Aside from typed, acceptable values for spacetime are flatxyz (11m~l:0,wski space in
Cartesian coordinates, where all the GHP quantities vanish), schw (the Schwarzschild
spacetime, a specialization of type D where -r = -r' = 0 and all other quantities
are real) and none (completely arbitrary spacetime, this is the default if spacetime
is unspecified). The user is free to change the value of spacetime in the middle of
a worksheet and only subsequent evaluations will be affected. For simplicity, we
will henceforth restrict our attention to examples with typed specified. The GHP
equations and Bianchi identities (as well as their primes, complex conjugates and
conjugate primes) are implemented as Maple procedures so that their specification to
the declared spacetime is returned. For example, if typed is specified, then
> GHP1();
> GHPipc () ;
th(p) = p2
thp(pl) = pl2
> BI2() ;
> BI2p();
th(W2) = 3 p 2
thp(W2) = 3 pl 2
The real usefulness of GHPtools comes not from its bookkeeping abilities, but
rather its ability to perform symbolic computations within the GHP formalism.
These abilities begin with the DGHP () procedure, which expands derivatives of objects
occurring in an expression in accordance with the rules of derivations. For example
> expr := rho*rhol + taustaul (conjugate(rho)*rhol)^3 +
> In(conjugate(tau)*conjugate(taul));
exp~r := p pl + -r 71 pl3 p3 n- -rl)
> th(expr);