t: Re: [Jprogramming] Plotting complex lists
Thanks Linda! The 'aspect 1' makes the plot square. Do you know how to make
circles circular?
Fra: Linda Alvord
Til: programm...@jsoftware.com
Sendt: 2:48 torsdag den 19. september 2013
Emne: Re: [Jprogramming] Plottin
>> Verb ratio calculates (max - min of imaginary parts) % (max - min of real
>> parts)
On a slightly related note: I use
pd 'aspect ',(":do_jwplot_ '(YMax-YMin)%(XMax-XMin)'),';show'
to force equal ratio on the existing 2d plot. It used to be on a hotkey, but
then I moved it to a verb.
x27; plot data
>>>>>
>>>>> appear circular.
>>>>>
>>>>> --Kip Murray
>>>>>
>>>>> Sent from my iPad
>>>>>
>>>>>> On Sep 21, 2013, at 4:08 AM, km wrote:
>>>>>>
&g
@forums.jsoftware.com] On Behalf Of Bo Jacoby
Sent: Wednesday, September 18, 2013 9:52 PM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Plotting complex lists
Thanks Linda! The 'aspect 1' makes the plot square. Do you know how to make
circles circular?
___
x27;aspect 0.5' plot ((,-)2j1) ,: _1^(%~i:)60
>>>>
>>>> and
>>>>
>>>> 'aspect 1' plot _1^(%~i:)60
>>>>
>>>> --Kip Murray
>>>>
>>>> Sent from my iPad
>>>>
>>>>&g
, so the
>>>>> circle is deformed. How do I make the circle circular?
>>>>> plot ((,-)2j1),:_1^(%~i:)60 NB. This is different, but not correct
>>>>> either.
>>>>>
>>>>>
>>>>>> _
t;>>
>>>>> Fra: Linda Alvord
>>>>> Til: programm...@jsoftware.com
>>>>> Sendt: 3:39 lørdag den 21. september 2013
>>>>> Emne: Re: [Jprogramming] Plotting complex lists
&
axes, so the circle is
>>> deformed. How do I make the circle circular?
>>>plot ((,-)2j1),:_1^(%~i:)60 NB. This is different, but not correct
>>> either.
>>>
>>>
>>>>
>>>> Fra: Linda Alvord
>&
w do I make the circle circular?
>>plot ((,-)2j1),:_1^(%~i:)60 NB. This is different, but not correct either.
>>
>>
>>> ____
>>> Fra: Linda Alvord
>>> Til: programm...@jsoftware.com
>>> Sendt: 3:39 lørdag den 21. september 2013
>>> Emne: Re:
2013 5:08 AM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Plotting complex lists
Try
'aspect 0.5' plot ((,-)2j1) ,: _1^(%~i:)60
and
'aspect 1' plot _1^(%~i:)60
--Kip Murray
Sent from my iPad
> On Sep 21, 2013, at 3:15 AM, Bo Jacoby wrote:
>
>&
Kip,
-Original Message-
From: programming-boun...@forums.jsoftware.com
[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of km
Sent: Saturday, September 21, 2013 5:08 AM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Plotting complex lists
Try
'aspec
Til: programm...@jsoftware.com
>> Sendt: 3:39 lørdag den 21. september 2013
>> Emne: Re: [Jprogramming] Plotting complex lists
>>
>>
>> Square isn't so square either. Linda (Yet again, life is a series of
>> approximations.)
>>
>> -Or
ect either.
>
> Fra: Linda Alvord
>Til: programm...@jsoftware.com
>Sendt: 3:39 lørdag den 21. september 2013
>Emne: Re: [Jprogramming] Plotting complex lists
>
>
>Square isn't so square either. Linda (Yet again, life is a series of
>approximat
gramm...@jsoftware.com
Subject: Re: [Jprogramming] Plotting complex lists
Thanks Linda! The 'aspect 1' makes the plot square. Do you know how to make
circles circular?
>
> Fra: Linda Alvord
>Til: programm...@jsoftware.com
>Sendt: 2:48 torsdag den 1
Thanks Linda! The 'aspect 1' makes the plot square. Do you know how to make
circles circular?
