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