The construction of the sphere implies it cannot be convex but you will
have to find a topologist to prove it to you.
The sphere is the collection of points whose distance to the origin is
equal to the radius of the sphere.
The ball or volume is comprised of the points whose distance to the origi
No zeroes for sec or csc, from the definition:
csc A = 1 / (sin A)
sec A = 1 / (cos A)
cot A = 1 / (tan A)
sin and cos vary from 1 to -1 passing by zero so there is no way of getting
a zero from 1/sin or 1/cos
tan on the other hand varies from plus infinity to minus infinity so you
obtain zeroes
Has the n-sphere become concave in higher dimension?
Вт, 15 авг 2017, Jimmy Gauvin написал(а):
> Funny how the n-Sphere volume dwindles for the higher dimensions.
> Not quite intuitive but the factorial always "win" even with bigger radii.
>
> The hypercubes do not share this characteristic (V= e
Thanks Raul. It shows that I haven't used J for any trig in aboug 20 years.
Here is almost what I want.
Hoever the cot looks good. Shouldn't there be some 0's in the sec and csc?
*(%"0)3 2 1 (o."0 1) t
1 1 1 1 0 _1 _1 _1 _1 1 1 1 0 _1 _1 _1 _1
1 1 1 1 1 _1 _1 _1 _1 _1 _1 _1 _1 1 1 1
Yes; I began writing the message but had to leave unexpectedly.
Let me explain what I want for a rank 2 array:
Given the index vector I of an element of the array and its shape, I want
all the elements in lines which are horizontal, vertical, or diagonal,
and which pass through I. In addition, ele
Maybe
https://www.youtube.com/watch?v=uU_Q2a0S0zI&index=9&list=PL2FF649D0C4407B30
especially at 28 minute marker in the video discusses this very issue. I
recommend the rest of the videos in the list too.
Thanks,
Vijay.
On Tue, Aug 15, 2017 at 4:52 PM, Don Guinn wrote:
> Just had to try it.
>
>
Just had to try it.
plot 1 sphvol i:30
Don't know if it even makes any sense, but the plot is curious.
On Tue, Aug 15, 2017 at 2:27 PM, Jimmy Gauvin
wrote:
> Funny how the n-Sphere volume dwindles for the higher dimensions.
> Not quite intuitive but the factorial always "win" even with bigge
Funny how the n-Sphere volume dwindles for the higher dimensions.
Not quite intuitive but the factorial always "win" even with bigger radii.
The hypercubes do not share this characteristic (V= edge ^ n)
On Tue, Aug 15, 2017 at 3:33 PM, Ben Gorte - CITG
wrote:
> A little surprise (to me) was
>
It loses accuracy somewhere between n=150 and n=200.
Keep in mind though that the dimensions of these "volumes" are not comparable.
Each "n-volume" of dimension n-1 is "paper thin (or thinner)" than the
"n-volume" of dimension n.
That said, I have not sat down and verified the results by hand, I
Nice sentence.
Is it accurate for higher dimensions too? To me it seems a bit
counterintuitive that after n=6, the n-volume rapidly declines until almost
zero.
For instance:
load 'plot'
plot 1 sphvol i. 100
Best regards,
Jan-Pieter
On 15 Aug 2017 7:55 p.m., "Raul Miller" wrote:
>sphvol=:
I am having problems understanding what you are asking for.
I'll try creating some examples which represent my understanding of
what you seem to be asking for, and maybe that can help you tell me
where I've gone off track:
"Given an array index vector i,"
For example:
i=: i.4 5
"how would yo
A little surprise (to me) was
plot 1 sphvol i.30
(for example)
Can you predict it?
greetings,
Ben
From: Programming [programming-boun...@forums.jsoftware.com] on behalf of Raul
Miller [rauldmil...@gmail.com]
Sent: Tuesday, August 15, 2017 19:55
To: P
In this case? I'd probably use ;: but for the general case it's
probably safer to use <"1 (if I understand your intent properly).
Thanks,
--
Raul
On Tue, Aug 15, 2017 at 2:40 PM, Skip Cave wrote:
> How could you box each string?
>
> Skip Cave
> Cave Consulting LLC
>
> On Tue, Aug 15, 2017 at
Hi,
Given an array index vector i, how would you go about
finding efficiently all indices (or elements at them) of an
array for which the index in each dimension is either the
same as that in i, or is offset by +/- n, where n is the same
for all dimensions, and keep them grouped by “direction”?
I
How could you box each string?
Skip Cave
Cave Consulting LLC
On Tue, Aug 15, 2017 at 12:07 PM, Raul Miller wrote:
> I'd meet that specification like this:
>
> require'stats'
> perms=: A.&i.~ !
>
> gen=:4 :0
> x{~,/(perms y){"1/y comb #x
> )
>
> But note that the result format is different.
>
sphvol=: (1p1&^%!)@-:@] * ^
1 sphvol 3
4.18879
1 sphvol i.7
1 2 3.14159 4.18879 4.9348 5.26379 5.16771
Left argument is the radius of the "n-sphere".
Right argument is the number of dimensions.
I put "n-volume" in quotes, because if the dimension is 2 (for
example), the "n-volume" is wh
Raul's solution was much faster than my original, though my argument to perm
was not a constant, so one alternative
# 10 #."1 /:~ ,/ (perm@#@{. {"_ 1 ]) 3 >:@:comb 9504
From: Jimmy Gauvin
To: programm...@jsoftware.com
Sent: Tuesday, August 15, 2017 1:47 PM
Subject: Re: [Jprogramming]
Or you could do:
cot=: %@(tan=: 3&o.)
sec=: %@(cos=: 2&o.)
csc=: %@(sin=: 1&o.)
