Or, more simply

   22j10*^j.o.15%180
18.6622j15.3533

That said, you could also use J's notation for entering complex
numbers using polar coordinates

   22j10*1ad15
18.6622j15.3533

I hope this makes sense,

-- 
Raul

On Thu, Dec 7, 2023 at 12:20 PM Henry Rich <henryhr...@gmail.com> wrote:
>
>     22j10 (* ^@:j.@:o.&(%&180)) 15
> 18.6622j15.3533
>
> Make the middle part a named verb if you like.
>
> Henry Rich
>
> On 12/7/2023 11:48 AM, 'PMA' via Programming wrote:
> > A slightly different approach.  Rather than search out all alignments
> > and then deduce their degrees of rotation, I mean now to specify as
> > input the degrees for which rotations are to be generated.
> >
> > Example: given a graph of one dot -- 22j10 -- I'd input that value
> > with a rotation choice -- 15 degrees counterclockwise -- and expect a
> > single integer-rounded output value of approximately 19j15.
> > (Those two "15"s are coincidental.)
> >
> > My question is, what J syntax will generate that output?
> >
> > Thanks again for your consideration!
> > Peter A
> >
> >
> > On 11/16/23 09:26, Henry Rich wrote:
> >> This is my reply to a question someone posed yesterday.  This
> >> afternoon I will post a complete solution.  It's like the puzzle
> >> problems I posed you, but just a little longer and comes from a real
> >> user need.  If you want to solve it yourself you will need the
> >> primitives
> >>
> >> j. dyad, / monad, / dyad, ~, -. dyad, ^ monad, | dyad, -, /: dyad, *.
> >> monad
> >>
> >> hhr
> >>
> >> On 11/15/2023 6:49 PM, Henry Rich wrote:
> >>> I would find the angles from each point to each other point, take
> >>> modulus(pi/2), concatenate the list with its negative, and sort.
> >>> Rotation by each angle produces a new alignment.  Only J primitives
> >>> are needed.
> >>>
> >>> Use complex numbers to represent the (x,y) values, and *. to convert
> >>> to angles.
> >>>
> >>> Henry Rich
> >>>
> >>> On 11/15/2023 5:52 PM, 'PMA' via Wiki wrote:
> >>>>
> >>>> Dear J-Wiki,
> >>>>
> >>>> I want to make a script that, given the X/Y values of a 2D
> >>>> dot-graph, will rotate the graph around its designated origin,
> >>>> looking for instances of 2 or more points coming into new
> >>>> horizontal &/or vertical alignment, and at each such instance
> >>>> output the full set of current X/Y values (integer-rounded).
> >>>>
> >>>> Could you point me to the main needed ingredients?
> >>>>
> >>>> Thanks in advance,
> >>>>
> >>>> Peter Armstrong
> >>>>
> >>>
> >>
> >> ----------------------------------------------------------------------
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> > ----------------------------------------------------------------------
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>
> ----------------------------------------------------------------------
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