If you're going to use dissect, get 3.6.42 (released today). Previous
versions had a confusing title for the verbs.
Even with the picture it's amazing what this little phrase does. Two
nested powers, with the result of one power feeding back into the
exponent of the next iteration of the same verb.
Henry Rich
On 2/18/2015 7:12 PM, Jose Mario Quintana wrote:
((2x&*) &1) 3
8
((2x&*)^:3) 1
8
((3x&*) &1) 2
9
((3x&*)^:2) 1
9
Does dissect
http://www.jsoftware.com/jwiki/action/show/Vocabulary/Dissect?action=show&redirect=Addons%2Fdebug%2Fdissect
help to follow the execution of the sentences?
On Wed, Feb 18, 2015 at 4:14 PM, 'Pascal Jasmin' via Programming <
[email protected]> wrote:
I don't follow this completely either. Though I am pretty sure the answer
is rooted in applying a bonded verb dyadically.
see right and bottom of:
http://www.jsoftware.com/help/dictionary/d630n.htm
----- Original Message -----
From: Fausto Saporito <[email protected]>
To: programming <[email protected]>
Cc:
Sent: Wednesday, February 18, 2015 1:00 PM
Subject: Re: [Jprogramming] Fwd: Hello all!
Hello,
just a clarification about the "up" verb defined above.
I know "&" is a conjuction bond, used for example in expressions like
"10^&"... but I don't understand the "&1" format ...
Please could you explain this ?
thanks
Fausto
2015-02-18 18:29 GMT+01:00 Fausto Saporito <[email protected]>:
yes... there's also another definition (recursive) called hyperoperation.
https://en.wikipedia.org/wiki/Hyperoperation
2015-02-18 18:20 GMT+01:00 R.E. Boss <[email protected]>:
Link?
Notice that Conway (who else?) in The Book of Numbers wrote a
generalization
of Knuth's up-notation (actually the Ackermann notation), his chained
arrow
notation.
R.E. Boss
-----Original Message-----
From: [email protected] [mailto:programming-
[email protected]] On Behalf Of John Baker
Sent: woensdag 18 februari 2015 16:15
To: [email protected]
Subject: Re: [Jprogramming] Fwd: Hello all!
Very slick. I was just reading Scott Aronson's fine blog post about the
Busy
Beaver problem and he commented on Knuth's up up notation. If anyone's
interested in very large numbers Aronson's post is a superb overview.
Sent from my iPhone
On Feb 17, 2015, at 3:05 PM, Jose Mario Quintana
<[email protected]> wrote:
This a way to produce numbers using the Knuth up arrow notation in J:
Knuth=. &* NB. (adv)
up=. &1 NB. (adv)
2x Knuth up up 4 5
65536
2003529930406846464979072351560255750447825475569751419265016973710
8940595563114530895061308809333481010382343429072631818229493821188
1266886950636476154702916504187191635158796634721944293092798208430
9104855990570159318959639524863372367203002916969...
# @: ": 2x Knuth up up 5
19729
6x Knuth up up 3
2659119772153226779682489404387918594905342200269924300660432789497
0735598738829091213422929061755830324406828265067234256016357755902
7938964261261109302039893034777446061389442537960087466214788422902
2133853819192905427915750759274952935109319020362271989...
#@: ": 6x Knuth up up 3
36306
3x Knuth up up up 0 1 2
1 3 7625597484987
2x Knuth up up 6 NB. It is toooooooooooo big!
On Tue, Feb 17, 2015 at 2:23 PM, Fausto Saporito
<[email protected]>
wrote:
Hello,
yes the number is very big, but why if I don't use the extended
precision I have "infinity" as result, and if I use it I got an
error
?
I should get infinity anyways.
this is my J session:
^/ 2 2 2 2
65536
^/ 2 2 2 2 2 NB. do not use extended precision and I have
"+inf"
_
^/ 2 2 2 2 2 2 NB. do not use extended precision and I have "+inf"
_
^/ x: 2 2 2 2 2 NB. using extended precision I have the result
(part
of
it)
2003529930406846464979072351560255750447825475569751419265016973710
8940595563114530895061308809333481010382343429072631818229493821188
1266886950636476154702916504187191635158796634721944293092798208430
9104855990570159318959639524863372367203002916969592156...
^/ x: 2 2 2 2 2 2 NB. using extended precision I have error... not
"+inf"
|limit error
| ^/x:2 2 2 2 2 2
https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
thanks,
Fausto
2015-02-17 18:55 GMT+01:00 'Pascal Jasmin' via Programming
<[email protected]>:
2 ^. ^/ 5 # 2x
65536
so at just 5, it is a 65k bit number
at 6, the 2log of that number would be that 65kbit number. The
number
of atoms in the universe is an 80 bit number.
----- Original Message -----
From: Raul Miller <[email protected]>
To: Programming forum <[email protected]>
Cc:
Sent: Tuesday, February 17, 2015 12:32 PM
Subject: Re: [Jprogramming] Fwd: Hello all!
I would guess that the number you are generating is too big to be
represented using J's data structures (which would also suggest
that
it would be too big to fit into memory).
Thanks,
--
Raul
On Tue, Feb 17, 2015 at 12:12 PM, Fausto Saporito
<[email protected]> wrote:
HI!
I'm a new J user with a little experience of APL and LISP.
In these days I'm playing with big numbers... very big indeed,
and I
found a bug (?) in the exteded precision implementation of J.
I'm not sure if I can call it a bug, but if I use the standard
precision number I got a "infinity" as result... as should be.
I'm talking about knuth-up-arrow notation, to build the "tower of
power". In J the syntax is amazingly simple : ^/ 2 2 2 2
2^^4 is 2 * (2* (2* 2)) = 65536
Now 2^^5 is _ with standard precision... but if I use x: (i.e.
^/ x:
2 2 2 2 2) can get most of number... it's quite big indeed.
The problem arises with 2^^6 or 3^^4 I get "limit error" instead
of _
... why ?
Is it an expected behaviour ?
thanks in advance,
Fausto
----------------------------------------------------------------------
For information about J forums see
http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see
http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see
http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see
http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see
http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
