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evfun

Run Example
(%i1)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
declare(makegamma, evfun);
(%o1)                                done
(%i2) declare(makefact, evfun);
(%o2)                                done
(%i3) a1:(n-1)!, makegamma;
(%o3)                              gamma(n)
(%i4) a1, makefact, factorial_expand:true;
                                      n!
(%o4)                                 --
                                      n
(%i5) a2:(n-2)!, makegamma;
(%o5)                            gamma(n - 1)
(%i6) a2, makefact, factorial_expand:true;
                                      n!
(%o6)                              ---------
                                   (n - 1) n
(%i7) a3:(n-3)!, makegamma;
(%o7)                            gamma(n - 2)
(%i8) a4: a3, makefact, factorial_expand:true;
                                      n!
(%o8)                          -----------------
                               (n - 2) (n - 1) n
(%i9) num(a4), makegamma, gamma_expand:true;
(%o9)                             n gamma(n)
(%i10) denom(a4);
(%o10)                         (n - 2) (n - 1) n
(%i11) gamma(n), makefact;
(%o11)                             (n - 1)!
(%i12) 
Run Example
trigsimp(tan(x));
                                    sin(x)
(%o1)                               ------
                                    cos(x)
(%i2) tan(x), trigsimp;
(%o2)                               tan(x)
(%i3) declare(trigsimp, evfun);
(%o3)                                done
(%i4) tan(x), trigsimp;
                                    sin(x)
(%o4)                               ------
                                    cos(x)
(%i5) cos(x)^2, trigexpand;
                                       2
(%o5)                               cos (x)
(%i6) tellsimp(cos(x)^2, 1-sin(x)^2);
(%o6)                         [^rule1, simpexpt]
(%i7) cos(x)^2, trigexpand;
                                         2
(%o7)                             1 - sin (x)
(%i8) cos(x), trigsimp;
(%o8)                               cos(x)
(%i9) tellsimp(cos(x), cot(x)*sin(x));
(%o9)                        [cosrule1, simp-%cos]
(%i10) cos(x), trigsimp;
(%o10)                              cos(x)
(%i11) cos(x), trigexpand;
(%o11)                           cot(x) sin(x)
(%i12) cos(x), trigsimp, expand;
(%o12)                              cos(x)
(%i13) simp;
(%o13)                               true
(%i14) cos(x);
(%o14)                           cot(x) sin(x)
(%i15) cos(x), simp:false;
(%o15)                           cot(x) sin(x)
(%i16) cos(x), trigsimp:false;
(%o16)                           cot(x) sin(x)
(%i17) cos(x), trigsimp:true;
(%o17)                           cot(x) sin(x)
(%i18) matchdeclare(a, true);
(%o18)                               done
(%i19) let(cos(a), cot(a)*sin(a));
(%o19)                     cos(a) --> cot(a) sin(a)
(%i20) letsimp(cos(x));
(%o20)                           cot(x) sin(x)
(%i21) 

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