rtest_clifford.mac

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

tests for version
 v 1.5
 
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),
 /*
  %path:read("Path to package"),
  %path:append ([%path,"$$$.{mac,mc}"]),
  */
  %path:"C:/Dropbox/maxima/$$$.{mac,mc}",
  file_search_maxima:append (file_search_maxima , [%path]),
  %start : absolute_real_time(),
  load("clifford"),
  'done);
'done$
get('clifford,'version);
v19$
permsign([a,c,b]);
-1$
permsign([a,b,c]);
1$
permsign([a,b,c*d]);
0$
/* init clifford" */
clifford(e,1,1,1);
[1,-1,0]$
/*matrix([1,0,0],[0,-1,0],[0,0,0])$*/
elements();
[e[1],e[2],e[3],e[1] . e[2],e[1] . e[3],e[2] . e[3],e[1] . e[2] . e[3]]$
/* clifford product tests" */
e[1].e[1];
1$
e[2].e[2];
-1$
e[3].e[3];
0$
e[2].e[1];
-e[1] . e[2]$
dotsimpc(e[2] . e[1] . e[2]);
e[1]$
e[1].e[2].e[1];
-e[2]$
e[1].e[1].e[2];
e[2]$
e[1].e[1].e[2].e[1];
-e[1] . e[2]$
e[1].e[1].e[2].e[1].e[2];
e[1]$
e[1].e[1].e[1].e[2].e[1];
-e[2]$
clifford(e,3,1);
[1,1,1,-1]$
dotsimpc(e[2] . e[1] . e[2]. e[3]);
-e[1] . e[3]$
oppart(e[2] . e[1] *x. e[2]. e[3], lambda([u], freeof(".", u)));
[-1,(e[1] . e[2])*(e[2] . e[3] . x)]$
dotsimpc(e[2] . e[1] . e[2]. e[3]*x);
-(e[1] . e[3])*x$
dotsimpc(e[2] . e[1] *x. e[2]. e[3]);
-e[1] . e[3] . x$
(declare(y, scalar),
dotsimpc(e[2] . e[1] .y. e[2]. e[3]));
-(e[1] . e[3])*y$