Ah, I see. I was somehow thinking that these were parametric curves. Thanks,
-- Raul On Fri, Feb 19, 2016 at 1:16 AM, Kip Murray <[email protected]> wrote: > In your example, 0 1 is the polynomial coefficients for the straight line > being rotated. In usual math notation this is the line y = x = 0 + 1 x . > When you rotate this line by 1p1 radians about the origin 0 0 you get the > same straight line, described by 0 1 which is the answer given. (I am > "cleaning", of course.) > > Also when you consider the straight line y = 1 + 2x (described by 1 2) you > notice the point 0 1 is on this line so when you rotate this line by 1p1 > radians about the point 0 1 you get the same line, described by the answer > 1 2 . > > It helps to draw pictures of the indicated straight lines. Hope this helps. > > --Kip > > On Thursday, February 18, 2016, Raul Miller <[email protected]> wrote: > >> Changing the center of rotation to 0 0 doesn't seem to make a difference. >> >> 0 1 linrot 1p1;0 0 >> 1.11022e_16 1 >> >> But presumably this means I am not understanding what it means to >> "rotate a linear polynomial"? >> >> -- >> Raul >> >> On Thu, Feb 18, 2016 at 11:46 PM, Kip Murray <[email protected] >> <javascript:;>> wrote: >> > No, because his center of rotation is not 0 0 . In his first two >> examples >> > the center of rotation is 0 1 and in the third it is 1 1 . --Kip >> > >> > On Thursday, February 18, 2016, Raul Miller <[email protected] >> <javascript:;>> wrote: >> > >> >> I'm not quite sure I follow what you are doing here. >> >> >> >> Shouldn't 2p1 be a neutral rotation, with 1p1 being a reversal of >> >> direction? >> >> >> >> Thanks, >> >> >> >> -- >> >> Raul >> >> >> >> >> >> On Thu, Feb 18, 2016 at 10:23 PM, Louis de Forcrand <[email protected] >> <javascript:;> >> >> <javascript:;>> wrote: >> >> > To continue with the rotation challenges, write a verb that rotates a >> >> linear >> >> > polynomial (coeffs in x) by 0 {:: y with a centre of 1 {:: y: >> >> > >> >> > 1 2 linrot 1p1 ; 0 1 >> >> > 1 2 >> >> > 1 2 linrot 1r2p1 ; 0 1 >> >> > 1 _0.5 >> >> > 1 2 linrot 1p1;1 1 >> >> > _3 2 >> >> > >> >> > My take: >> >> > linrot=: ({: %. 1 ,. {.)@rotposmat >> >> > rotposmat=: centre + j./@posmat |:@:+.@:* r.@angle >> >> > centre=: 1&({::)@] >> >> > posmat=: (] ,: p.)&0 1@[ - centre >> >> > angle=: 0&({::)@] >> >> > >> >> > It uses matrix division on a rotated set of two points from the >> original >> >> > polynomial. Not very elegant, but I’m pretty sure it works. >> >> > >> >> > Best regards, >> >> > Louis >> >> > >> >> >> On 17 Feb 2016, at 06:40, Kip Murray <[email protected] >> <javascript:;> >> >> <javascript:;>> wrote: >> >> >> >> >> >> Not bad. I didn't know about r. . For clean I use >> >> >> >> >> >> clean =: (* *!.1e_14@|)"0&.+. >> >> >> >> >> >> --Kip >> >> >> >> >> >> On Tuesday, February 16, 2016, Raul Miller <[email protected] >> <javascript:;> >> >> <javascript:;> <mailto:[email protected] <javascript:;> >> <javascript:;>>> wrote: >> >> >> >> >> >>> Well... >> >> >>> >> >> >>> rottheta=: (rot~ r.)