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HELP FOR: greqn2set
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CALLING SEQUENCE:  greqn2set ( object )

      PARAMETERS: object - name of a GRTensorII object

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SYNOPSIS:

 - This function returns the components of a tensor-equation as a set of
   equations which can be used as input to the standard MapleV equation
   solving routines (eg. solve(), dsolve(), etc.).

 - Tensor equations can be defined using grdef(), as in the following example:

     > grdef ( `EEqn{(a b)} := G{a b} = 8*Pi*T{a b}` ):

   The right-hand side of this definition (to the right of the `:=') is
   in the form of an equation, with consistent indices across the equality.
   When EEqn(dn,dn) is calculated, each component will contain an individual
   equation which is the matching of the components of G(dn,dn) with that of
   T(dn,dn). The greqn2set() function can then be used to extract this set
   of equations an attempt to solve them.

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EXAMPLES:

> qload ( static ):

Calculated ds for static. (0.010000 sec.) 
                           Default spacetime = static
 
                           For the static spacetime:
 
                                  Coordinates
 
                             a
                           x   = [ r, theta, phi, t ]
 
                                  Line element
 
                2
        2    d r      2         2     2           2       2             2
      ds  = ------ + r   d theta   + r  sin(theta)   d phi   - h(r)  d t
             h(r)
 
                    Static, spherically symmetric spacetime
 
> grdef ( `A{a} := [ 0, 0, 0, -Q/r ]` ):
Components assigned for metric: static
Created definition for A(dn)

> grdef ( `F{[a b]} := -2*A{[a;b]}` );
Created a definition for    A(dn,cdn)
Created definition for F(dn,dn)

> grdef ( `T{(a b)} :=  1/(4*Pi)*(F{a c} *F{b ^c} - (1/4)*g{a b}*F{d e}*
   F{^d ^e})` );
Created definition for F(dn,up) 
Created definition for F(up,up) 
Created definition for T(dn,dn)

> grdef ( `Eeqn{(a b)} := G{a b} = 8*Pi*T{a b}` );
Created definition for lhs_Eeqn(dn,dn)
Created definition for rhs_Eeqn(dn,dn)
Created definition for Eeqn(dn,dn)

> grcalc ( Eeqn(dn,dn) ):
 
> eqns := greqn2set ( Eeqn(dn,dn) );
 
                      Eeqn[r] [r],  changed to 88 (words)
 
                  Eeqn[theta] [theta],  changed to 86 (words)
 
                    Eeqn[phi] [phi],  changed to 134 (words)
 
                      Eeqn[t] [t],  changed to 88 (words)
 
         /  d      \
         |---- h(r)| r - 1 + h(r)         2
         \ dr      /                     Q
eqns := {------------------------ = - -------,
                        2                   4
                  h(r) r              h(r) r
 
                     /   2      \        2
 /  d      \         |  d       |  2    Q
 |---- h(r)| r + 1/2 |----- h(r)| r  = ----,
 \ dr      /         |   2      |        2
                     \ dr       /       r
 
                                             /   2      \                2  2
 /  d      \             2                 2 |  d       |  2   sin(theta)  Q
 |---- h(r)| r sin(theta)  + 1/2 sin(theta)  |----- h(r)| r  = --------------,
 \ dr      /                                 |   2      |             2
                                             \ dr       /            r
 
        //  d      \             \
   h(r) ||---- h(r)| r - 1 + h(r)|    2
        \\ dr      /             /   Q  h(r)
 - ------------------------------- = -------}
                   2                     4
                  r                     r
 
> dsolve ( eqns[1], h(r) );
 
                                     2    2
                                    r  + Q  + _C1 r
                             h(r) = ---------------
                                            2
                                           r
 
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SEE ALSO: grdef, grcomponent, grarray, grt_objects.
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