Re: cubic quaternion based surface

*To*: mathgroup at smc.vnet.net*Subject*: [mg53557] Re: cubic quaternion based surface*From*: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>*Date*: Tue, 18 Jan 2005 05:07:57 -0500 (EST)*Organization*: Uni Leipzig*References*: <cs5ap3$3qj$1@smc.vnet.net> <cs9c22$jkk$1@smc.vnet.net> <cscpfe$du4$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, do you mean that Mathematica should see that aMatrix^n_Integer is aMatrix.aMatrix. .. ? You can try to remove the Listable attribute from Power[] and set up a rule, try In[]:=m = {{a, b}, {c, d}}; m^2 gives Out[]={{a^2, b^2}, {c^2, d^2}} with Unprotect[Power] ClearAttributes[Power, Listable] Power[m_?MatrixQ, n_Integer] := MatrixPower[m, n] Protect[Power] the Power[] function will work for a matrix. But be carefull because some other functions will use the Listable attribute of Power[] Regards Jens "Roger Bagula" <tftn at earthlink.net> schrieb im Newsbeitrag news:cscpfe$du4$1 at smc.vnet.net... > Jens-Peer Kuska wrote: > >> Hi, >> >> you mean >> x[t_]=x0/(Sqrt[2]-t0) >> y[t_]=y0/(Sqrt[2]-t0) >> z[t_]=z0/(Sqrt[2]-t0) >> >> without the SetDelayed[] because otherwise the t_ pattern >> is not replaced by p in your second call of ParametricPlot3D[] >> >> Regards >> Jens >> >> "Roger L. Bagula" <rlbtftn at netscape.net> schrieb im Newsbeitrag >> news:cs5ap3$3qj$1 at smc.vnet.net... >> >>>Clear[x0,y0,z0,t,p,x,y,z] >>>(* four space coordinates*) >>>x0=Cos[t-0]; >>>y0=Cos[t-Pi]; >>>z0=Cos[t+2*Pi/3]; >>>t0=Cos[t-Pi/6]; >>>(*Clifford torus projection*) >>>x[t_]:=x0/(Sqrt[2]-t0) >>>y[t_]:=y0/(Sqrt[2]-t0) >>>z[t_]:=z0/(Sqrt[2]-t0) >>>g=ParametricPlot3D[{x[t],y[t],z[t]},{t,-Pi,Pi}] >>>(* this resulting surface is a projective plane of a quaternionic type*) >>>g2=ParametricPlot3D[{x[t]*z[p],y[t]*x[p],z[t]*y[p]},{t,-Pi,Pi},{p,-Pi,Pi}, >>> Boxed->False,Axes->False,PlotPoints->60,PlotRange->All] >>>Show[g2,ViewPoint->{0.001, -0.045, 3.383}] >>>Show[g2,ViewPoint->{-3.360, -0.024, 0.397}] >>> >> >> >> > You're probably right. > I just put in the ":=" so I could get > the whole thing in a screen capture. > My big problem is I'd like to get Mathematica to consider i,j,k as > matrices instead of numbers. > These groups can be generalized to i^n, j^n,k^n, > but they make more sense as SU(2) type matrices. > Roger >