/* Copyright (C) 2004 Viktor T. Toth <http://www.vttoth.com/>
 * 
 * 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.
 *
 * ITENSOR frames, torsion, and nonmetricity demo
 */

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

("Partial differentiation with respect to a coordinate")$
ishow(idiff(f([],[]),k))$
ishow(idiff(v([i],[]),k))$
ishow(idiff(a([i],[j]),k))$
("Partial differentiation is a commutative operation")$
ishow(idiff(idiff(v([i],[]),k),l)-idiff(idiff(v([i],[]),l),k))$
("Unless a frame base is used")$
iframe_flag:true;
ishow(idiff(idiff(v([i],[]),k),l)-idiff(idiff(v([i],[]),l),k))$
iframe_flag:false;
("To undo a partial differentation, use the undiff function")$
ishow(v([i],[],k))$
exp:ishow(undiff(%))$
("Use rediff to evaluate all occurrences of idiff() again")$
ishow(rediff(exp))$
("These are useful for tensors that cannot be evaluated in derivative form")$
exp:ishow('icurvature([i,j,k],[m],n))$
("Evaluation of this expression causes an error")$
errcatch(ev(exp,nouns));
("Here is when undiff, ev, rediff helps, which is what evundiff does")$
ishow(evundiff(exp))$

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