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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