/* 
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2 of
 * the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be
 * useful, but WITHOUT ANY WARRANTY; without even the implied
 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
 * PURPOSE.  See the GNU General Public License for more details.
 *
 * Tensor index contraction
 */

if get('itensor,'version)=false then load(itensor);

("defcon() assigns contraction properties to tensors")$
defcon(e,f,g)$
ishow(e([a],[b])*f([b],[c]))$
ishow(contract(%))$

("kdelta is the Kronecker delta with special contraction properties")$

dim:3;
ishow(contract(kdelta([a],[b])*kdelta([b],[a])))$
ishow(ev(%,kdelta))$

("The imetric() function sets up contraction properties for the metric")$
remcomps(g);
imetric(g)$
ishow(g([i,j],[]))$
ishow(g([],[j,k]))$
ishow(%th(1)*%th(2))$
ishow(contract(rename(expand(%))))$

("The contract() function can also raise and lower indices")$
defcon(Ti);
ishow(Te([i,j],[k,l])*Ti([k,m])*Ti([l,n]))$
ishow(contract(%))$
ishow(Te([i,j],[k,l])*Ti([],[i,n])*Ti([],[j,m]))$
ishow(contract(%))$

/* End of demo -- comment line needed by MAXIMA to resume demo menu */