The next challenge is to write a conjunction hyperbola so that
a hyperbola b is a verb that creates complex numbers for both
branches of the hyperbola y^2/a^2 - x^2/b^2 = 1 (opens up and
down not left and right) . The command
plot a hyperbola b [ c to d
plots the hyperbola. You have to work to move a stray
straight line to the edge of the plot. Give it a try.
Verb "to" is
to =: [ + -~ * 1r512 * [: i. 513"_
NB. c to d produces 513 equally spaced values from (real) c to d
--Kip Murray
Sent from my iPad
On Sep 14, 2013, at 9:57 PM, Henry Rich <[email protected]> wrote:
> Yes, that's better.
>
> Henry Rich
>
> On 9/14/2013 6:38 PM, km wrote:
>> Very cool, Henry! You can also use
>>
>> ellipse2 =: [: j./ ((cos ,: sin) 0 to 2p1) * ,
>>
>> An advantage of complex number plots is they are easy to rotate and
>> translate. Try
>>
>> plot (^&j. _1r4p1) * 2 ellipse 1 NB. rotates -45 degrees
>>
>> --Kip Murray
>>
>> Sent from my iPad
>>
>>
>> On Sep 14, 2013, at 12:04 PM, Henry Rich <[email protected]> wrote:
>>
>>> Verb rather than conjunction:
>>>
>>> ellipse =: [: +.^:_1 ((cos ,. sin) 0 to 2p1) *"1 ,
>>>
>>> If you just want to plot, you can leave the real/imaginary separate:
>>>
>>> ellipse2 =: ((cos ; sin) 0 to 2p1) *&.> ,
>>>
>>> Henry Rich
>>>
>>> On 9/13/2013 6:22 PM, km wrote:
>>>> You can plot a complex list.
>>>>
>>>> Try
>>>>
>>>> L =: _1j1 0 1j1
>>>>
>>>> and
>>>>
>>>> plot L
>>>>
>>>> plot 0j1 + L
>>>>
>>>> plot 0j1 * L
>>>>
>>>> (It is easy to translate and rotate a plot defined by a complex list.)
>>>>
>>>>
>>>> Challenge: devise a conjunction ellipse that produces a complex list for
>>>> plotting the ellipse
>>>>
>>>> 1 = (*: x % a) + (*: y % b) NB. In algebra x^2/a^2 + y^2/b^2 = 1
>>>>
>>>> The command
>>>>
>>>> plot a ellipse b
>>>>
>>>> should produce a plot of the above ellipse.
>>>>
>>>>
>>>> Easier: devise an adverb parabola that produces complex numbers for
>>>> plotting the parabola
>>>>
>>>> (*: x) = 4 * p * y
>>>>
>>>> You want the command
>>>>
>>>> plot p parabola c to d
>>>>
>>>> to plot the above parabola for x in the interval from c to d.
>>>>
>>>>
>>>> Here is verb "to"
>>>>
>>>> to =: [ + -~ * 1r512 * [: i. 513"_
>>>>
>>>> NB. c to d produces 513 equally spaced values from (real) c to d
>>>>
>>>>
>>>> Above tested on my iPad
>>>>
>>>> IFIPAD
>>>> 1
>>>> VERSION
>>>> 1.3 5
>>>>
>>>>
>>>> --Kip Murray
>>>>
>>>> Sent from my iPad
>>>>
>>>> ----------------------------------------------------------------------
>>>> 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
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
