Yes! It is quite cool to have this in the core language. Esa
Sent from my Samsung Galaxy smartphone. -------- Original message -------- From: Roger Hui <rogerhui.can...@gmail.com> Date: 2/6/20 00:25 (GMT+02:00) To: programm...@jsoftware.com Subject: Re: [Jprogramming] Derivatives 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://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FWilkinson%2527s_polynomial&data=01%7C01%7C%7C1f66023d8bde4b3d86ed08d7aa8a49c6%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=0OvS4sCtmBm0PVIyoL%2BdQVrW5yMyXB18YagG10Ycs80%3D&reserved=0>. 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%7C1f66023d8bde4b3d86ed08d7aa8a49c6%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=A7nwqlUNU4TUa9CKMhXronD%2FKcbvfXRofZH8vWwOF0k%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%7C1f66023d8bde4b3d86ed08d7aa8a49c6%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=A7nwqlUNU4TUa9CKMhXronD%2FKcbvfXRofZH8vWwOF0k%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%7C1f66023d8bde4b3d86ed08d7aa8a49c6%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=A7nwqlUNU4TUa9CKMhXronD%2FKcbvfXRofZH8vWwOF0k%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%7C1f66023d8bde4b3d86ed08d7aa8a49c6%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=A7nwqlUNU4TUa9CKMhXronD%2FKcbvfXRofZH8vWwOF0k%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 > https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=01%7C01%7C%7C1f66023d8bde4b3d86ed08d7aa8a49c6%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=A7nwqlUNU4TUa9CKMhXronD%2FKcbvfXRofZH8vWwOF0k%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%7C1f66023d8bde4b3d86ed08d7aa8a49c6%7C5090e269dbea4e98a9aa3e70be5890f7%7C0&sdata=A7nwqlUNU4TUa9CKMhXronD%2FKcbvfXRofZH8vWwOF0k%3D&reserved=0 Taman viestin sisalto liitteineen on luottamuksellinen ja tarkoitettu vain sen vastaanottajalle. Jos et ole viestin tarkoitettu vastaanottaja, pyydamme sinua poistamaan viestin liitteineen ja sen jalkeen ilmoittamaan asiasta valittomasti viestin lahettajalle. Viestin sisallon paljastaminen, kopioiminen tai muu kaytto 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