~ >> >> >>> 1r2p1 rottheta 3 4 >> >> >>> _4 3 >> >> >>> 1r4p1 rottheta _1 1 >> >> >>> _1.41421 1.11022e_16 >> >> >>> >> >> >>> I remember there being a concise phrase to clean irrelevant bits >> near >> >> >>> zero in a complex number, but I can't remember what I need to search >> >> >>> on to find it, and my foggy memory of how to write it is failing me >> at >> >> >>> the moment. >> >> >>> >> >> >>> Still, this gets you close. >> >> >>> >> >> >>> -- >> >> >>> Raul >> >> >>> >> >> >>> >> >> >>> On Tue, Feb 16, 2016 at 11:50 PM, Kip Murray < >> [email protected] <javascript:;> >> >> <javascript:;> >> >> >>> <javascript:;>> wrote: >> >> >>>> I'm retired with time to "fool around". Finding an old rot90 verb >> >> that >> >> >>>> used multiplication by a 2 by 2 matrix, I sought a more direct way >> >> using >> >> >>>> complex numbers and found one of the solutions that was posted. I >> >> also >> >> >>>> learned a lot from the other solutions posted, thanks everyone! >> >> >>>> >> >> >>>> New puzzle: find a complex analysis way to do a rotation given its >> >> angle >> >> >>> in >> >> >>>> radians, examples: >> >> >>>> >> >> >>>> 1r2p1 rottheta 3 4 >> >> >>>> _4 3 >> >> >>>> >> >> >>>> 1r4p1 rottheta _1 1 >> >> >>>> _1.414213562 0 >> >> >>>> >> >> >>>> --Kip >> >> >>>> >> >> >>>> I'm also a former math professor! >> >> >>>> >> >> >>>> On Tuesday, February 16, 2016, David Lambert <[email protected] >> <javascript:;> >> >> <javascript:;> >> >> >>> <javascript:;>> wrote: >> >> >>>> >> >> >>>>> >> >> >>>>> what's your agenda, are you writing a book? Isn't there a >> homogeneous >> >> >>>>> coordinate system/transformation lab? >> >> >>>>> >> >> >>>>>> >> >> >>>>>> On 02/16/2016 06:16 PM, [email protected] >> <javascript:;> >> >> <javascript:;> >> >> >>> <javascript:;> wrote: >> >> >>>>>> >> >> >>>>>>> Date: Tue, 16 Feb 2016 15:18:43 -0600 >> >> >>>>>>> From: Kip Murray<[email protected] <javascript:;> >> <javascript:;> >> >> <javascript:;>> >> >> >>>>>>> To:"[email protected] <javascript:;> <javascript:;> >> <javascript:;>" < >> >> >>> [email protected] <javascript:;> <javascript:;> >> <javascript:;>> >> >> >>>>>>> Subject: [Jprogramming] A plane rotation >> >> >>>>>>> Message-ID: >> >> >>>>>>> < >> >> >>> caofworgvydb1nmjwxkb0wosyfnlubxcdz20sv11uksfcfay...@mail.gmail.com >> <javascript:;> >> >> <javascript:;> >> >> >>> <javascript:;>> >> >> >>>>>>> Content-Type: text/plain; charset=UTF-8 >> >> >>>>>>> >> >> >>>>>>> Fairly easy: write a verb that rotates a point in the plane by >> the >> >> >>> angle >> >> >>>>>>> of >> >> >>>>>>> a given complex number. For example >> >> >>>>>>> >> >> >>>>>>> 1j1 rot 1 1 NB. Rotate 1 1 counterclockwise 45 degrees >> >> >>>>>>> 0 1.414213562 >> >> >>>>>>> >> >> >>>>>>> Background information: when you multiply two complex numbers >> the >> >> >>>>>>> magnitudes are multiplied and the angles are added. >> >> >>>>>>> >> >> >>>>>>> --Kip Murray >> >> >>>>>>> >> >> >>>>>>> >> >> >>>>>> >> >> >>>>> >> >> ---------------------------------------------------------------------- >> >> >>>>> For information about J forums see >> >> http://www.jsoftware.com/forums.htm >> >> >>>> >> >> >>>> >> >> >>>> >> >> >>>> -- >> >> >>>> Sent from Gmail Mobile >> >> >>>> >> ---------------------------------------------------------------------- >> >> >>>> For information about J forums see >> >> http://www.jsoftware.com/forums.htm >> >> >>> >> ---------------------------------------------------------------------- >> >> >>> For information about J forums see >> http://www.jsoftware.com/forums.htm >> >> >> >> >> >> >> >> >> >> >> >> -- >> >> >> Sent from Gmail Mobile >> >> >> >> ---------------------------------------------------------------------- >> >> >> For information about J forums see >> http://www.jsoftware.com/forums.htm >> >> <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 >> > >> > >> > >> > -- >> > Sent from Gmail Mobile >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > Sent from Gmail Mobile > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
