Henry, this is outstanding. I didn't know about plotting a table of complex
numbers.
Two comments. First, as I specified
a hyperbola b
for
y^2/a^2 - x^2/b^2 = 1 ,
you need comma tilde (,~) not comma.
Second, you could have used + (conjugate) instead of - (negative).
Cribbing from you, I have
hyperb =: 2 : '[: (,: +) [: j./ (n,m) * (sinh ,: cosh)'
toh =: [: to/ [: arcsinh %~
NB. b toh c,d is (arcsinh c%b) to (arcsinh d%b)
The command
plot a hyperb b [ b toh c,d
plots the hyperbola y^2/a^2 - x^2/b^2 = 1 for x going from c to d .
--Kip Murray
Sent from my iPad
On Sep 15, 2013, at 3:51 PM, Henry Rich <[email protected]> wrote:
> hyperbola =: [: (,: -) [: j./ ((sinh ,: cosh) _0.4p1 to 0.4p1) * ,
>
> Henry Rich
>
> On 9/15/2013 12:27 AM, km wrote:
>> 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
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
