Thank you Skip!
You are right and I was wrong.
(x^x)=2*x is not solved by (p.) because it is a transcendental equation.
The only positive solution is x=2.
Bo.
Den torsdag den 6. februar 2020 07.26.35 CET skrev Skip Cave
<s...@caveconsulting.com>:
Roger,
Very impressive!
Looks like I will need to brush up on my 50-some-year-old Algebra skills,
so I can convert
the (x^x)=2*x equation into polynomial form, so I can use J's p. verb.
I was hoping the Newton Raphson approach would allow me to avoid that
exercise.
Skip
On Wed, Feb 5, 2020 at 4:25 PM Roger Hui <rogerhui.can...@gmail.com> wrote:
> To find polynomial roots, p. is the primitive of choice. Given the
> coefficients, p. finds the roots; given the roots and a multiplier, p.
> finds the coefficients.
>
> p. <1+i.20 NB. coefficients from roots and multiplier (here 1)
> 2432902008176640000 _8752948036761600000 13803759753640704000
> _12870931245150988800 8037811822645051776 _3599979517947607200
> 1206647803780373360 _311333643161390640 63030812099294896
> _10142299865511450 1307535010540395 _135585182899530 11310276995381
> _7561...
>
> p. p. <1+i.20 NB. roots and multiplier from coefficients
> ┌─┬──────────────────────────────────────────────────┐
> │1│20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1│
> └─┴──────────────────────────────────────────────────┘
>
> The polynomial above is Wilkinson's polynomial
> <https://en.wikipedia.org/wiki/Wilkinson%27s_polynomial>.
>
>
> On Wed, Feb 5, 2020 at 1:57 PM Lippu Esa <esa.li...@varma.fi> wrote:
>
> > If I remember correctly you should deflate the original equation by
> > dividing it by x-x1 where x1 is the first root found in order to find x2
> > the second root.
> >
> > Esa
> >
> >
> >
> >
> >
> > Sent from my Samsung Galaxy smartphone.
> >
> >
> > -------- Original message --------
> > From: Skip Cave <s...@caveconsulting.com>
> > Date: 2/5/20 21:49 (GMT+02:00)
> > To: "programm...@jsoftware.com" <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 <henryhr...@gmail.com> 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 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|break NB. After waiting a while...
> > > > | _2 0 1&p.Newton 1
> > > > NB. Failure to terminate...
> > > >
> > > >
> > > > On Wed, Feb 5, 2020 at 7:34 AM Henry Rich <henryhr...@gmail.com>
> > wrote:
> > > >
> > > >> 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 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
> > > >>>
> > > >>> Skip Cave
> > > >>> Cave Consulting LLC
> > > >>>
> > ----------------------------------------------------------------------
> > > >>> For information about J forums see
> >
> https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=01%7C01%7C%7Cf73805d19a944a8ea1e608d7aa747a61%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=LCHRYwGvI5EXRoKUQbKA%2BWG8v1vyKu9MDopz6xEBcSE%3D&reserved=0
> > > >>
> ----------------------------------------------------------------------
> > > >> For information about J forums see
> >
> https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=01%7C01%7C%7Cf73805d19a944a8ea1e608d7aa747a61%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=LCHRYwGvI5EXRoKUQbKA%2BWG8v1vyKu9MDopz6xEBcSE%3D&reserved=0
> > > >>
> > > >
> > >
> > > ----------------------------------------------------------------------
> > > For information about J forums see
> >
> https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=01%7C01%7C%7Cf73805d19a944a8ea1e608d7aa747a61%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=LCHRYwGvI5EXRoKUQbKA%2BWG8v1vyKu9MDopz6xEBcSE%3D&reserved=0
> > >
> > ----------------------------------------------------------------------
> > For information about J forums see
> >
> https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=01%7C01%7C%7Cf73805d19a944a8ea1e608d7aa747a61%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=LCHRYwGvI5EXRoKUQbKA%2BWG8v1vyKu9MDopz6xEBcSE%3D&reserved=0
> >
> >
> > T?m?n viestin sis?lt? liitteineen on luottamuksellinen ja tarkoitettu
> vain
> > sen vastaanottajalle. Jos et ole viestin tarkoitettu vastaanottaja,
> > pyyd?mme sinua poistamaan viestin liitteineen ja sen j?lkeen ilmoittamaan
> > asiasta v?litt?m?sti viestin l?hett?j?lle. Viestin sis?ll?n
> paljastaminen,
> > kopioiminen tai muu k?ytt? on kielletty.
> >
> > The contents of this message and any attachments are confidential and
> > meant solely for the intended recipient. If you are not the intended
> > recipient, we kindly ask that you delete the message and its attachments,
> > and immediately notify the sender of the email. Disclosing, copying or
> > using the contents of the message is strictly prohibited.
> > ----------------------------------------------------------------------
> > 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
