Maxima Manual. Node: Introduction to Ctensor

37.1: Introduction to Ctensor

- Component Tensor Manipulation Package. To use the CTENSR package, type TSETUP(); which automatically loads it from within MACSYMA (if it is not already loaded) and then prompts the user to input his coordinate system. The user is first asked to specify the dimension of the manifold. If the dimension is 2, 3 or 4 then the list of coordinates defaults to [X,Y], [X,Y,Z] or [X,Y,Z,T] respectively. These names may be changed by assigning a new list of coordinates to the variable OMEGA (described below) and the user is queried about this. ** Care must be taken to avoid the coordinate names conflicting with other object definitions **. Next, the user enters the metric either directly or from a file by specifying its ordinal position. As an example of a file of common metrics, see TENSOR;METRIC FILE. The metric is stored in the matrix LG. Finally, the metric inverse is computed and stored in the matrix UG. One has the option of carrying out all calculations in a power series. A sample protocol is begun below for the static, spherically symmetric metric (standard coordinates) which will be applied to the problem of deriving Einstein's vacuum equations (which lead to the Schwarzschild solution) as an example. Many of the functions in CTENSR will be displayed for the standard metric as examples.

```(C2) TSETUP();

Enter the dimension of the coordinate system:
4;
Do you wish to change the coordinate names?
N;
Do you want to
1. Enter a new metric?
2. Enter a metric from a file?
3. Approximate a metric with a Taylor series?
Enter 1, 2 or 3
1;
Is the matrix  1. Diagonal  2. Symmetric  3. Antisymmetric  4. General
Answer 1, 2, 3 or 4
1;
Row 1 Column 1:  A;
Row 2 Column 2:  X^2;
Row 3 Column 3:  X^2*SIN(Y)^2;
Row 4 Column 4:  -D;
Matrix entered.
Enter functional dependencies with the DEPENDS function or 'N' if none
DEPENDS([A,D],X);
Do you wish to see the metric?
Y;
[ A  0       0        0  ]
[                        ]
[     2                  ]
[ 0  X       0        0  ]
[                        ]
[         2    2         ]
[ 0  0   X  SIN (Y)   0  ]
[                        ]
[ 0  0       0       - D ]
Do you wish to see the metric inverse?
N;

```
Ctensor Ctensor Definitions for Ctensor