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/*
* 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.
*
* Indicial tensor basics
*/
if get('itensor,'version)=false then load(itensor);
("Tensors are indexed objects. To show a tensor use ishow()")$
ishow(g([a,b],[c,i],i2,i1))$
("Tensor components can be assigned using components().
As an example, consider a conformally flat metric:")$
declare(e,constant);
remcomps(g);
imetric(g);
components(g([i,j],[]),e([i,j],[])*p([],[]));
components(g([],[i,j]),e([],[i,j])/p([],[]));
ishow(g([i,j],[]))$
ishow(g([],[i,j]))$
("Tensor components can also be assigned as MAXIMA functions:")$
t(l1,l2):=c*a(l1,l2)+b(l1,l2)$
ishow(t([i,k],[]))$
ishow(t([],[j,m]))$
("Here is the Euler equation")$
Eu(l1,l2):=d_t*v(l1,[])+v([],[j])*v(l1,[],j)+
1/rho([])*diff(p([],[]),l1[1])+diff(phi([],[]),l1[1])$
ishow(Eu([i],[]))$
("Another definition can be given using the metric g")$
Eu(l1,l2):=block([j1:idummy()], if l2=[] then
d_t* v(l1,[])+v([],[j1])*v(l1,[],j1)+
1/rho([])*diff(p([],[]),l1[1])+diff(phi([],[]),l1[1])
else d_t*v([],l2)+v([],[j1])*v([],l2,j1)+
g([],[l2[1],j1])*(diff(p([],[]),j1)/rho([])+diff(phi([],[]),j1)))$
ishow(Eu([i],[]))$
ishow(Eu([],[i]))$
("The dummy index character can be changed from % using idummyx:")$
idummyx:n$
ishow(Eu([i],[]))$
("The indices() command lists the free and dummy indices")$
indices(Eu([i],[]));
("The variable icounter controls the dummy index numbering")$
icounter;
icounter:100;
ishow(Eu([i],[]))$
idummyx:"%"$
/* End of demo -- comment line needed by MAXIMA to resume demo menu */
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