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
