[Jprogramming] Exponentiation with subtraction

[Roger Hui]

To get rid of the constants from my solution, 
replace the first 0 by -~@[ and the others by = . 



----- Original Message ----- 
From: "Oleg Kobchenko" <olegykj at yahoo.com>
To: "Programming forum" <programming at jsoftware.com>
Sent: Wednesday, January 25, 2006 10:23 PM
Subject: Re: [Jprogramming] Exponentiation with subtraction

With N=12 on 256 Mb limit this solution gives
"limit error".

One solution that I have is better than
x*k^i.N on ts by factors of 7.2 2.1
with N=1000x .

I just thought, for additional bonus point,
the expression would not use any constants
other than the three x,k and N.



--- Roger Hui <RHui000 at shaw.ca> wrote:

> Spoiler solution at the end of msg.
> 
> 
> 
> ----- Original Message ----- 
> From: "Oleg Kobchenko" <olegykj at yahoo.com>
> To: "Programming forum" <programming at jsoftware.com>
> Sent: Wednesday, January 25, 2006 5:55 PM
> Subject: [Jprogramming] Exponentiation with subtraction
> 
> This is a little simple puzzle, so who knew may hold for
> those who actually has to figure it out.
> 
> Find an expression for a sequence
> 
>    x*k^i.N   for any real x and positive integers k, N
> 
> e.g.
> 
>    7.5*5^i.8
> 7.5 37.5 187.5 937.5 4687.5 23437.5 117188 585938
> 
> using subtraction (dyadic -) as the only numeric operation.
> That is only structural operations are allowed besides 
> constants (i. or @. are OK, x o. or m b. are not).
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
>    plus =: [ - 0 - ]
>    times=: plus /@$~"0  NB. x+i
>    pow  =: times/@$~"0  NB. x^i
> 
>    7.5 times times/\ 1,7$5
> 7.5 37.5 187.5 937.5 4687.5 23437.5 117188 585938
> 
>    7.5 times 5 pow i.8
> 7.5 37.5 187.5 937.5 4687.5 23437.5 117188 585938