Well, itensor is not really designed to deal with numeric indices. Indices
are just abstract placeholders, and are supposed to be unevaluated symbols.
Your problem can be easily dealt with by using symbols in place of your
numeric indices, e.g.,
(%i5)
kdelta([a],[i])*kdelta([b],[j])*g([i,j],[])*kdelta([c],[k])*kdelta([d],[p])*
g([k,p],[])$
(%i6) ishow(contract(%))$
(%t6) g g
a b c d
If you wish, you can then replace the symbols with numeric indices after the
contraction:
(%i7) %,a=1,b=1,c=1,d=1$
(%i8) ishow(%)$
2
(%t8) g
1 1
But once you have done this and you have numeric indices, you should not
expect itensor's facilities, like contract(), to work. So it's best to leave
this step last, to present a final result in the desired form.
Viktor
-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Yaroslav Alekseev
Sent: Thursday, August 12, 2010 12:12 PM
To: maxima at math.utexas.edu
Subject: itensor: error during contract
Hi to all,
I have a error using itensor:
(%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 $CANFORM in DEFUN
(%o1) /usr/local/share/maxima/5.22.0/share/tensor/itensor.lisp
(%i2) imetric(g);
(%o2) done
(%i3)
kdelta([1],[i])*kdelta([1],[j])*g([i,j],[])*kdelta([1],[k])*kdelta([1],[p])*
g([k,p],[])$
(%i4) contract(%);
g g has improper indices
1 1 1 1
-- an error. To debug this try: debugmode(true);
(%i5)
or (actually the same thing):
(%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 $CANFORM in DEFUN
(%o1) /usr/local/share/maxima/5.22.0/share/tensor/itensor.lisp
(%i2) defcon(g,g,kdelta);
(%o2) done
(%i3)
kdelta([1],[i])*kdelta([1],[j])*g([i,j],[])*kdelta([1],[k])*kdelta([1],[p])*
g([k,p],[])$
(%i4) contract(%);
g g has improper indices
1 1 1 1
-- an error. To debug this try: debugmode(true);
(%i5)
correct answer is something like g([1,1],[])^2 in both cases.
Thanks in advance,
Yaroslav
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