rtest_clifford2.mac

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

tests for version
 v 2.5
 
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),
  %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$
block(
	"init clifford complex",
	clifford(e,0,1,0),
	mtable2()
);
matrix([1,e[1]],[e[1],-1])$
block(
	"init clifford split-complex",
	clifford(e,1,0,0),
	mtable2()
);
matrix([1,e[1]],[e[1],1])$
block(
	"init clifford dual",
	clifford(e,0,0,1),
	mtable2()
);
matrix([1,e[1]],[e[1],0])$
block(
	"init clifford quaternion",
	clifford(e,0,2,0),
	mtable2()
);
matrix([1,e[1],e[2],e[1] . e[2]], 
[e[1],-1,e[1] . e[2],-e[2]],
[e[2],-e[1] . e[2],-1,e[1]],
[e[1] . e[2],e[2],-e[1],-1])$
/* clifford simplification tests" */
e[1] . e[2] . e[1] . e[2], dotsimpc;
-1$
e[2] . e[1] . e[1] . e[2], dotsimpc;
1$
/*inverses*/
1/e[2],dotinvsimp;
-e[2]$
1/e[1] . e[2], dotinvsimp;
-e[1] . e[2]$
1/(1+e[1]),dotinvsimp;
(1-e[1])/2$
(e[1]- e[2])^^2,expand;
-2$
(e[1]- e[2])^2,expand;
e[1]^2-2*e[1]*e[2]+e[2]^2$
block(
	"init clifford geom/pauli",
	clifford(e,3),
	mtable1()
);
matrix([1,e[1],e[2],e[3]],
[e[1],1,e[1] . e[2],e[1] . e[3]],
[e[2],-e[1] . e[2],1,e[2] . e[3]],
[e[3],-e[1] . e[3],-e[2] . e[3],1])$
1/(e[1] . e[2]. e[3]), dotinvsimp;
-e[1] . e[2] . e[3]$
5/(e[1] .   e[3]), dotinvsimp;
-5*(e[1] . e[3])$
1/e[1]-e[1],dotinvsimp;
0$
/* tripple product tests" */
e[1]| (-%iv. (e[2]&e[3]));
1$
e[2]| (-%iv. (e[3]&e[1]));
1$
e[3]| (-%iv. (e[1]&e[2])),dotsimpc;
1$
e[1]| ( (e[2]&e[3]));
0$
-%iv.(e[1]& (-%iv. (e[2]&e[3]))),dotsimpc;
0$
e[2]. (e[1]|e[3])+e[3]. (e[1]|e[2]);
0$
-(%iv. e[1]) & (- %iv. (e[2] & e[3])),dotsimpc;
-e[1] . e[2] . e[3]$
clihdual(e[1] &e[2]),dotsimpc;
e[3]$
clihdual(e[3] &e[1]),dotsimpc;
e[2]$
clihdual(e[2] &e[3]),dotsimpc;
e[1]$
block(
	jacobprod(a,b,c):= ( a & b & c + b & c & a + c & a & b),
	ev(jacobprod(e[1] ,e[2], e[3]), dotsimpc)
);
3*(e[1] . e[2] . e[3])$