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MathGroup Archive 2005

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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
> 



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