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dotscrules

? dotscrules;

Calculate

dotscrules

? dotscrules;

Calculate

dotscrules

Run Example
(%i1)declare(theta,scalar,phi,scalar);
(%o1)                                done
(%i2) declare(T12, nonscalar ,T14c, nonscalar ,T14e,nonscalar,B,nonscalar,A,nonscalar);
(%o2)                                done
(%i3) dotscrules:true;
(%o3)                                true
(%i4) I(X):=(X^^(-1));
                                         <- 1>
(%o4)                           I(X) := X
(%i5) T(X):=X.I(T12).T14c.I(T14e).T12.I(X).T14e;
(%o5)  T(X) := X . (I(T12) . (T14c . (I(T14e) . (T12 . (I(X) . T14e)))))
(%i6) T(T12+a*A)-T(T12);
                       <- 1>              <- 1>                    <- 1>
(%o6) (T12 + a A) . T12      . T14c . T14e      . T12 . (T12 + a A)      . T14e
                                                                         - T14c
(%i7) 
Run Example
declare(a,scalar);
(%o1)                                done
(%i2) declare(T12, nonscalar ,T14c, nonscalar ,T14e,nonscalar);
(%o2)                                done
(%i3) dotscrules:true;
(%o3)                                true
(%i4) I(X):=(X^^(-1));
                                         <- 1>
(%o4)                           I(X) := X
(%i5) T(X):=X.I(T12).T14c.I(T14e).T12.I(X).T14e;
(%o5)  T(X) := X . (I(T12) . (T14c . (I(T14e) . (T12 . (I(X) . T14e)))))
(%i6) B:((T(T12+a*S)-T(T12))/a);
                        <- 1>              <- 1>                    <- 1>
(%o6) ((T12 + a S) . T12      . T14c . T14e      . T12 . (T12 + a S)
                                                               . T14e - T14c)/a
(%i7) limit(B,a,0);
                               <- 1>              <- 1>
(%o7) limit  ((T12 + a S) . T12      . T14c . T14e      . T12
      a -> 0
                                                         <- 1>
                                            . (T12 + a S)      . T14e - T14c)/a
(%i8) 
Run Example
declare(a,scalar);
(%o1)                                done
(%i2) declare(T12, nonscalar ,T14c, nonscalar ,T14e,nonscalar);
(%o2)                                done
(%i3) dotscrules:true;
(%o3)                                true
(%i4) I(X):=(X^^(-1));
                                         <- 1>
(%o4)                           I(X) := X
(%i5) T(X):=X.I(T12).T14c.I(T14e).T12.I(X).T14e;
(%o5)  T(X) := X . (I(T12) . (T14c . (I(T14e) . (T12 . (I(X) . T14e)))))
(%i6) B:expand((T(T12+a*S)-T(T12))/a);
             <- 1>              <- 1>                    <- 1>
(%o6) S . T12      . T14c . T14e      . T12 . (T12 + a S)      . T14e
                                   <- 1>                    <- 1>
                        T14c . T14e      . T12 . (T12 + a S)      . T14e   T14c
                      + ------------------------------------------------ - ----
                                               a                            a
(%i7) limit(B,a,0);
                     <- 1>              <- 1>                    <- 1>
(%o7) limit  (S . T12      . T14c . T14e      . T12 . (T12 + a S)      . T14e
      a -> 0
                                  <- 1>                    <- 1>
                       T14c . T14e      . T12 . (T12 + a S)      . T14e   T14c
                     + ------------------------------------------------ - ----)
                                              a                            a
(%i8) 

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