clifford2.dem

/* Copyright (C) 2015 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.
 *
 * Clfford 1.0 demo based on atensor demo by Viktor T. Toth  
 */

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

("Clifford implements Clifford algebra for Maxima.")$

("Let us begin with the complex algebra")$
clifford(e,0,1,0);

("complex multiplication table")$
mtable2();

("split-complex algebra")$
clifford(e,1,0,0);

("split-complex multiplication table")$
mtable2();

("dual number algebra")$
clifford(e,0,0,1);

("dual number full  multiplication table")$
mtable2();

("Quaternion algebra")$
clifford(e,0,2,0);

("here are all elements of the algebra")$
elements();

("quaternion multiplication table")$
mtable2();

("anticommutativity")$
e[2].e[1];

e[1].e[2].e[1].e[2];
("simplification of products")$
e[1].e[2].e[1].e[2], dotsimpc;
e[2].e[1].e[1].e[2];
e[2].e[1].e[1].e[2], dotsimpc;

("simplification of inversions")$
1/e[2] ;
1/e[2], dotinvsimp;
1/(e[1].e[2]);
1/(e[1].e[2]), dotinvsimp;

("full simplification")$
1/(1+e[1]);
1/(1+e[1]), cliffsimpall;

("scalar product")$
e[1]*e[2];
(1+e[1])*(1+e[1]),expand;

("outer product")$
e[1] & e[2];
(1+e[1])&(1+e[1]),expand;
("computation of Quaternion inverses")$
block(
	declare([a,b,c,d],scalar),
	cc:cc:a+b*e[1]+c*e[2]+d*e[1].e[2],
	dd:cinv(cc)
);
("checking the result")$
dd.cc, expand, ratsimp;
%,cliffsimpall;
/* End of demo -- comment line needed by MAXIMA to resume demo menu */