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riemann-sin

riemann;

da^2+(sin(a))^2*db^2+...

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riemann

riemann;

dx^2 + dy^2 + dz^2;

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riemann-true

riemann(true);

dt^2-a(t)^2*dx^2;

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riemann

riemann;

dx^2 -2*y*dy^2;

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riemann-true

riemann(true);

l^2/z^2*(-dt^2+dx^2+d...

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riemann

riemann;

dx^2 + dy^2=ds^2;

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riemann-sin-true

riemann(true);

-(1-2*f(r))*dt^2 + (...

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riemann

? riemann;

dx^2 + dy^2 + z*dz^2;

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riemann

riemann;

dx^2 + dy^2 + dz^2;

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riemann

? riemann;

z^2;

Calculate

riemann

Run Example
(%i1)load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) (cframe_flag:false,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) lg:diag_matrix(1,-r^2,-r^2,-r^2);
                            [ 1   0     0     0   ]
                            [                     ]
                            [       2             ]
                            [ 0  - r    0     0   ]
(%o3)                       [                     ]
                            [             2       ]
                            [ 0   0    - r    0   ]
                            [                     ]
                            [                   2 ]
                            [ 0   0     0    - r  ]
(%i4) ct_coords:[t,r,th,ph];
(%o4)                           [t, r, th, ph]
(%i5) cmetric(false);
(%o5)                                done
(%i6) christof(mcs);
                                             1
(%t6)                           mcs        = -
                                   2, 2, 2   r

                                             1
(%t7)                           mcs        = -
                                   2, 3, 3   r

                                             1
(%t8)                           mcs        = -
                                   2, 4, 4   r

                                              1
(%t9)                          mcs        = - -
                                  3, 3, 2     r

                                              1
(%t10)                         mcs        = - -
                                  4, 4, 2     r

(%o10)                               done
(%i11)  riemann(true);
                                                1
(%t11)                       riem           = - --
                                 2, 3, 2, 3      2
                                                r

                                                1
(%t12)                       riem           = - --
                                 2, 4, 2, 4      2
                                                r

                                               1
(%t13)                        riem           = --
                                  3, 3, 2, 2    2
                                               r

                                               1
(%t14)                        riem           = --
                                  3, 4, 3, 4    2
                                               r

                                               1
(%t15)                        riem           = --
                                  4, 4, 2, 2    2
                                               r

                                                1
(%t16)                       riem           = - --
                                 4, 4, 3, 3      2
                                                r

(%o16)                               done
(%i17) ricci(true);
                                           2
(%t17)                           ric     = --
                                    2, 2    2
                                           r

(%o17)                               done
(%i18) 
Run Example
load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) (cframe_flag:false,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) lg:diag_matrix(1,-r^2,-r^2,-(r^2));
                            [ 1   0     0     0   ]
                            [                     ]
                            [       2             ]
                            [ 0  - r    0     0   ]
(%o3)                       [                     ]
                            [             2       ]
                            [ 0   0    - r    0   ]
                            [                     ]
                            [                   2 ]
                            [ 0   0     0    - r  ]
(%i4) ct_coords:[t,r,th,ph];
(%o4)                           [t, r, th, ph]
(%i5) cmetric(false);
(%o5)                                done
(%i6) christof(mcs);
                                             1
(%t6)                           mcs        = -
                                   2, 2, 2   r

                                             1
(%t7)                           mcs        = -
                                   2, 3, 3   r

                                             1
(%t8)                           mcs        = -
                                   2, 4, 4   r

                                              1
(%t9)                          mcs        = - -
                                  3, 3, 2     r

                                              1
(%t10)                         mcs        = - -
                                  4, 4, 2     r

(%o10)                               done
(%i11)  riemann(true);
                                                1
(%t11)                       riem           = - --
                                 2, 3, 2, 3      2
                                                r

                                                1
(%t12)                       riem           = - --
                                 2, 4, 2, 4      2
                                                r

                                               1
(%t13)                        riem           = --
                                  3, 3, 2, 2    2
                                               r

                                               1
(%t14)                        riem           = --
                                  3, 4, 3, 4    2
                                               r

                                               1
(%t15)                        riem           = --
                                  4, 4, 2, 2    2
                                               r

                                                1
(%t16)                       riem           = - --
                                 4, 4, 3, 3      2
                                                r

(%o16)                               done
(%i17) ricci(true);
                                           2
(%t17)                           ric     = --
                                    2, 2    2
                                           r

(%o17)                               done
(%i18) 
Run Example
load(ctensor);
(%o1)          /usr/share/maxima/5.21.1/share/tensor/ctensor.mac
(%i2) (cframe_flag:false,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) lg:diag_matrix(-1,2,r^2,(sin(%theta)*r)^2);
                        [ - 1  0  0          0        ]
                        [                             ]
                        [  0   2  0          0        ]
                        [                             ]
(%o3)                   [          2                  ]
                        [  0   0  r          0        ]
                        [                             ]
                        [                2          2 ]
                        [  0   0  0   sin (%theta) r  ]
(%i4) ct_coords:[t,r,%theta,%phi];
(%o4)                        [t, r, %theta, %phi]
(%i5) depends(%nu,[r,t],%lambda,[r,t]);
(%o5)                     [%nu(r, t), %lambda(r, t)]
(%i6) cmetric(false);
(%o6)                                done
(%i7) christof(mcs);
                                             1
(%t7)                           mcs        = -
                                   2, 3, 3   r

                                             1
(%t8)                           mcs        = -
                                   2, 4, 4   r

                                              r
(%t9)                          mcs        = - -
                                  3, 3, 2     2

                                        cos(%theta)
(%t10)                     mcs        = -----------
                              3, 4, 4   sin(%theta)

                                           2
                                        sin (%theta) r
(%t11)                   mcs        = - --------------
                            4, 4, 2           2

(%t12)              mcs        = - cos(%theta) sin(%theta)
                       4, 4, 3

(%o12)                               done
(%i13)  riemann(true);
                                                1
(%t13)                       riem           = - -
                                 3, 4, 3, 4     2

                                             2
                                          sin (%theta)
(%t14)                   riem           = ------------
                             4, 4, 3, 3        2

(%o14)                               done
(%i15) ricci(true);
                                            1
(%t15)                            ric     = -
                                     3, 3   2

                                         2
                                      sin (%theta)
(%t16)                      ric     = ------------
                               4, 4        2

(%o16)                               done
(%i17) R:scurvature();
                                      1
(%o17)                                --
                                       2
                                      r
(%i18) 

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