clifford_eula.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."$
"Euler-Lagrange problems in G(3)"$
 clifford(e,3);

 derivabbrev:true$
 "initialize variables"$
	AA: celem(A,[t,x,y,z]);
	dependsv(A,[t,x,y,z]);
	r:cvect([x,y,z]);
	
	"F-multivector"$
	F:mvectdiff(AA,t-r);
	
	"Lagrangian density"$
	L:lambda([x],1/2*scalarpart(cliffsimpall(x.x)))(F);
	
	"scalar, vector and bivector parts"$
	S:scalarpart(F);
	V:vectorpart(F);
	Q:grpart(F,2);
	
	"identity"$
	L-1/2*(S.S+V.V+Q.Q),cliffsimpall;
	
	"Euler- Lagrange equations"$
	dA:mvectdiff(AA,r);
	
	ELeq:ciELfdiff(L, t+r,[AA,dA]);
	
	"matrix form"$
	bdecompose(ELeq);
	
	 derivabbrev:false$
 
/* End of demo -- comment line needed by MAXIMA to resume demo menu */