problem about using itensor to demonstrate the riemann tensor' symmetry
- Subject: problem about using itensor to demonstrate the riemann tensor' symmetry
- From: 163
- Date: Thu, 2 May 2013 22:07:09 +0800
my code is below. why can't i get the answer zero. thanks.
load(itensor)$
remcomps(g);
imetric(g);
decsym(g,2,0,[sym(all)],[]);
decsym(g,0,2,[],[sym(all)]);
rt(i,j,k,l) := idiff( ichr1([j,l,i]),k ) - idiff( ichr1([j,k,i]),l )
+ ichr1([i,l,r])*ichr2([j,k],[r]) - ichr1([i,k,r])*ichr2([j,l],[r])$
expr:rt(i,j,k,l) + rt(j,i,k,l);
expand(expr)$
canform(%)$
nterms(%);
ishow( conmetderiv(simpmetderiv(canform(contract(rename(%th(2))))),g))$
nterms(%);
ishow( conmetderiv(simpmetderiv(canform(contract(rename(%th(2))))),g))$
nterms(%);