/* 
 * 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.
 *
 * Cartan algebra of exterior forms
 */

("The Cartan package implements index-free exterior calculus")$
if get('cartan,'version)=false then load(cartan);
derivabbrev:true;
("Initialize the package by supplying the list of coordinates")$
init_cartan([x,y,z]);
("The basis will be stored in cartan_basis")$
cartan_basis;
("Let us define a vector as a list of elements")$
vr:[v1,v2,v3];
("This is an example of a 1-form")$
f1:x~dy+z~dz;
("This one is a 2-form")$
f2:dz~f1;
("Contraction with a vector space is denoted by the | operator")$
vr|f1;
("The exterior derivative of a form is computed by ext_diff")$
ext_diff(f1);
ext_diff(f3(x,y,z)~dx);
("Let use define vr now as a vector field over the coordinates")$
depends(v1,[x,y,z],v2,[x,y,z],v3,[x,y,z]);
("The Lie derivative of a form with respect to a scalar")$
lie_diff(vr,f2);
("Let us define another vector field")$
depends(w1,[x,y,z],w2,[x,y,z],w3,[x,y,z]);
wr:[w1,w2,w3];
("And compute its Lie-derivative")$
lie_diff(vr,wr);