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From: ForthNet@willett.pgh.pa.us (ForthNet articles from GEnie)
Newsgroups: comp.lang.forth
Subject: ANS TC Magnet for Division
Message-ID: <2645.UUL1.3#5129@willett.pgh.pa.us>
Date: 18 Apr 91 02:57:14 GMT
Organization: (n.) to be organized.  But that's not important right now.
Lines: 39

Category 10,  Topic 17
Message 82        Wed Apr 17, 1991
R.BERKEY                     at 01:57 PDT
 
  Zarko Berberski writes, 91-04-09,

 > ..."the mathematical use of" MOD is not as an operator but as a
 > qualifier of equivalence statemant...


From Graham, Knuth, Patashnik, _Concrete Mathametics_, Addison-Wesley
Publishing Co.: 1989, p. 82, Chapter 3.4, 'MOD': THE BINARY OPERATION:


         x mod y = x - (y * floor(x/y)),  for  y <> 0.      (3.21)

      This defines 'mod' as a binary operation, just as addition
      and subtraction are binary operations.  Mathematicians have
      used mod this way informally for a long time, taking various
      quantities mod 10, mod 2*pi, and so on, but only in the last
      twenty years has it caught on formally.  Old notion, new
      notation.


 > ...so there is no popular computer language that implements the MOD
 > the way we are using it in mathematics.

This statement allows that there are some "unpopular" languages that implement
the MOD.  Languages implementing the MOD function on at least the positive
integer domain of y include PASCAL, Modula-2, Smalltalk, APL, Ada, FORTRAN and
Forth.  (FORTRAN's syntax of "MOD" is something different: the name used there
for the MOD operator is "MODULUS".)

Robert Berkey
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