Re: cubic quaternion based surface

*To*: mathgroup at smc.vnet.net*Subject*: [mg53521] Re: cubic quaternion based surface*From*: Roger Bagula <tftn at earthlink.net>*Date*: Sat, 15 Jan 2005 21:07:49 -0500 (EST)*References*: <cs5ap3$3qj$1@smc.vnet.net> <cs9c22$jkk$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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