Maxima Function
decsym (tensor, m, n, [cov_1, cov_2, ...], [contr_1, contr_2, ...])
Declares symmetry properties for tensor of m covariant and
n contravariant indices. The cov_i and contr_i are
pseudofunctions expressing symmetry relations among the covariant and
contravariant indices respectively. These are of the form
symoper(index_1, index_2,...)
where symoper
is one of
sym
, anti
or cyc
and the index_i are integers
indicating the position of the index in the tensor. This will
declare tensor to be symmetric, antisymmetric or cyclic respectively
in the index_i. symoper(all)
is also an allowable form which
indicates all indices obey the symmetry condition. For example, given an
object b
with 5 covariant indices,
decsym(b,5,3,[sym(1,2),anti(3,4)],[cyc(all)])
declares b
symmetric in its first and second and antisymmetric in its third and
fourth covariant indices, and cyclic in all of its contravariant indices.
Either list of symmetry declarations may be null. The function which
performs the simplifications is canform
as the example below
illustrates.
(%i1) load(itensor); (%o1) /share/tensor/itensor.lisp (%i2) expr:contract( expand( a([i1, j1, k1], []) *kdels([i, j, k], [i1, j1, k1])))$ (%i3) ishow(expr)$ (%t3) a + a + a + a + a + a k j i k i j j k i j i k i k j i j k (%i4) decsym(a,3,0,[sym(all)],[]); (%o4) done (%i5) ishow(canform(expr))$ (%t5) 6 a i j k (%i6) remsym(a,3,0); (%o6) done (%i7) decsym(a,3,0,[anti(all)],[]); (%o7) done (%i8) ishow(canform(expr))$ (%t8) 0 (%i9) remsym(a,3,0); (%o9) done (%i10) decsym(a,3,0,[cyc(all)],[]); (%o10) done (%i11) ishow(canform(expr))$ (%t11) 3 a + 3 a i k j i j k (%i12) dispsym(a,3,0); (%o12) [[cyc, [[1, 2, 3]], []]]