I think that indeterminate is slightly better and seems to be the word
generally used for mathematics.
Don
On 2020-02-11 4:53 a.m., Raul Miller wrote:
On Mon, Feb 10, 2020 at 10:12 PM Don Kelly wrote:
I also should have written "indeterminate"
This seems to be another example where one choi
Many thanks to both Raul and Roger for Falkoff's paper. Fascinating!
> On Feb 11, 2020, at 11:49 AM, Roger Hui wrote:
>
> I am skeptical of this particular use of "indeterminant" in Falkoff's
> *APL\360
> History*. I typed in the web page
> http://www.jsoftware.com/papers/apl360history.htm co
I am skeptical of this particular use of "indeterminant" in Falkoff's *APL\360
History*. I typed in the web page
http://www.jsoftware.com/papers/apl360history.htm contents from a printed
Proceedings, and as noted in the web page,
The Proceedings state that “Mr. Falkoff’s [address] … has been tran
On Mon, Feb 10, 2020 at 10:12 PM Don Kelly wrote:
> I also should have written "indeterminate"
This seems to be another example where one choice being valid does not
mean that a different choice is invalid. (A common issue when using
the english language -- or, more generally, any human language.
> On Feb 10, 2020, at 10:31 PM, Don Kelly wrote:
>
> Thank you and
good night?? Jeeze, even the shortest message in this thread goes over my head!
--
For information about J forums see http://www.jsoftware.com/forums.htm
Thank you and
On 2020-02-09 7:10 a.m., Henry Rich wrote:
See https://arxiv.org/pdf/math/9205211.pdf esp. p. 6
Henry Rich
On 2/9/2020 12:29 AM, Don Kelly wrote:
Reading again, I apologize for mistaking x^x for x*x- and getting an
easy to get polynomial with 2 roots . Your original x^x =2*x is
Thank you for this. I agree and my point is that n^0 is 1 if n is not 0
but 0^n is another kettle of fish. However, in applying the mat to the
real world, I cannot think of anything where such discontinuity actually
exists-so it is a nice philosophical matter. I've looked at Knuth and am
not s
On Sun, Feb 9, 2020 at 12:29 AM Don Kelly wrote:
> _ _ _ HUH? 0 0 0 where i am using HUH? to indicate that for x=0 the
> result is indeterminant. Creep up on 0 and no matter how close to 0
> you get -the results are the same. Crossing 0 is a discontinuous jump
> directly from infinity to 0
See https://arxiv.org/pdf/math/9205211.pdf esp. p. 6
Henry Rich
On 2/9/2020 12:29 AM, Don Kelly wrote:
Reading again, I apologize for mistaking x^x for x*x- and getting an
easy to get polynomial with 2 roots . Your original x^x =2*x is not
actually a normal polynomial.Newton could be used but
Reading again, I apologize for mistaking x^x for x*x- and getting an
easy to get polynomial with 2 roots . Your original x^x =2*x is not
actually a normal polynomial.Newton could be used but the derivative
is so messy that a cut and try approach seems easier.
When you do to get 0^x and get _
f=.(^ ]) - +:
newton=.- f % f"0 D.1
(newton^:_) 0 3
0.346323 2
NB. these are the two solutions
Den fredag den 7. februar 2020 17.46.50 CET skrev Henry Rich
:
t. has been removed from J9.01.
Henry Rich
On 2/7/2020 11:45 AM, Brian Schott wrote:
> I am still havin
t. has been removed from J9.01.
Henry Rich
On 2/7/2020 11:45 AM, Brian Schott wrote:
I am still having trouble with j9 relative to j8 as shown by the two
results below.
^ t. i.6
|spelling error
| ^ t. i.6
| ^
JVERSION
Engine: j901/j64avx/darwin
Release-c: commercial/2020-01-11T12
I am still having trouble with j9 relative to j8 as shown by the two
results below.
^ t. i.6
|spelling error
| ^ t. i.6
| ^
JVERSION
Engine: j901/j64avx/darwin
Release-c: commercial/2020-01-11T12:22:31
Library: 9.01.20
Platform: Darwin 64
Installer: J901 install
InstallPath: /users/bri
For polynomial roots, see
https://www.jsoftware.com/help/dictionary/samp27.htm for an alternative,
Kerner's Method. It finds all the roots (approximations thereof,
of course) all at once. Also described in Section 3.2 of Iverson's Turing
Lecture https://www.jsoftware.com/papers/tot.htm.
-
Also it is a good thing if you can plot the function for visual inspection.
t. Esa
-Original Message-
From: Programming On Behalf Of Henry
Rich
Sent: Friday, February 7, 2020 12:18 PM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Derivatives
Newton's method is goo
Newton's method is good for final polishing of a root when you are very
close. It can do weird things when you are not close. Like here. Study
this case and see what happened.
