rtest_clifford4.mac

/*******************************
Clifford algebra
a lightweight package for performing Geometric Algebra calculations

tests for version
 v 25
 
usage:
file_search_maxima: append (file_search_maxima,["/path/to/clifford.mac"]);
batch("rtest_clifford", test);

@depends clifford.mac

**********************************
 * @license This library is free software; you can redistribute it and/or
 *      modify it under the terms of the GNU Lesser General Public
 *      License as published by the Free Software Foundation; either
 *      version 2.1 of the License, or (at your option) any later version.
 *
 *      This library 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
 *       Lesser General Public License for more details.
 *
 *      You should have received a copy of the GNU Lesser General Public
 *      License along with this library; if not, write to the Free Software
 *      Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */
 (kill(all),
  %start : absolute_real_time(),
    %path:"C:/Dropbox/maxima/$$$.{mac,mc}",
  file_search_maxima:append (file_search_maxima , [%path]),
  load("clifford"),
  'done);
'done$
get('clifford,'version);
v25$
/*a | b + a & b;
a.b$
(A1: a & b &c + b & c & a + c& a &b, 
ratsimp(A1+(- a . b . c - a . c . 'cinvolve(b)+a . 'cinvolve(c) . 'cinvolve(b)+
'cinvolve(a) . 'cinvolve(b) . 'cinvolve(c)- b . a . 'cinvolve(c)+b . 'cinvolve(a)
 . 'cinvolve(c)- b . c . a+'cinvolve(b) . 'cinvolve(c) . 'cinvolve(a)- c . a . b - 
c . b . 'cinvolve(a)+c . 'cinvolve(b) . 'cinvolve(a)+'cinvolve(c) . 'cinvolve(a)
 . 'cinvolve(b))/4));
 0$
 */
clifford(e,3);
[1,1,1]$
celem(A,[t,x,y,z]);
A[t]+e[1]*A[x]+e[2]*A[y]+e[3]*A[z]$
scalarp(A);
true$
scalarp(z);
true$
(d:cvect([x1,y1,z1]),
scalarp(z1));
true$
(v1:cvect(v,[x,y,z]),
scalarp(v));
true$
(clifford(g,1,3),
vectorp(g[1]));
true$
rr:cvect([t,x,y,z]);
g[1]*t+g[2]*x+g[3]*y+g[4]*z$
(
declare(phi, scalar),
R1: cos(phi/2)+ g[2].g[3]*sin(phi/2),
R2: dotreverse(R1)
);
cos(phi/2)-(g[2] . g[3])*sin(phi/2)$
rot:R1.rr.R2,expand, dotsimpc;
(g[1]*cos(phi/2)^2+g[1]*sin(phi/2)^2)*t+(g[2]*cos(phi/2)^2+2*g[3]*cos(phi/2)*sin(phi/2)-g[2]*sin(phi/2)^2)*x+
(g[3]*cos(phi/2)^2-2*g[2]*cos(phi/2)*sin(phi/2)-g[3]*sin(phi/2)^2)*y+(g[4]*cos(phi/2)^2+g[4]*sin(phi/2)^2)*z$
trigreduce(rot);
g[1]*t+g[2]*cos(phi)*x+g[3]*sin(phi)*x+g[3]*cos(phi)*y-g[2]*sin(phi)*y+g[4]*z$
/*
clidet([e[1] ,e[2],e[3] ,e[1]]);
0$
clidet([e[1] ,e[2],e[3] ,e[2]]);
0$
clidet([e[1] ,e[2],e[3] ,e[3]]);
0$
*/