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dotident

Run Example
(%i1)dotassoc:true;
(%o1)                                true
(%i2) dotdistrib:true;
(%o2)                                true
(%i3) dot0simp:true;
(%o3)                                true
(%i4) dotconstrules:true;
(%o4)                                true
(%i5) dotexptsimp:true;
(%o5)                                true
(%i6) dotident:true;
(%o6)                                true
(%i7) dotscrules:true;
(%o7)                                true
(%i8) declare(a,scalar);
(%o8)                                done
(%i9) I(X):=(X^^-1);
                                         <- 1>
(%o9)                           I(X) := X
(%i10) T(X):=X.I(T12).T14c.I(T14e).T12.I(X).T14e;
(%o10) T(X) := X . (I(T12) . (T14c . (I(T14e) . (T12 . (I(X) . T14e)))))
(%i11) limit((1/a)*(T(T12+a.S)-T(T12)),a,0);
                         <- 1>              <- 1>                    <- 1>
(%o11) limit  (a (S . T12      . T14c . T14e      . T12 . (T12 + a S)
       a -> 0
                              <- 1>                    <- 1>
         . T14e) + T14c . T14e      . T12 . (T12 + a S)      . T14e - T14c)/a
(%i12) 
Run Example
dotassoc:true;
(%o1)                                true
(%i2) dotdistrib:true;
(%o2)                                true
(%i3) dot0simp:true;
(%o3)                                true
(%i4) dotconstrules:true;
(%o4)                                true
(%i5) dotexptsimp:true;
(%o5)                                true
(%i6) dotident:true;
(%o6)                                true
(%i7) dotscrules:true;
(%o7)                                true
(%i8) declare(a,scalar);
(%o8)                                done
(%i9) I(X):=(X^^-1);
                                         <- 1>
(%o9)                           I(X) := X
(%i10) T(X):=X.I(T12).T14c.I(T14e).T12.I(X).T14e;
(%o10) T(X) := X . (I(T12) . (T14c . (I(T14e) . (T12 . (I(X) . T14e)))))
(%i11) tex(limit((1/a)*(T(T12+a.S)-T(T12)),a,0));
$$\lim_{a\rightarrow 0}{{{a\,S\cdot {\it T_{12}}^ {-\langle 1
 \rangle }\cdot {\it T14c}\cdot {\it T14e}^ {-\langle 1\rangle }
 \cdot {\it T_{12}}\cdot \left({\it T_{12}}+a\,S\right)^ {-\langle 1
 \rangle }\cdot {\it T14e}+{\it T14c}\cdot {\it T14e}^ {-\langle 1
 \rangle }\cdot {\it T_{12}}\cdot \left({\it T_{12}}+a\,S\right)
 ^ {-\langle 1\rangle }\cdot {\it T14e}-{\it T14c}}\over{a}}}$$
(%o11)                               false
(%i12) limit((1/a)*((X+a).(X+a)-X.X),a,0);
(%o12)                                2 X
(%i13) 
Run Example
dotassoc:true;
(%o1)                                true
(%i2) dotdistrib:true;
(%o2)                                true
(%i3) dot0simp:true;
(%o3)                                true
(%i4) dotconstrules:true;
(%o4)                                true
(%i5) dotexptsimp:true;
(%o5)                                true
(%i6) dotident:true;
(%o6)                                true
(%i7) dotscrules:true;
(%o7)                                true
(%i8) declare(a,scalar);
(%o8)                                done
(%i9) scalarp(a);
(%o9)                                true
(%i10) I(X):=(X^^-1);
                                         <- 1>
(%o10)                          I(X) := X
(%i11) T(X):=X*I(T12)*T14c*I(T14e)*T12*I(X)*T14e;
(%o11)            T(X) := X I(T12) T14c I(T14e) T12 I(X) T14e
(%i12) scalarp(X);
(%o12)                               false
(%i13) limit((1/a)*(T(T12+a*S)-T(T12)),a,0);
                             <- 1>                    <- 1>            <- 1>
(%o13) limit  (T14c T14e T14e      T12 (T12 + a S) T12      (T12 + a S)
       a -> 0
                                                      <- 1>    2     <- 1> 2
                                      - T14c T14e T14e      T12  (T12     ) )/a
(%i14) 

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