itensor: covdiff(metric)



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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