CanonDefine.mws

Function: Canon[CanonDefine] - Define symmetries of a tensor (or an indexed object)

Calling Sequence:
CanonDefine(tensor, rank, symmetries, base);

Parameters:
tensor - the tensor name (without indices)

rank - the number of indices

symmetries - a set of permutations (signed or not) representing the tensor symmetries or the names Symmetric or AntiSymmetric

base - (optional) base for the the generating set.

> with(Canon):

The following defines a tensor of rank 3 symmetric in the last 2 indices:

> CanonDefine(T, 3, {[[2,3]]}); The following defines the symmetries of the Riemann tensor:

> CanonDefine(R, 4, {[-1,[[1,2]]],[-1,[[3,4]]],[[1,3],[2,4]]}); The following defines a totally symmetric tensor of rank 5:

> CanonDefine(S, 5, Symmetric); Checking the symmetries:

> print(CanonSymmetryTable);    Next command is equivalent to state: T[b,a]=-T[b,a], which implies a vanishing tensor.

> CanonDefine(Z, 2, {[[1,2]],[-1,[[1,2]]]}); See Also: CanonPrint , CanonUnPrint , Canonical , CanonicalOne