Henry Rich
On 2/6/2020 9:23 PM, Skip Cave wrote:
]x=.i:3
_3 _2 _1 0 1 2 3
0^x
_ _ _ 1 0 0 0
x=.0
(x^x)=2*x
0
on 1
2
-Original Message-
From: Programming On Behalf Of Brian
Schott
Sent: Thursday, February 6, 2020 5:37 PM
To: Programming forum
Subject: Re: [Jprogramming] Derivatives
Henry et al,
I have 2 questions.
How would the second root at 2 be found with Skip's problem?
Why do
]x=.i:3
_3 _2 _1 0 1 2 3
0^x
_ _ _ 1 0 0 0
x=.0
(x^x)=2*x
0 NB. Zero is not a root
(x^x)=2*x
0
x^x
1
2*x
0
So why does Newton Raphson show a zero root for (x^x)=2*x?
(^~ - +:) Newton 2
2
(^~ - +:) Newton 1
0 NB. Something wrong here!
(x^x)=2*x ?
Skip Cave
Cave Consulting LLC
Bo is correct
There is a "zero rule" so n^0 =1 if n is not equal to 0. Bo is correct
the only possible 0^0 is the same as 0*0
Possibly the coding for ^ should take this into account.
On 2020-02-05 10:14 p.m., Skip Cave wrote:
Bo,
The original equation is:
(x^x)=2*x
2 is clearly a root. 0 i
solve: (x^x)=2*x
JVERSION
Engine: j901/j64avx2/windows
Release-e: commercial/2020-01-29T11:17:19
Library: 9.01.18
Qt IDE: 1.8.5/5.12.6
Platform: Win 64
Installer: J901 install
InstallPath: c:/users/skip/j901
Contact: www.jsoftware.com
load 'math/calculus'
Newton =: adverb : ']-u%(u der
1. Choose a different starting guess
2. Update the addon
Henry Rich
On 2/6/2020 10:36 AM, Brian Schott wrote:
Henry et al,
I have 2 questions.
How would the second root at 2 be found with Skip's problem?
Why do I get the following error?
server:~ brian$ /Users/brian/j901/bin/jconsole ; exit
Henry et al,
I have 2 questions.
How would the second root at 2 be found with Skip's problem?
Why do I get the following error?
server:~ brian$ /Users/brian/j901/bin/jconsole ; exit;
JVERSION
Engine: j901/j64avx/darwin
Release-c: commercial/2020-01-11T12:22:31
Library: 9.01.20
Platform: Darwi
Write down the equation on paper and then use android
mathway app to take a photo of it, and it solved
x=0.34632336,2
--
regards,
GPG key 1024D/4434BAB3 2008-08-24
gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3
--
t; >
> >
> >
> >
> > Sent from my Samsung Galaxy smartphone.
> >
> >
> > Original message
> > From: Skip Cave
> > Date: 2/5/20 21:49 (GMT+02:00)
> > To: "programm...@jsoftware.com"
> > Subject: Re: [
d x2
> > the second root.
> >
> > Esa
> >
> >
> >
> >
> >
> > Sent from my Samsung Galaxy smartphone.
> >
> >
> > Original message
> > From: Skip Cave
> > Date: 2/5/20 21:49 (GMT+02:00)
> > T
Bo,
The original equation is:
(x^x)=2*x
2 is clearly a root. 0 is clearly not, as 0^0 = 1
Skip Cave
On Wed, Feb 5, 2020 at 2:37 PM 'Bo Jacoby' via Programming <
programm...@jsoftware.com> wrote:
> Skip. (x^x)-(2*x) = x*(x-2) is zero for x=0 and x=2. Two real roots.
> Newton Raphson finds on
Yes! It is quite cool to have this in the core language.
Esa
Sent from my Samsung Galaxy smartphone.
Original message
From: Roger Hui
Date: 2/6/20 00:25 (GMT+02:00)
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Derivatives
To find polynomial roots, p. is the
> From: Skip Cave
> Date: 2/5/20 21:49 (GMT+02:00)
> To: "programm...@jsoftware.com"
> Subject: Re: [Jprogramming] Derivatives
>
> Won't (x^x)-(2*x) = 0 have two roots? A real one, and a complex one?
>
> Will Newton Raphson find both?
>
> Skip
&
: "programm...@jsoftware.com"
Subject: Re: [Jprogramming] Derivatives
Won't (x^x)-(2*x) = 0 have two roots? A real one, and a complex one?