Thanks,
--
Raul
On Tue, Aug 15, 2017 at 1:11 PM, Jimmy Gauvin wrote:
> Hi,
>
> problem is with 4 5 6 which denote the following:
>
>coh=: 4&o.NB. sqrt (1+(y^2))
>sinh=: 5&o. NB. hyperbolic s
Completely agree with Skip as I'm also at the beginning of the learning
curve.
One of the idioms that really amazed me is the way Raul does the selection
of the combinations with the permutations using the table verb:
(perms 3) {"1 /1+3 comb 9
I was working along similar lines with this sele
Sorry for the mangled output,
this should be better:
cot *A* = 1 / (tan *A*)
sec *A* = 1 / (cos *A*)
csc *A* = 1 / (sin *A*)
@Don
The inverses are the arc functions and have different definitiions
On Tue, Aug 15, 2017 at 1:12 PM, Don Guinn wrote:
> Negative left number gives inverses.
>
>
Negative left number gives inverses.
1 o.1
0.841471
_1 o.1
1.5708
_1 o. 1 o. 1
1
On Tue, Aug 15, 2017 at 11:01 AM, Raul Miller wrote:
> Which rows are cotangent, secant and cosecant?
>
> (I see sine, cosine, tangent, square root, hyperbolic sine and
> hyperbolic cosine.)
>
> Thanks,
>
Hi,
problem is with 4 5 6 which denote the following:
coh=: 4&o.NB. sqrt (1+(y^2))
sinh=: 5&o. NB. hyperbolic sine of y
cosh=: 6&o. NB. hyperbolic cosine of y
see: http://code.jsoftware.com/wiki/Vocabulary/odot#dyadic
There dosen't seem to be specific numbers for co
I'd meet that specification like this:
require'stats'
perms=: A.&i.~ !
gen=:4 :0
x{~,/(perms y){"1/y comb #x
)
But note that the result format is different.
Thanks,
--
Raul
On Tue, Aug 15, 2017 at 12:58 PM, Skip Cave wrote:
> I believe that the general case would be:
> Design a J verb tha
Which rows are cotangent, secant and cosecant?
(I see sine, cosine, tangent, square root, hyperbolic sine and
hyperbolic cosine.)
Thanks,
--
Raul
On Tue, Aug 15, 2017 at 12:41 PM, Linda Alvord wrote:
>
>
> Sent from AOL Mobile Mail
>
>
> From: Linda Alvord
> Date: Tuesday, August 15, 2017
>
Linda, according to the vocab,
1 2 3 4 5 6 o.
are respectively
sin cos tan (>:&.*:) sinh cosh
OK?
Mike
On 15/08/2017 17:41, Linda Alvord wrote:
Sent from AOL Mobile Mail
From: Linda Alvord
Date: Tuesday, August 15, 2017
Subject: FW: why are there no negative signs for cot,sec and csc?
I believe that the general case would be:
Design a J verb that will generate all possible unique strings of a
specific fixed length using only specified set of symbols, where each
generated string has no repeated symbols.
x gen y
Where x specifies a set of symbols (characters, numbers), and y
Sent from AOL Mobile Mail
From: Linda Alvord
Date: Tuesday, August 15, 2017
Subject: FW: why are there no negative signs for cot,sec and csc?
Cc: lindaalvord

From: Linda Alvord [mailto:lindaalv...@verizon.net]
Sent: Tuesday, August 15, 2017 11:22 AM
To: 'programm...@jsoftware.com'
For really big problems you could go to a larger base than 10 like
hexadecimal. Or even bigger using more letters.
On Tue, Aug 15, 2017 at 10:10 AM, Raul Miller wrote:
> To compare them for equality you need to sort them.
>
> However, the task was to generate the integers.
>
> (If the example li
To compare them for equality you need to sort them.
However, the task was to generate the integers.
(If the example list of numbers was a part of the specification then
we probably should not be considering seven digit integers as
relevant.)
Thanks,
--
Raul
On Tue, Aug 15, 2017 at 10:37 AM, A
I agree Groeneveld's solution is elegant and it's certainly more efficient
for larger problems, My approach was the result of a couple of minutes
thought;
it turned out to be quite adequate for Skip's original requirement.
Consider the count of such n-digit numbers,
nq =: ! * !&9
nq 1 2 3
To compare both you need to do the following:
10 ts 'R=./:~,10#.(perms 7){"1/1+7 comb 9'
0.0288779 2.4132e7
10 ts 'G=.,10 #. ((],"1 0 -."1)^:6 ,.)1+i.9'
0.0258377 2.30737e7
R-:G
1
Looks like a draw.
Op 15-08-17 om 16:16 schreef Raul Miller:
I cannot comment on elegance, but I can dis
I cannot comment on elegance, but I can disagree about the efficiency issue:
timespacex ',10#.(perms 7){"1/1+7 comb 9'
0.015591 2.15104e7
timespacex '10 #. (,/@:(],"1 0 -."1)^:6 ,.)1+i.9'
0.036695 3.7755e7
Thanks,
--
Raul
On Tue, Aug 15, 2017 at 9:53 AM, R.E. Boss wrote:
> I suggest y
I suggest you use larger numbers for your performance tests.
(10#.(#~(-:~.)"1) >: 9#.inv i. 9^6)-: 10 #.(,/@:(],"1 0 -."1)^:5 ,.)>:i.9
1
ts'10#.(#~(-:~.)"1) >: 9#.inv i. 9^6'
0.39192919 1.7905766e8
ts'10 #.(,/@:(],"1 0 -."1)^:5 ,.)>:i.9'
0.010126433 9442816
The Groeneveld solution is mor
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