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The Maxima on-line user's manual

Algebra Calculator

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Covdiff 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) 

Covdiff Example

Related Examples