### The Maxima on-line user's manual

Algebra Calculator

#### Covdiff

Function: covdiff (<expr>, <v_1>, <v_2>, ...) Yields the covariant derivative of <expr> with respect to the variables <v_i> in terms of the Christoffel symbols of the second kind (`ichr2`). In order to evaluate these, one should use `ev(<expr>,ichr2)`.

```          (%i1) load(itensor);
(%o1)      /share/tensor/itensor.lisp
(%i2) entertensor()\$
Enter tensor name: a;
Enter a list of the covariant indices: [i,j];
Enter a list of the contravariant indices: [k];
Enter a list of the derivative indices: [];
k
(%t2)                                a
i j
(%i3) ishow(covdiff(%,s))\$
k         %1     k         %1     k
(%t3)     - a     ichr2    - a     ichr2    + a
i %1      j s    %1 j      i s    i j,s```

k %1 + ichr2 a %1 s i j

`          (%i4) imetric:g;`
`          (%o4)                                  g`
`          (%i5) ishow(ev(%th(2),ichr2))\$`
`                   %1 %4  k`
`                  g      a     (g       - g       + g      )`
`                          i %1   s %4,j    j s,%4    j %4,s`
`          (%t5) - ------------------------------------------`
`                                      2`
`              %1 %3  k`
`             g      a     (g       - g       + g      )`
`                     %1 j   s %3,i    i s,%3    i %3,s`
`           - ------------------------------------------`
`                                 2`
`              k %2  %1`
`             g     a    (g        - g        + g       )`
`                    i j   s %2,%1    %1 s,%2    %1 %2,s     k`
`           + ------------------------------------------- + a`
`                                  2                         i j,s`
`          (%i6)`

```(%o1)                                true
(%i2) ```

### Related Examples

imetric(g);

components(g([i,j],[]...

Calculate

##### covdiff

? covdiff;

Calculate

imetric(g);

components(g([i,j],[]...

Calculate

imetric(g);

components(g([i,j],[]...

Calculate

? covdiff;

Calculate