Transformation represents a transformation of expression; it is a super type for all transformations (e.g. Expand or EliminateMetrics). Transformation can be applied to expression using >> operator. & operator; e.g. Expand & EliminateMetrics will first expand out products of sums and then eliminate metric tensors.Transformation using >> operator is equivalent to direct invocation of method .transform(exp).Identity transformation does nothing (expr == Identity >> expr)
Expand is a Transformation that expands out product of sums:
println Expand >> '(a+b)*(c+d)'.t
> a*c + a*d + b*c + b*d
Expression lhs = rhs is both Tensor and Transformation:
println 'f_a[x_a] = x_a'.t >> 'g^b[z_a] = f^b[z^i]'.t
> g^b[z_a] = z^b
Combine transformations using &:
def tr = Expand & EliminateMetrics println tr >> '(g_ab*g_cd + g_ac*g_bd)*g^bc'.t
> 2*g_{da}
One can define a custom transformation using closures:
def customTr = { expr -> 2*expr } as Transformation
println customTr >> 'z + t'.t
> 2*(z + t)Define transformation that inverts indices:
def tr = { expr ->
//invert indices
(expr.indices % expr.indices.inverted) >> expr
} as Transformation
println tr >> 'f_ab^cd'.t
> f^ab_cd