Those are some nice ones, and I sort of wish I could go back in time
and use your "trainspotting" as the subject line for this thread.
Also, worth trying:
2 -~/\^:11 f"0 i. 34
(given the definition of 'f' which you spotted.)
I had not realized before that projecting that series backwards would
make so much sense.
Thanks,
--
Raul
On Thu, Jan 16, 2014 at 12:02 AM, Roger Hui <rogerhui.can...@gmail.com> wrote:
> Dyalog APL will have forks in the next version, an occasion which led me to
> make up a list of evocative forks ("trainspotting"). Some selections from
> this list, transcribed back into J from APL:
>
>>./ - <./ range
> +,-,*,% “function vector”
> _10&< *. <&10 open interval; numbers between _10 and 10
> _10&<: *. <:&10 closed interval
> 1 = *:@(1&o.) + *:@(2&o.) Pythagorean theorem for the unit circle
> f=: i. +/ .! |.@i. Try f"0 i.12
> bc=: 1&, + ,&1 next set of binomial coefficients; e.g. bc^:(i.12) 1 .
> See Figure 1 of Falkoff and Iverson, *The
> APL\360 Terminal System
> <http://www.jsoftware.com/papers/APL360TerminalSystem.htm>*, 1967.
> m|^ called “powermod” in Mathematica
> 1 i.~ c also 0 i.~ c, for c one of < <: = ~: >: >
> (0.5 * ] + %)^:_~ square root by Newton iteration
>
>
>
>
> On Wed, Jan 15, 2014 at 8:44 PM, Roger Hui <rogerhui.can...@gmail.com>wrote:
>
>> http://keiapl.org/anec/#nvv
>>
>> sin=: 1 o. ]
>> cos=: 2 o. ]
>> (^@j. = cos + 0j1 * sin) 1 2 3 0.1j_0.2
>> 1 1 1 1
>>
>> (^@j. = cos j. sin) 1 2 3 0.1j_0.2
>> 1 1 1 1
>>
>> The insight that led to the invention of the j. function illustrates what
>> separate genius from mere mortals. Who would think of inventing a function
>> whose monad is 0j1*y and whose dyad is x+0j1*y? Too simple.
>>
>> The above equation is Euler's formula, a special case of which is Euler's
>> identity, 0 = 1 + ^ 1p1 * 0j1, the most beautiful equation in all of
>> mathematics. Concerning Euler's identity, let me share with you something
>> I came across recently:
>>
>> e raised to the pi times i,
>> And plus 1 leaves you nought but a sigh,
>> This fact amazed Euler,
>> That genius toiler,
>> And still gives us pause, bye the bye.
>>
>> —— John Scholes, http://dfns.dyalog.com/n_Euler.htm
>>
>>
>>
>>
>>
>>
>> On Wed, Jan 15, 2014 at 8:03 PM, Raul Miller <rauldmil...@gmail.com>wrote:
>>
>>> I think we some simple, evocative fork examples which are not mean.
>>>
>>> One possibility is fahrenheit to centigrade conversion:
>>>
>>> (5r9 * -&32)
>>>
>>> Another might be area of a circle with the given radius:
>>>
>>> (2 * o.)
>>>
>>> What might some others be? Perhaps a dyadic use of fork could be both
>>> simple to express and easy to think of as useful?
>>>
>>> Thanks,
>>>
>>> --
>>> Raul
>>> ----------------------------------------------------------------------
>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>
>>
>>
> ----------------------------------------------------------------------
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