, you'll see that it originated
with a French movie of that name, that dealt with sado-masochistic
events. I was aware of this.
Eugene
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