[Jprogramming] forward differences

[Henry Rich]

Tacitly,

  diffadv =: (}. - }:) ^:

 > My guess, interpreting the verb-making form, is that ]
> denotes values that differ on each cycle. If this is
> accurate, I've learned something about power.
> 
I don't think you have this right, but I'm not clear about
what you're saying.

Henry Rich

> -----Original Message-----
> From: programming-bounces at jsoftware.com 
> [mailto:programming-bounces at jsoftware.com] On Behalf Of Tracy Harms
> Sent: Thursday, December 13, 2007 2:55 PM
> To: programming at jsoftware.com
> Subject: [Jprogramming] forward differences
> 
> Thank you, Messrs. Rich, Boss, Miller and McCormick
> for the helpful replies.
> 
> I can add to the list of solutions the following:
> 
>    diffadv=: 1 :'(}. - }:)^:u'
>    2 diffadv (i.10)^5
> 30 180 570 1320 2550 4380 6930 10320
>    
> Although I don't know how to refer to them, I find two
> very different contexts in J composition. One is where
> verbs are *used*, the other is where verbs are
> *formed.* Examples of each, here:
> 
>    list=: (i.10)^5
>    order=: 3   NB. i.e. third-order
> 
>    ]noun=: (}. - }:)^:order list
> 150 390 750 1230 1830 2550 3390
>    
>    ]verb=: (}. - }:)@]^:[
> ] (}. - }:)@]^:[
>    order verb list
> 150 390 750 1230 1830 2550 3390
>    
> I do not yet properly grasp why the two nouns that
> come into play must be reorganized between these two
> modes. To demonstrate that they must, this is what
> happens when we try to use the verb-forming
> construction for immediate calculation:
> 
>    ]noun=: (}. - }:)@list^:order
> |domain error
> |   ]noun=:    (}.-}:)@list^:order
> 
> Not that this would look right to me in the absence of
> an error message, for the diff function (}. - }:)
> needs to be processing distinct data on each pass, and
> this seems to specify that the same data should be
> bound each time. 
> 
> My guess, interpreting the verb-making form, is that ]
> denotes values that differ on each cycle. If this is
> accurate, I've learned something about power.
> 
> What still eludes me, though, is a naturalness in
> reading, such that I anticipate this reversal of
> power-specification and data when moving from full
> calculation to tacit definition.
> 
> At this point, however, I have several engaging
> variations in hand for study. Thanks, again.
> 
> 
> Tracy
> 
> 
>       
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