clifford3.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")$

"Clifford implements Clifford algebra for Maxima."$

"Inner and outer products in G(3)"$
 	clifford(e, 3);
	
	"initialize variables"$
 	a1:cvect(a),b1:cvect(b), c1:cvect(c);
 	b1:cvect(b);
 	c1:cvect(c);
	
	"assocativity of outer product"$
 	L1:(a1 & b1 )& c1, factor;
 	L2:a1 & (b1 & c1) ,factor;	
	L1-L2;
	
 	L1:a1 | (b1 & c1);
 	L2:(a1| b1).c1 - (a1 | c1) .b1,expand;
 	L1-L2;
	
	"cross prduct"$
 	D1:c1| (-%iv. (a1 & b1)),dotsimpc;
 	
	"matrix  representation"$
 	M1: matrix(
 	[a[1],a[2],a[3]], 
 	[b[1],b[2],b[3]], 
 	[c[1],c[2],c[3]]
 	);
 	D2:determinant(M1);
 	
 	equal(D1,D2),pred;
	
	e[1] &e[2] &e[3];
	(1+e[1])&(1+e[1]);		
	(1+e[1])&(1-e[1]);
	"outer product multiplication table"$
		
	mtable2o();	

	"left contraction"$
	
	inprotype:'lc;
	((1+e[1])/2)|( (1+e[1])/2),factor;		
	mtable2i();
	
	"right contraction"$
	inprotype:'rc;
	mtable2i();
	
	"symmetric"$
	inprotype:'sym;
	mtable2i();