Next: Functions and Variables for ctensor, Previous: ctensor, Up: ctensor [Contents][Index]
ctensor is a component tensor manipulation package. To use the ctensor
package, type load("ctensor").
To begin an interactive session with ctensor, type csetup(). You are
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 ct_coords (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.
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 ctensor will be
displayed for the standard metric as examples.
(%i1) load("ctensor");
(%o1) /share/tensor/ctensor.mac
(%i2) csetup();
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?
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 ]
(%o2) done
(%i3) christof(mcs);
a
x
(%t3) mcs = ---
1, 1, 1 2 a
1
(%t4) mcs = -
1, 2, 2 x
1
(%t5) mcs = -
1, 3, 3 x
d
x
(%t6) mcs = ---
1, 4, 4 2 d
x
(%t7) mcs = - -
2, 2, 1 a
cos(y)
(%t8) mcs = ------
2, 3, 3 sin(y)
2
x sin (y)
(%t9) mcs = - ---------
3, 3, 1 a
(%t10) mcs = - cos(y) sin(y)
3, 3, 2
d
x
(%t11) mcs = ---
4, 4, 1 2 a
(%o11) done
Next: Functions and Variables for ctensor, Previous: ctensor, Up: ctensor [Contents][Index]