1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
|
/*
* 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 simplification and symmetries
*/
if get('itensor,'version)=false then load(itensor);
("Take a tensor s. Remove any symmetry rules")$
remsym(s,2,0);
exp:ishow(s([i,j],[])-s([j,i],[]))$
("The canform function applies symmetry rules. None yet defined")$
ishow(canform(exp))$
("We tell MAXIMA that s is symmetric using decsym")$
decsym(s,2,0,[sym(all)],[])$
canform(exp);
("The flag allsym causes all tensors to be treated as symmetric")$
allsym:true;
canform(a([i,j],[])-a([j,i],[]));
("But this setting can lead to incorrect results, so it's off by default")$
allsym:false;
("The function rename can be used on dummy indices")$
exp:ishow(a([i,j1],[])*b([],[j1,k])+a([i,j2],[])*b([],[j2,k]))$
ishow(rename(exp))$
("The variable idummyx controls the dummy name, icounter is the counter")$
idummyx:n;
ishow(rename(exp))$
("To simplify tensor expressions, use rename, canform and canten")$
declare(e,constant);
("In this example, we want to drop terms higher order in l")$
(ratfac:false,ratvars(l),ratweight(l,1),ratwtlvl:1);
remcomps(g);
imetric(g);
components(g([i,j],[]),e([i,j],[])+2*l*p([i,j],[]));
components(g([],[i,j]),e([],[i,j])-2*l*p([],[i,j]));
ishow(g([i,j],[]))$
ishow(g([],[i,j]))$
exp:ishow(icurvature([s,u,n],[y]))$
exp:ev(exp)$
("Look the number of terms with nterms")$
nterms(exp);
ishow(canform(contract(rename(ratexpand(exp)))))$
/* End of demo -- comment line needed by MAXIMA to resume demo menu */
|