>
> Fra: Linda Alvord
>Til: programm...@jsoftware.com
>Sendt: 2:48 torsdag den 19. september 2013
>Emne: Re: [Jprogramming] Plotting complex
: programm...@jsoftware.com
Subject: Re: [Jprogramming] Plotting complex lists
One benefit of using complex numbers is that you may forget about
trigonometry.
load'plot'
circle=._1^n=.(%~i:)60
ellipse=.(circle*-.a)+(+circle)*a=.0.8
hyperbola=.-:((+%)j.(-%))^n
plot circl
anksley, Jr"
>Til: Programming forum
>Sendt: 18:19 tirsdag den 17. september 2013
>Emne: Re: [Jprogramming] Plotting complex lists
>
>
>Bo Jacoby wrote:
>> One benefit of using complex numbers is that you may forget about
>> trigonometry.
>> load&#x
On Sep 17, 2013, at 11:19 AM, "William Tanksley, Jr"
wrote:
>
> I definitely don't understand what Kip means when he says y=1/x is not
> a hyperbola. It is -- it's the second order polynomial xy=0. The
> asymptotes happen to be the axes, but that's exactly what rotation
> solves.
>
> -Wm
>
>Til: "programm...@jsoftware.com"
>Sendt: 0:40 tirsdag den 17. september 2013
>Emne: Re: [Jprogramming] Plotting complex lists
>
>
>Summary of results. The strategy of hyperbola below (plotting a complex
>table) is not well known. Henry Rich found it and report
Bo Jacoby wrote:
> One benefit of using complex numbers is that you may forget about
> trigonometry.
>load'plot'
>circle=._1^n=.(%~i:)60
>ellipse=.(circle*-.a)+(+circle)*a=.0.8
>hyperbola=.-:((+%)j.(-%))^n
>plot circle,ellipse,:hyperbola
Thanks, Bo; that's what I was thinking
You can certainly use the standard algebraic formulas y = mx + b, x^2 =
4py, x^2/a^2 + y^2/b^2 = 1, y^2/a^2 - x^2/b^2 = 1 for line, parabola,
ellipse/circle, and hyperbola, solving for y and plotting as I do below
for the parabola. There is an ingenious way for dealing with y = (+ or
minus) bl
Is it possible to do these plots using only algebraic functions -- for
example, using 1/x and then a rotation to plot the hyperbolae? I know
of an algebraic parameterization for the unit circle, but I'm not sure
about the ellipse.
-Wm
On Mon, Sep 16, 2013 at 3:40 PM, km wrote:
> Summary of resu
Summary of results. The strategy of hyperbola below (plotting a complex table)
is not well known. Henry Rich found it and reported it.
Bo Jacoby gave the best way to change the sign of the real part of a complex
number.
Simply do [: + - .
NB. Complex Analytic Geometry
NB. How to calcula
-+5j6
> _5j6
>
>
>
>
>
>
>>
>> Fra: Roger Hui
>> Til: Programming forum
>> Sendt: 7:46 mandag den 16. september 2013
>> Emne: Re: [Jprogramming] Plotting complex lists
>>
>>
>>> For comp
Your solution is very nice! I had a much longer sequence of steps.
More visibly your steps are
0j_1 * + 0j1 * 3j4
_3j4
that is
0j1 * 3j4
_4j3
+ 0j1 * 3j4
_4j_3
0j_1 * + 0j1 * 3j4
_3j4
--Kip Murray
Sent from my iPad
On Sep 16, 2013, at 12:46 AM, Roger Hui wrote:
>
+-5j6
_5j6
-+5j6
_5j6
>
> Fra: Roger Hui
>Til: Programming forum
>Sendt: 7:46 mandag den 16. september 2013
>Emne: Re: [Jprogramming] Plotting complex lists
>
>
>> For complex analysis purists, it is possible to change
> For complex analysis purists, it is possible to change the sign of the
real part using only multiplication and conjugation -- an exercise left for
the reader.
+&.j. 3j4
_3j4
--
For information about J forums see http://www.j
Henry, we can change the sign of the real part.
csr =: [: j./ _1 1 * +. NB. change sign of real part
csr 1j2
_1j2
For complex analysis purists, it is possible to change the sign of the real
part using only multiplication and conjugation -- an exercise left for the
reader.
What would hap
I didn't know about a table of complex numbers either, till I tried it.
It seems to recognize each row as a separate dataset, thus avoiding
the line between them. Thorough man, that Chris.
+ for - would work for this hyperbola, but for the other orientation you
would need to change sign on t
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).
Crib
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
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 t
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 d
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 P
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
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
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