clifford_potential.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.
 *
 * Potential problems demo
 */

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

"Clifford implements Clifford algebra for Maxima."$

"Potential problems in G(3)"$
 clifford(e,3);

"initialize variables"$
	
    r:cvect([x,y,z]);
	
	"Green's function"$
	
	G:r/sqrt(-cnorm(r))^3;
	
	"differentiation of Green's function"$
	mvectdiff(G,r);
	
	"Potential function"$
	P:-1/sqrt(-cnorm(r));
	
	"differentiation of potential function"$
	D1:mvectdiff(P,r);
	
	"checking for  equality"$
	equal(GG_c, D2),pred;
	
	mvectdiff(P,r,2);

	"define cyclindrical coordinates"$
	declare( [rho, phi], scalar);
	cyl_eq:[x=rho*cos(phi), y=rho*sin(phi)];
	
	
	"coordinate substitution"$
	rc:coordsubst(r, cyl_eq);
	
	GG_c:coordsubst(G, cyl_eq),factor;
	V:coordsubst(P,cyl_eq);
	
	"differentiation of Green's function"$
	mvectdiff(GG_c,rc);	

	"differentiation of potential function"$
	D2:mvectdiff(V,rc);
	
	"checking for  equality"$
	equal(GG_c, D2),pred;
	
	/* End of demo -- comment line needed by MAXIMA to resume demo menu */