In some circumstances you can do work with exponential towers much taller than 2^10^100. For example, what are the last 20 decimal digits of 37^41^43^5000 ? Answer: http://www.jsoftware.com/jwiki/Essays/Multiplicative_Order
----- Original Message ----- From: Roger Hui <[email protected]> Date: Friday, April 10, 2009 8:31 Subject: Re: [Jchat] 2147483647|16807^2147483646 To: Chat forum <[email protected]> > As already described in this thread, you need to do: > > 16807x (2147483647x&|@^) 2147483646x > 1 > 16807 (2147483647&|@^) 2147483646 > 1 > > The reason why the mathematically equivalent > > 2147483647|16807^2147483646 > |NaN error > | 2147483647 |16807^2147483646 > > doesn't work is that with this the system FIRST > computes 16807^2147483646 , getting infinity, > whence 2147483647|blah generates NaN. > > a m&|@^ b allows computation of things that you'd > never be able to do with m|a^b . For example, > what are the last 6 decimal digits of 2^10^100 ? > This number has 10^100 bits, larger than the number > of particles in the universe, so you can not first > compute 2^10^100 and then find its residue mod 1e6. > Instead: > > 2 (1e6&|@^) 10^100x > 109376 > > > > ----- Original Message ----- > From: bill lam <[email protected]> > Date: Friday, April 10, 2009 1:43 > Subject: [Jchat] 2147483647|16807^2147483646 > To: JChat <[email protected]> > > > In At play with J 8.3, the author said > > "2147483647|16807^2147483646 is > > equal 1". When I tried to verify it, > > 2147483647|16807^2147483646 > > |NaN error > > | 2147483647 |16807^2147483646 > > 2147483647|16807^2147483646x > > |limit error > > | 2147483647|16807 ^2147483646 > > > > Did the author just prove it instead of try it? Or that can > only be > > run in APL\360? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
