itensor: covdiff(metric)



On 22.08.2010 22:08, Viktor T. Toth wrote:
> This would be one way:
>
> (%i1) load(itensor);
> (%o1) /usr/share/maxima/5.21.0/share/tensor/itensor.lisp
> (%i2) imetric(g);
> (%o2)                      done
> (%i3) decsym(g,2,0,[sym(all)],[]);
> (%o3)                      done
> (%i4) covdiff(g([i,j],[]),k)$
>
> (%i5) ishow(ev(%,ichr2))$
>           %1 %3
>          g      g     (g       - g       + g      )
>                  i %1   k %3,j    j k,%3    j %3,k
> (%t5) - ------------------------------------------
>                              2
>           %1 %2
>          g      g     (g       - g       + g      )
>                  %1 j   k %2,i    i k,%2    i %2,k
>        - ------------------------------------------ + g
>                              2                         i j,k
> (%i6) canform(contract(rename(expand(%))));
> (%o6)                        0
>
>
> Although this works, there are indeed expressions that canform should be
> smart enough to be able to simplify, but it isn't.
>
>
> Viktor
>
>
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
> On Behalf Of Yaroslav Alekseev
> Sent: Sunday, August 22, 2010 1:14 PM
> To: maxima at math.utexas.edu
> Subject: itensor: covdiff(metric)
>
> Hi to all,
> how to simplify covdiff(g([i,j],[]),k) ?
> I have in maxima:
>
> Maxima 5.22.1 http://maxima.sourceforge.net
> using Lisp SBCL 1.0.34
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> (%i1) load(itensor);
> STYLE-WARNING: redefining $NAME in DEFUN
> STYLE-WARNING: redefining DERIV in DEFUN
> STYLE-WARNING: redefining SDIFF in DEFUN
> STYLE-WARNING: redefining I-$DEPENDENCIES in DEFUN
> STYLE-WARNING: redefining $DECSYM in DEFUN
> STYLE-WARNING: redefining $CANFORM in DEFUN
> (%o1)      /usr/local/share/maxima/5.22.1/share/tensor/itensor.lisp
> (%i2) imetric(g);
> (%o2)                                done
> (%i3) decsym(g,2,0,[sym(all)],[]);
> (%o3)                                done
> (%i4) decsym(g,0,2,[],[sym(all)]);
> (%o4)                                done
> (%i5) q:covdiff(g([i,j],[]),k);
> (%o5) - g([i, %1], []) ichr2([j, k], [%1]) - g([%1, j], []) ichr2([i,
> k], [%1])
>                                                                + g([i,
> j], [], k)
> (%i6) ishow(canform(ev(q,ichr2)))$
>            %1 %2  %8 %9                      %1 %2  %6 %7
>           g      g      g     g     g       g      g      g     g      g
>                   ,%2    %1 j  %8 i  %9 k           ,k     %1 j  %2 %6  %7 i
> (%t6) - ------------------------------- + --------------------------------
>                          2                                 2
>                            %1 %2  %16 %17
>                           g      g        g       g      g
>       %1 %2                       ,j       %1 %16  %17 k  %2 i
>    - g      g     g     + ------------------------------------
>       ,k     %1 i  %2 j                    2
>       %1 %2  %14 %15                        %1 %2  %12 %13
>      g      g        g      g      g       g      g        g       g      g
>              ,%1      %14 j  %15 k  %2 i           ,k       %1 %12  %13
> j  %2 i
>    - ----------------------------------- +
> ------------------------------------
>                       2                                     2
>       %1 %2  %10 %11
>      g      g        g     g       g
>              ,i       %1 j  %10 %2  %11 k
>    + ------------------------------------
>                       2
> (%i7) kill(all);
> (%o0)                                done
> (%i1)
>
> Thanks in advance,
> Yaroslav
>
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>
>    
Thanks