Re: ctensor - components as a matrix

 Hi Viktor,
Thank you for your answer, nice example.
Of course, you can obtain the same result with:
mat_trace(diag_matrix(ρ,-p,-p,-p));

and you don't need "ctensor" for that.
Daniel Volinski.
    En martes, 7 de abril de 2026, 22:42:30 GMT+3, Viktor T. Toth <[email protected]> escribió:  
 
  
Dear Daniel,
 
On the face of it, the component-wise definition of a tensor is indeed fundamentally at odds, philosophically, with the abstract index formalism that itensor aims to represent.
 
Having said that, I could think of a few legitimate use cases, including, e.g., mixed-index rank-2 tensors in particular, which are unchanged under a change of coordinates. Having said that, it's not a construct I ever used much myself.
 
Still, here's a silly but valid example (trace of the perfect fluid stress-energy tensor):
 
load(itensor);
 imetric(g);
 components(T([m],[n]),diag_matrix(rho,-p,-p,-p));
 ishow(g([m,n],[])*T([],[m,n]))$
 ishow(contract(%))$
 sum(%,n,1,dim),eval;
 
 
 
Viktor
 

 
 

 
 On 2026-04-06 02:27, Daniel Volinski via Maxima-discuss wrote:
  
 
 Hi all, 
  In the package "ctensor" I can define the components of a tensor in 4 ways, The second is to define the components as a matrix, like this:   lg:-ident(4)$lg[1,1]:1$lg;
   components(g([i,j],[]),lg);
   ishow(g([i,j],[]))$
  I've never found a usage for that. Do you know of any usage of this construct? i.e. something that will be useful for further calculations. 
  Thank you, 
  Daniel Volinski 
   
  
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