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dotconstrules

? dotconstrules;

Calculate

dotconstrules

? dotconstrules;

Calculate

dotconstrules

Run Example
(%i1)dotassoc:true;
(%o1)                                true
(%i2) dotdistrib:true;
(%o2)                                true
(%i3) dot1simp:true;
(%o3)                                true
(%i4) dotconstrules:true;
(%o4)                                true
(%i5) dotexptsimp:true;
(%o5)                                true
(%i6) declare(a,scalar);
(%o6)                                done
(%i7) I(X):=(X^^-1);
                                         <- 1>
(%o7)                           I(X) := X
(%i8) T(X):=X.I(T12).T14c.I(T14e).T12.I(X).T14e;
(%o8)  T(X) := X . (I(T12) . (T14c . (I(T14e) . (T12 . (I(X) . T14e)))))
(%i9) limit((1/a)*(T(T12+a*S)-T(T12)),a,0);
                         <- 1>              <- 1>                    <- 1>
(%o9) limit  ((a S) . T12      . T14c . T14e      . T12 . (T12 + a S)
      a -> 0
                                <- 1>                    <- 1>
            . T14e + T14c . T14e      . T12 . (T12 + a S)      . T14e - T14c)/a
(%i10) limit((1/a).((X+a).(X+a)-X.X),a,0);
                         1             1     <2>    1
(%o10)          limit  ((-) . X . a + (-) . a    + (-) . a . X)
                a -> 0   a             a            a
(%i11) 
Run Example
load(vect);
(%o1)           /usr/share/maxima/5.21.1/share/vector/vect.mac
(%i2) load(vector);
(%o2)          /usr/share/maxima/5.21.1/share/vector/vector.mac
(%i3) dotconstrules:true;
(%o3)                                true
(%i4) T(x):=x*y^2;
                                            2
(%o4)                            T(x) := x y
(%i5) setcoord(c[x, y, z]);
(%o5)                         setcoord(c       )
                                        x, y, z
(%i6) declare(express,evfun);
(%o6)                                done
(%i7) declare(apply, evfun);
(%o7)                                done
(%i8) dl:[dx, dy, dz];
(%o8)                            [dx, dy, dz]
(%i9) grad(T(x));
                                  2
(%o9)                           [y , 2 x y, 0]
(%i10) grad(T(x)).dl;
                        2                   2
(%o10) [[dx, dy, dz] . y  + [0, 0, 0] . (x y ), 
                                                                         2
                              2 ([dx, dy, dz] . (x y)) + [0, 0, 0] . (x y ), 0]
(%i11) apply(".", [grad(T(x)),[dx,0,0]]);
                                         2
(%o11)                               dx y
(%i12) apply(".", [grad(T(x)),[0,dy,0]]);
(%o12)                             2 dy x y
(%i13) apply(".", [grad(T(x)),[0,0,dz]]);
(%o13)                                 0
(%i14) apply(".", [grad(T(x)),[dx,dy,0]]);
                                   2
(%o14)                         dx y  + 2 dy x y
(%i15) apply(".", [grad(T(x)),[dx,dy,dz]]);
                                   2
(%o15)                         dx y  + 2 dy x y
(%i16) div([T(x), T(x), T(x)]);
                                   2
(%o16)                            y  + 2 x y
(%i17) plot2d(T(x), [x, 0, 4], [y, 0, 4]);
plotplot2d(T(x), [x, 0, 4], [y, 0, 4]);
Run Example
dotassoc:true;
(%o1)                                true
(%i2) dotdistrib:true;
(%o2)                                true
(%i3) dot1simp:true;
(%o3)                                true
(%i4) dotconstrules:true;
(%o4)                                true
(%i5) dotexptsimp:true;
(%o5)                                true
(%i6) I(X):=(X^^-1);
                                         <- 1>
(%o6)                           I(X) := X
(%i7) T(X):=X.I(T12).T14c.I(T14e).T12.I(X).T14e;
(%o7)  T(X) := X . (I(T12) . (T14c . (I(T14e) . (T12 . (I(X) . T14e)))))
(%i8) limit((1/a)*(T(T12+a*S)-T(T12)),a,0);
                         <- 1>              <- 1>                    <- 1>
(%o8) limit  ((a S) . T12      . T14c . T14e      . T12 . (T12 + a S)
      a -> 0
                                <- 1>                    <- 1>
            . T14e + T14c . T14e      . T12 . (T12 + a S)      . T14e - T14c)/a
(%i9) limit((1/a)*((X+a).(X+a)-X.X),a,0);
                                                  <2>
                                 X . a + a . X + a
(%o9)                     limit  --------------------
                          a -> 0          a
(%i10) 

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