rtest_cliffordan1.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("cliffordan"),
  'done);
'done$
get('cliffordan,'version);
v15$
/* init clifford" */
clifford(e,3);
[1,1,1]$
(dependsv(F,[t,x,y,z]),
member(F(t,x,y,z), dependencies));
true$
 r:cvect([x,y,z]);
e[1]*x+e[2]*y+e[3]*z$
mvectdiff(F,r);
e[1]*('diff(F,x,1))+e[2]*('diff(F,y,1))+e[3]*('diff(F,z,1))$
mvectdiff(F,r,2);
'diff(F,x,2)+'diff(F,y,2)+'diff(F,z,2)$
ctotdiff(log(r),r);
3/(e[1]*x+e[2]*y+e[3]*z)$
mvectdiff(r,r);
3$
mvectdiff(r,r,2);
0$
mvectdiff(r/sqrt(-cnorm(r)),r);
2/sqrt(x^2+y^2+z^2)$
mvectdiff(r/(-cnorm(r)),r);
1/(x^2+y^2+z^2)$
mvectdiff(-(2*e[1]*x)/(x^2+y^2+z^2)^(3/2)-(2*e[2]*y)/(x^2+y^2+z^2)^(3/2)-(2*e[3]*z)/(x^2+y^2+z^2)^(3/2),r);
0$
mvectdiff(exp(r),r);
3*%e^(e[1]*x+e[2]*y+e[3]*z)$
mvectdiff(log(r),r),factor;
(3*(e[1]*x+e[2]*y+e[3]*z))/(x^2+y^2+z^2)$
mvectdiff((-cnorm(r)),r),factor;
2*(e[1]*x+e[2]*y+e[3]*z)$
(declare(k, scalar),
ev(mvectdiff((-cnorm(r))^k/2,r),factor)
);
k*(e[1]*x+e[2]*y+e[3]*z)*(x^2+y^2+z^2)^(-1+k)$
mvectdiff(k*sin(r),r);
3*k*cos(e[1]*x+e[2]*y+e[3]*z)$
mvectdiff(k*sinh(r+1),r);
3*k*cosh(1+e[1]*x+e[2]*y+e[3]*z)$
(depends(A, [x,y,z]),
declare(A,scalar),
P:celem(A,[[],x,y,z])
);
e[1]*A[x]+e[2]*A[y]+e[3]*A[z]$
mvectdiff(log(cnorm2(P))/2,r);
(e[1]*(A[x]*('diff(A[x],x,1))+A[y]*('diff(A[y],x,1))+A[z]*('diff(A[z],x,1)))+e[2]*(A[x]*('diff(A[x],y,1))+A[y]*('diff(A[y],y,1))+A[z]*('diff(A[z],y,1)))+e[3]*
(A[x]*('diff(A[x],z,1))+A[y]*('diff(A[y],z,1))+A[z]*('diff(A[z],z,1))))/(A[x]^2+A[y]^2+A[z]^2)$