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The Maxima on-line user's manual

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Evfun Calculator

Evfun

-- Property: evfun When a function <F> has the evfun property, the expressions ev(<expr>, <F>) and <expr>, <F> (at the interactive prompt) are equivalent to <F>(ev(<expr>)).

If two or more evfun functions <F>, <G>, etc., are specified, the functions are applied in the order that they are specified.

load(vect);
load(vector);
dotconstrules:true;
T(x):=x*y^2;
setcoord(c[x, y, z]);
declare(express,evfun);
declare(apply, evfun);
dl:[dx, dy, dz];
grad(T(x));
grad(T(x)).dl;
apply(".", [grad(T(x)),[dx,0,0]]);
apply(".", [grad(T(x)),[0,dy,0]]);
apply(".", [grad(T(x)),[0,0,dz]]);
apply(".", [grad(T(x)),[dx,dy,0]]);
apply(".", [grad(T(x)),[dx,dy,dz]]);
div([T(x), T(x), T(x)]);
plot2d(T(x), [x, 0, 4], [y, 0, 4]);

The expression declare(<F>, evfun) gives the evfun property to the function <F>.

The functions which have the evfun property by default are the following: bfloat, factor, fullratsimp, logcontract, polarform, radcan, ratexpand, ratsimp, rectform, rootscontract, trigexpand, and trigreduce.

Examples:

          (%i1) x^3 - 1;
                                        3
          (%o1)                        x  - 1
          (%i2) x^3 - 1, factor;
                                          2
          (%o2)                 (x - 1) (x  + x + 1)
          (%i3) factor (x^3 - 1);
                                          2
          (%o3)                 (x - 1) (x  + x + 1)
          (%i4) cos(4 * x) / sin(x)^4;
                                      cos(4 x)
          (%o4)                       --------
                                         4
                                      sin (x)
          (%i5) cos(4 * x) / sin(x)^4, trigexpand;
                           4           2       2         4
                        sin (x) - 6 cos (x) sin (x) + cos (x)
          (%o5)         -------------------------------------
                                          4
                                       sin (x)
          (%i6) cos(4 * x) / sin(x)^4, trigexpand, ratexpand;
                                     2         4
                                6 cos (x)   cos (x)
          (%o6)               - --------- + ------- + 1
                                    2          4
                                 sin (x)    sin (x)
          (%i7) ratexpand (trigexpand (cos(4 * x) / sin(x)^4));
                                     2         4
                                6 cos (x)   cos (x)
          (%o7)               - --------- + ------- + 1
                                    2          4
                                 sin (x)    sin (x)
          (%i8) declare ([F, G], evfun);
          (%o8)                         done
          (%i9) (aa : bb, bb : cc, cc : dd);
          (%o9)                          dd
          (%i10) aa;
          (%o10)                         bb
          (%i11) aa, F;
          (%o11)                        F(cc)
          (%i12) F (aa);
          (%o12)                        F(bb)
          (%i13) F (ev (aa));
          (%o13)                        F(cc)
          (%i14) aa, F, G;
          (%o14)                      G(F(cc))
          (%i15) G (F (ev (aa)));
          (%o15)                      G(F(cc))

(%o1)                                true
(%i2) 

Evfun Example

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