itensor and ctensor: indexed objects in moving frames in specific coordinate systems and frame basis

09.02.2011 15:52, Yaroslav Alekseev ?????:
> Viktor T. Toth <vttoth at vttoth.com> ?????(?) ? ????? ?????? Tue, 08 Feb 
> 2011 22:39:04 +0300:
>
>> I think the only step missing is an evaluation of ifb before 
>> converting to a
>> ctensor expression. Try this:
>>
>> load(itensor);
>> load(ctensor);
>> iframe_flag:true;
>> cframe_flag:true;
>> ct_coordsys(polar)$
>> depends([V,ifg,ifr,ifri],ct_coords)$
>> ishow(covdiff(V([],[j]),j))$
>> ishow(ev(%,icc2,ifc2,ifc1,ifb))$
>> eqn:eq=%$
>> ceqn:ic_convert(eqn)$
>> ev(ceqn);
>>
>> A word of warning: Presently, ic_convert has no explicit knowledge 
>> about the
>> meaning of the symbols ifg, ifr, and ifri. It just treats them as it 
>> would
>> treat any other indexed objects. In the present example, it is not 
>> relevant
>> as the symbols cancel; in other cases, however, you may need to take 
>> steps
>> to identify the itensor symbols ifr, ifri, and ifg with the 
>> corresponding
>> ctensor matrices fri, ifri, and lfg/ufg as appropriate.
>>
>>
>> Viktor
>
> Ok, thank you for response.
> I have to define symbols ifr, ifri, and ifg. So, I've tried this:
>
> load(itensor);
> load(ctensor);
> iframe_flag:true;
> cframe_flag:true;
> ct_coordsys(polar)$
> depends(V,ct_coords)$
> ishow(covdiff(V([],[j]),j))$
> ishow(ev(%,icc2,ifc2,ifc1,ifb))$
> eqn:eq=%$
> ceqn:ic_convert(eqn)$
> ifg:matrix([1,0],[0,1]);
> fri:matrix([1,0],[0,1/r]);
> ifri:matrix([1,0],[0,r]);
> ev(ceqn);
>
> But I've got very strange answer:
>
>
> (%i14) ev(ceqn);
>                                d          d
> (%o14)                        ---- (V ) + -- (V )
>                               dphi   2    dr   1
>
> It seems to me that the answer should be something like this (ordinary 
> divergence):
>
>
>                                 dV2
>                                 ----
>                                 dphi   dV1   V1
> (%o21)                          ---- + --- + --
>                                  r     dr    r
>
>
Seems you are mixing the co-variant (or con-travariant) components with 
ones for orthonormal
but non-coordinate basis. (I mean you can not get the basis component 
via differentiation)
Rgds