? dotscrules;

Calculate

? 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) ```

### Related Help

Help for Dotscrules