Will Newton Raphson find both?
Skip
On Wed, Feb 5, 2020 at 12:08 PM Henry Rich wrote:
> Yeah, a rational y wouldn't ever quite
Skip. (x^x)-(2*x) = x*(x-2) is zero for x=0 and x=2. Two real roots. Newton
Raphson finds one of these depending on the value of the initial guess.
Bo.
Den onsdag den 5. februar 2020 19.08.23 CET skrev Henry Rich
:
Yeah, a rational y wouldn't ever quite satisfy 0 = _2 0 1 p. y
Henry
Won't (x^x)-(2*x) = 0 have two roots? A real one, and a complex one?
Will Newton Raphson find both?
Skip
On Wed, Feb 5, 2020 at 12:08 PM Henry Rich wrote:
> Yeah, a rational y wouldn't ever quite satisfy 0 = _2 0 1 p. y
>
> Henry Rich
>
> On 2/5/2020 1:04 PM, Devon McCormick wrote:
> > You
Yeah, a rational y wouldn't ever quite satisfy 0 = _2 0 1 p. y
Henry Rich
On 2/5/2020 1:04 PM, Devon McCormick wrote:
You especially need guardrails if you try something like this:
_2 0 1&p. Newton 1 NB. OK - square root of 2
1.41421
_2 0 1&p. Newton 1x NB. Try extended precisi
You especially need guardrails if you try something like this:
_2 0 1&p. Newton 1 NB. OK - square root of 2
1.41421
_2 0 1&p. Newton 1x NB. Try extended precision
C-c C-c|breakNB. After waiting a while...
| _2 0 1&p.Newton 1
NB. Failure to terminate...
On Wed
I misread your function.
(^~ - +:) Newton 1.1
0.346323j1.2326e_32
(^~ - +:) Newton 0.5
0.346323
Still need those guardrails!
Henry Rich
On 2/5/2020 2:21 AM, Skip Cave wrote:
In "Fifty Shades of J" chapter 23, the Newton Raphson algorithm is
described thusly:
Newton =: adverb : ']-u%(u
Given f, Newton finds where f is 0. Your function is x^2 - 2x = 0.
load 'math/calculus'
Newton =: adverb : ']-u%(u deriv_jcalculus_ 1)'(^:_)("0)
0 _2 1&p. Newton 1.1
2
Check:
p. 0 _2 1
+-+---+
|1|2 0|
+-+---+
Without guardrails, Newton may crash:
0 _2 1&p. Newton 1
|NaN error
NuVoc notes what replaces D. and d. on their respective pages.
In particular, from the math/calculus addon, we have
* deriv_jcalculus_ to replace d. and
* pderiv_jcalculus_ to replace D.
Skip Cave wrote:
> In "Fifty Shades of J" chapter 23, the Newton Raphson algorithm is
> described thusly:
>
In "Fifty Shades of J" chapter 23, the Newton Raphson algorithm is
described thusly:
Newton =: adverb : ']-u%(u D.1)'(^:_)("0)
How would that be defined using the new derivative verbs?
Also, what is the replacement for d.?
How would I find the roots of (x^x)=2*x using Newton Raphson?
Skip
Ski
(1&o.)`0:kappa 9
NB. radius of curvature is reciprocal of curvature
rc=: [: % kappa
Date: Tue, 3 Nov 2015 17:05:17 -0500 From: Raul Miller
To: Programming forum
Subject: Re: [Jprogramming] derivatives of
a gerund Message-ID:
Content-Type: text/plain; charset=UTF-8 Like this? dgerund=:3 :0
cool,
dgerund *:`^`(2&^)
- Original Message -
From: Raul Miller
To: Programming forum
Cc:
Sent: Tuesday, November 3, 2015 5:05 PM
Subject: Re: [Jprogramming] derivatives of a gerund
Like this?
dgerund=:3 :0"0
{.(y`:6 d.1)`''
)
r=:4 :0
dx=. dgerund x
dd
Like this?
dgerund=:3 :0"0
{.(y`:6 d.1)`''
)
r=:4 :0
dx=. dgerund x
ddx=. dgerund dx
NB. fill in the rest...
)
Note that if you have verbs which can't be handled by d. you'll have
to use a cover for d.1 which does what you need for those cases.
Thanks,
--
Raul
On Tue, Nov 3, 2015 at
In algebraic notation I have a parametric curve
x=u(t), y=v(t), z=v(t)
and need radius_of_curvature(t)
Would like the verb r taking a gerund argument,
u`v`w r t
but requires first and second derivatives.
In LaTeX linear notation, with \times representing cross product,
curvature is
\[\frac{\|\
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