====== Applying and manipulating transformations ======
Next topic: [[documentation:guide:substitutions]]
----
All transformations in Redberry are first-class objects which means that they can be assigned to variables and share a common way for their applying and manipulation. Consider the syntax used for applying [[documentation:ref:transformation]] to mathematical expression:
def tr = Expand
def t = '(A_k + B_k)*c'.t
def r = tr >> t,
l = t << tr
assert r == l
println r
> c*A_k+c*B_k
As it seen from the example, transformations are applied using left shift
''%%<<%%'' or right shift ''%%>>%%'' operator. It should be noted
that both operators are left-associative so in order to apply several
transformations subsequently, it is better to use a special ''&''
operator, which allows to join a set of transformations into a single one:
def t = '(a+b)*c'.t
//first expand then substitute
def expandAndSubs = Expand & 'c = a + b'.t
println expandAndSubs >> t
> a*(a+b)+b*(a+b)
//first substitute then expand
def subsAndExpand= 'c = a + b'.t & Expand
println subsAndExpand >> t
> a**2+2*a*b+b**2
Transformations (like tensors) are immutable in Redberry. Some transformations
may take required or optional arguments using square brackets:
def eliminateWhileExpand = Expand[EliminateMetrics]
def x = '(g_mn + d_m^a*g_na)*f^mn'.t
println eliminateWhileExpand >> x
> 2*f_m^m
def diff = Differentiate['x_m']
def y = 'x_m*x^m'.t
println diff >> y
> 2*x^m
In this example, the [[documentation:ref:Expand]] takes an optional parameter, which is a transformation to be applied on each level of expand procedure. In contrast, the argument of [[documentation:ref:Differentiate]] is required. In both cases a new object will be created and assigned to a corresponding variable. The meaning of arguments is specific for each particular [[documentation:ref:Transformation]].
====See also====
* Related guides: [[documentation:guide:list_of_transformations]], [[documentation:guide:programming_with_redberry]]
* Related reference material: [[documentation:ref:Transformation]], [[documentation:ref:Tensor]]