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HELP FOR: grconstraint
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CALLING SEQUENCE:  grconstraint ( metric ):

      PARAMETERS:  metric - the name of a previously loaded metric

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SYNOPSIS:

- GRTensorII allows the specification of constraint equations that must be
  satisfied by functions in the metric or basis.

- Constraint equations may be added to a spacetime, removed or re-arranged 
  using this command. grconstraint() is menu driven and prompts for 
  addition/modification/deletion of constraint equations.

- Constraints can be applied to an object calculated from a metric or basis
  by using gralter().

- Constraints specified using grconstraint() can be saved with the metric
  file using grsaveg().

- Constraints may also be specified by makeg(), and will be loaded
  automatically as the spacetime is loaded.

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EXAMPLE:
# In the following example, the bondi metric is loaded and the constraints
#           m(r,v) = M,  and  c(r,v) = C
# are specified. The Ricci tensor is calculated for the metric in terms
# of the general functions m(r,v) and c(r,v), and the constraints are then
# applied to show that the Ricci tensor is zero when these functions are
# constants.

> qload ( bondi ):

> grconstraint ( bondi ):

    Constraint specification and manipulation
 
    Do you wish to
    1) Add a constraint to the metric
    2) Remove a constraint from the metric
    3) Modify a metric constraint
    4) Display the existing constraints
    5) Exit

  Enter 1-5 > 1

    Please enter the new constraint as an equation (of the form 
    f(x,y) = g(x) + h(y), for example):

  Enter equation : m(r,v) = M

    The new constraint equation is :
                                  m(r, v) = M
 

    Constraint specification and manipulation
 
    Do you wish to
    1) Add a constraint to the metric
    2) Remove a constraint from the metric
    3) Modify a metric constraint
    4) Display the existing constraints
    5) Exit

  Enter 1-5 > 1

    Please enter the new constraint as an equation (of the form 
    f(x,y) = g(x) + h(y), for example):

  Enter equation : c(r,v) = C

    The new constraint equation is :
                                  c(r, v) = C
 

    Constraint specification and manipulation
 
    Do you wish to
    1) Add a constraint to the metric
    2) Remove a constraint from the metric
    3) Modify a metric constraint
    4) Display the existing constraints
    5) Exit

  Enter 1-5 > 4
                            For the bondi spacetime:
 
                                  constraints
 
                    constraint  = [m(r, v) = M, c(r, v) = C]
 

    Constraint specification and manipulation
 
    Do you wish to
    1) Add a constraint to the metric
    2) Remove a constraint from the metric
    3) Modify a metric constraint
    4) Display the existing constraints
    5) Exit

  Enter 1-5 > 5


> grcalc ( R(dn,dn) ):

> grdisplay ( R(dn,dn) ):

 
                            For the bondi spacetime:
 
                                Covariant Ricci
 
                                           d
                                         ---- c(r, v)
                                          dr
                           R [r] [r] = 2 ------------
                                           c(r, v) r
                                       .
                                       .
                                       .
                                      etc.


> gralter ( R(dn,dn) );

    Component Alteration of a grtensor object:
 
    (use ?name for help on a particular simplification routine)
 
    Choose which routine to apply:
     0)  none
     1)  simplify()          try all simplification techniques
     2)  simplify[trig]      apply trig simplification
     3)  simplify[power]     simplify powers, exp and ln
     4)  simplify[hypergeom] simplify hypergeometric functions
     5)  simplify[radical]   convert radicals,log,exp to canonical form
     6)  expand()
     7)  factor()
     8)  normal()
     9)  sort()
    10)  simplify[sqrt,symbolic] allows sqrt(r^2) = r
    11)  simplify[trigsin]       trig simp biased to sin
    12)  Apply constraints
    13)  Apply constraints repeatedly
    14)  other               user specified routine

  Number of routine to apply > 12;

Applying routine Apply constraints to object R(dn,dn)


> grdisplay ( R(dn,dn) );
 
                            For the bondi spacetime:
 
                                Covariant Ricci
 
                       R(dn,dn) = All components are zero

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SEE ALSO: makeg, gralter, grsaveg.
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