1.4. Parameters

In xTensor` the indexed objects can be fields on manifolds and/or functions of real parameters (for example proper time).

DefParameter            Define a real parameter
UndefParameter            Undefine a parameter
ParameterQ                Check a real parameter
$Parameters                List of defined parameters

Definition of a parameter

We define a real parameter that will be used below to compute parametric derivatives (see ParamD in subsection 6.4).

In[76]:=

DefParameter[time]

** DefParameter: Defining parameter time.

In[77]:=

? time

Global`time

Info[time]^={parameter,}
ObjectsOf[time]^={}
ParameterQ[time]^=True
PrintAs[time]^=time

Manifolds and parameters are the only possible "dependencies" of the objects in xTensor`. We shall later explain this in more detail.

An important question is the relation between fields on 1d manifolds and functions of a parameter. In decompositions of ADM-type it would be nice to have a way of going from a 4d structure to a 3+1 structure and then from here to a 3d structure plus a time parameter. I have no clue on how to program this idea. There are many things to change in a nontrivial way: tensor fields, covariant derivatives, metrics, etc. Help, please!

Created by Mathematica  (May 16, 2008) Valid XHTML 1.1!