(note I wrote this earlier and set it aside to research the question
about the distort verb.  This may now be stale...)

That was correct about ranks:

http://www.jsoftware.com/help/dictionary/dictf.htm
   "The ranks of the hook and fork are infinite."

That said, I believe learning j was trying to give you just enough
information to give you a basis for experimentation.  And, you should
be able to measure the rank of fork. So, given
http://www.jsoftware.com/help/learning/07.htm

   "the expression u b. 0 gives the ranks in the order monadic, left, right."

   (+/ %#) b. 0
_ _ _

Anyways, as to your original question, you can rephrase that in many
ways, but I think the core of it is something like this:

   plot  (2 %~ 1 + *@(_1 + 2 * ]) * [ (* % 1 + (2 * *) - +) |@(_1 + 2
* ]))"0/~ a

And I see a lot of scaling by two and adjusting by 1 there, to convert
between the domain of a (0..1) and numbers you need to work with.  So
I think I would work on pushing this transform out to the edges.  In
other words, I would try to write F&.(1 + 2 * ]).

(But I have not thought about this enough to decide what F would be.)

FYI,

-- 
Raul

On Fri, Nov 4, 2011 at 6:30 AM, Ricardo Forno <[email protected]> wrote:
> The thing that confused me is that I didn't know a fork has rank _ as
> Marshall wrote. Is that correct? Browsing through Learning J, I couldn't
> find if this fact is mentioned there.
>
> ----- Original Message -----
> From: "Henry Rich" <[email protected]>
> To: "Programming forum" <[email protected]>
> Sent: Friday, November 04, 2011 7:15 AM
> Subject: Re: [Jprogramming] Newbie question
>
>
>> Just a quibble with terminology: 'item' means _1-cell.  That concept
>> does not apply here.  If you define 'l-cell' to be the left rank of the
>> verb, and 'r-cell' the right rank, you could say
>>
>> ...it loops through all the l-cells of x, then for each of those, all
>> the r-cells of y...
>>
>> Henry Rich
>>
>> On 11/4/2011 12:13 AM, Marshall Lochbaum wrote:
>>> * has rank 0 already, so it isn't necessary. The definition of / is that
>>> it
>>> applies the verb with rank (left rank),_ . Essentially, this means that
>>> it
>>> loops through all the items of x, then for each of those, all the items
>>> of
>>> y, where an "item" is an item with the left rank of the verb. If you try
>>> magic/~ a with magic having rank _ (because it's a fork), you just get (a
>>> magic"_ _"_ _ a), which simply applies magic regularly.
>>>
>>> Marshall
>>>
>>> On Thu, Nov 3, 2011 at 11:57 PM, Ricardo
>>> Forno<[email protected]>wrote:
>>>
>>>> I have this verb:
>>>> magic =: * %>:@(+:@*) - +
>>>> that I use only as a dyad, and, say,
>>>> a =: 0.1 * i. 10
>>>> If I want to get a table of the * verb, I  write:
>>>> a * / a
>>>> If I write
>>>> a magic / a
>>>> I dont get a table. To get a table, I have to write:
>>>> a magic"0 / a
>>>> Why is it so, since both * and magic may be used as dyads?
>>>> Thanks.
>>>>
>>>>
>>>> ----------------------------------------------------------------------
>>>> 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
>
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