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 the real parts - it seemed safer to change
both.
Your toh is elegant.
Henry Rich
On 9/15/2013 7:39 PM, km wrote:
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
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