cliffordan.dem

/* Copyright (C) 2016 Dimiter Prodanov
 * 
 * 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.
 *
 * clffordan demo
 */

if get('clifford,'version)=false then load("clifford")$
if get('cliffordan,'version)=false then load("cliffordan")$

"Clifford implements Clifford algebra for Maxima."$
"Geometric calculus in G(3)"$
 clifford(e,3);

("initialize variables")$
 
 dependsv(F,[t,x,y,z]);
 r:cvect([x,y,z]);
 
 ("the vector derivative is")$
 mvectdiff(F,r);
 
 ("the Laplacian is")$
 mvectdiff(F,r,2);
 
 ("the simplest vector derivative")$ 
 mvectdiff(r,r);
 
("exponent")$ 
 mvectdiff(exp(r),r);

("logarithm")$  
 mvectdiff(log(r),r),factor;

 ("square")$  
 mvectdiff((-cnorm(r)),r),factor;
 
 ("inverse vector")$
 mvectdiff(r/(-cnorm(r)),r);
 
 ("unit vector")$
 mvectdiff(r/sqrt(-cnorm(r)),r);
 
 declare(k, scalar);

("k-power")$  
 mvectdiff((-cnorm(r))^k/2,r),factor;
 
("more complicated examples",
derivabbrev:true)$ 
 
dependsv(A, [x,y,z]);
P:celem(A,[[],x,y,z]);
mvectdiff(log(cnorm2(P))/2,r);
mvectdiff(log(cnorm2(F))/2,r);
 
 derivabbrev:false$
 
/* End of demo -- comment line needed by MAXIMA to resume demo menu */