Script started on Mon May  9 20:47:52 2011
Octopus 1 %  maple
    |\^/|     Maple 9 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2003
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> readlib(grii):
> grtensor():
                         GRTensorII Version 1.79 (R4)
                                6 February 2001
           Developed by Peter Musgrave, Denis Pollney and Kayll Lake
                      Copyright 1994-2001 by the authors.
        Latest version available from: http://grtensor.phy.queensu.ca/
                   Defaults read from the local grtensor.ini

> makeg(sphere);

Makeg 2.0: GRTensor metric/basis entry utility
 
To quit makeg, type 'exit' at any prompt.
 
Do you wish to enter a 1) metric [g(dn,dn)],
                       2) line element [ds],
                       3) non-holonomic basis [e(1)...e(n)], or
                       4) NP tetrad [l,n,m,mbar]?

makeg>3;
Enter coordinates as a LIST (eg. [t,r,theta,phi]):
makeg>[theta,phi];
Would you like to enter 1) covariant components,
                        2) contravariant components, or
                        3) both.
makeg>1;
Enter the covariant components of basis vector '1' as a LIST (eg. [1,0,0,0])
or differential (eg. d[x] + d[y]):
makeg>r*d[theta];
Enter the covariant components of basis vector '2' as a LIST (eg. [1,0,0,0])
or differential (eg. d[x] + d[y]):
makeg>r*sin(theta)*d[phi];
Is the basis inner product  1) Diagonal, or
                            2) Symmetric?
makeg>1;
Enter eta[1,1]:
makeg>1;
Enter eta[2,2]:
makeg>1;

If there are any complex valued coordinates, constants or functions
for this spacetime, please enter them as a SET ( eg. { z, psi } ).

Complex quantities [default={}]: 
makeg>;
{}
 
                       The values you have entered are:
                          Coordinates = [theta, phi]
                                Basis 1-forms:
                               omega[1] = [r, 0]
                         omega[2] = [0, r sin(theta)]
                        Inner product of basis vectors:
                                      [1    0]
                                eta = [      ]
                                      [0    1]

You may choose to 0) Use the metric WITHOUT saving it,
                  1) Save the metric as it is,
                  2) Re-enter a basis vector,
                  3) Re-enter the inner product,
                  4) Add/change constraints,
                  5) Add a text description, or
                  6) Abandon this metric and return to Maple.

makeg>0;
                          Default spacetime = sphere
                           For the sphere spacetime:
                                  Coordinates
                                     x(up)
                                a
                              x   = [theta, phi]
                              Basis inner product
                                 eta(bup, bup)
                               (a)  (b)   [1    0]
                            eta         = [      ]
                                          [0    1]
                                 Basis 1-forms
                                  e(bdn, dn)
                                     [r         0      ]
                      e [(a)]  [b] = [                 ]
                                     [0    r sin(theta)]

makeg() completed.
> grcalc(metric):grdisplay(metric);

                           For the sphere spacetime:
                            Covariant metric tensor
                                   g(dn, dn)

                                   [ 2                  ]
                                   [r           0       ]
                      g [a]  [b] = [                    ]
                                   [       2           2]
                                   [0     r  sin(theta) ]

> grcalc(rot(bup,bdn,bdn)):grdisplay(rot(bup,bdn,bdn));
Created definition for rot(bup,bdn,bdn) 
Created a definition for e(bdn,dn,pdn)

                           For the sphere spacetime:
                               rot(bup,bdn,bdn)

                           (2)                 cos(theta)
                     gamma      [ (1)  (2)] = ------------
                                              r sin(theta)

                          (1)                   cos(theta)
                    gamma      [ (2)  (2)] = - ------------
                                               r sin(theta)

> grcalc(R(bup,bdn,bdn,bdn)):grdisplay(R(bup,bdn,bdn,bdn));

                           For the sphere spacetime:
                              R(bup,bdn,bdn,bdn)

                          (1)                      1
                        R      [ (2)  (1)  (2)] = ----
                                                    2
                                                   r

                         (2)                        1
                       R      [ (1)  (1)  (2)] = - ----
                                                     2
                                                    r

> quit;
Octopus 2 %  exit

Script done on Mon May  9 20:50:03 2011