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The Maxima on-line user's manual

Algebra Calculator

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Ev Calculator

Ev

Function: ev (<expr>, <arg_1>, ..., <arg_n>) Evaluates the expression <expr> in the environment specified by the arguments <arg_1>, ..., <arg_n>. The arguments are switches (Boolean flags), assignments, equations, and functions. ev returns the result (another expression) of the evaluation.

The evaluation is carried out in steps, as follows.

1. First the environment is set up by scanning the arguments which may be any or all of the following.

* simp causes <expr> to be simplified regardless of the setting of the switch simp which inhibits simplification if false.

* noeval supresses the evaluation phase of ev (see step (4) below). This is useful in conjunction with the other switches and in causing <expr> to be resimplified without being reevaluated.

* nouns causes the evaluation of noun forms (typically unevaluated functions such as integrate or diff) in <expr>.

* expand causes expansion.

* expand (<m>, <n>) causes expansion, setting the values of maxposex and maxnegex to <m> and <n> respectively.

* detout causes any matrix inverses computed in <expr> to have their determinant kept outside of the inverse rather than dividing through each element.

* diff causes all differentiations indicated in <expr> to be performed.

* derivlist (<x>, <y>, <z>, ...) causes only differentiations with respect to the indicated variables.

* risch causes integrals in <expr> to be evaluated using the Risch algorithm. See risch. The standard integration routine is invoked when using the special symbol nouns.

* float causes non-integral rational numbers to be converted to floating point.

* numer causes some mathematical functions (including exponentiation) with numerical arguments to be evaluated in floating point. It causes variables in <expr> which have been given numervals to be replaced by their values. It also sets the float switch on.

* pred causes predicates (expressions which evaluate to true or false) to be evaluated.

* eval causes an extra post-evaluation of <expr> to occur. (See step (5) below.) eval may occur multiple times. For each instance of eval, the expression is evaluated again.

* A where A is an atom declared to be an evaluation flag (see evflag) causes A to be bound to true during the evaluation of <expr>.

* V: expression (or alternately V=expression) causes V to be bound to the value of expression during the evaluation of <expr>. Note that if V is a Maxima option, then expression is used for its value during the evaluation of <expr>. If more than one argument to ev is of this type then the binding is done in parallel. If V is a non-atomic expression then a substitution rather than a binding is performed.

* F where F, a function name, has been declared to be an evaluation function (see evfun) causes F to be applied to <expr>.

* Any other function names (e.g., sum) cause evaluation of occurrences of those names in <expr> as though they were verbs.

* In addition a function occurring in <expr> (say F(x)) may be defined locally for the purpose of this evaluation of <expr> by giving F(x) := expression as an argument to ev.

* If an atom not mentioned above or a subscripted variable or subscripted expression was given as an argument, it is evaluated and if the result is an equation or assignment then the indicated binding or substitution is performed. If the result is a list then the members of the list are treated as if they were additional arguments given to ev. This permits a list of equations to be given (e.g. [X=1, Y=A**2]) or a list of names of equations (e.g., [%t1, %t2] where %t1 and %t2 are equations) such as that returned by solve.

The arguments of ev may be given in any order with the exception of substitution equations which are handled in sequence, left to right, and evaluation functions which are composed, e.g., ev (<expr>, ratsimp, realpart) is handled as realpart (ratsimp (<expr>)).

The simp, numer, and float switches may also be set locally in a block, or globally in Maxima so that they will remain in effect until being reset.

If <expr> is a canonical rational expression (CRE), then the expression returned by ev is also a CRE, provided the numer and float switches are not both true.

2. During step (1), a list is made of the non-subscripted variables appearing on the left side of equations in the arguments or in the value of some arguments if the value is an equation. The variables (subscripted variables which do not have associated array functions as well as non-subscripted variables) in the expression <expr> are replaced by their global values, except for those appearing in this list. Usually, <expr> is just a label or % (as in %i2 in the example below), so this step simply retrieves the expression named by the label, so that ev may work on it.

3. If any substitutions are indicated by the arguments, they are carried out now.

4. The resulting expression is then re-evaluated (unless one of the arguments was noeval) and simplified according to the arguments. Note that any function calls in <expr> will be carried out after the variables in it are evaluated and that ev(F(x)) thus may behave like F(ev(x)).

5. For each instance of eval in the arguments, steps (3) and (4) are repeated.

Examples:

          (%i1) sin(x) + cos(y) + (w+1)^2 + diff (sin(w), w);
                                               d                    2
          (%o1)              cos(y) + sin(x) + -- (sin(w)) + (w + 1)
                                               dw
          (%i2) ev (%, numer, expand, diff, x=2, y=1);
                                         2
          (%o2)                cos(w) + w  + 2 w + 2.449599732693821

An alternate top level syntax has been provided for ev, whereby one may just type in its arguments, without the ev(). That is, one may write simply

<expr>, <arg_1>, ..., <arg_n>

This is not permitted as part of another expression, e.g., in functions, blocks, etc.

Notice the parallel binding process in the following example.

          (%i3) programmode: false;
          (%o3)                                false
          (%i4) x+y, x: a+y, y: 2;
          (%o4)                              y + a + 2
          (%i5) 2*x - 3*y = 3$
          (%i6) -3*x + 2*y = -4$
          (%i7) solve ([%o5, %o6]);
          Solution

                                                    1
          (%t7)                               y = - -
                                                    5

                                                   6
          (%t8)                                x = -
                                                   5
          (%o8)                            [[%t7, %t8]]
          (%i8) %o6, %o8;
          (%o8)                              - 4 = - 4
          (%i9) x + 1/x > gamma (1/2);
                                             1
          (%o9)                          x + - > sqrt(%pi)
                                             x
          (%i10) %, numer, x=1/2;
          (%o10)                      2.5 > 1.772453850905516
          (%i11) %, pred;
          (%o11)                               true

There are also some inexact matches for ev. Try ?? ev to see them.

(%o1)                                true
(%i2) 

Ev Example

Related Examples

ev-linsolve

jednacine:[x+y=30, 2*...

resenje:linsolve(jedn...

z:x*y;

Calculate

ev-integrate-nouns-sinh

'integrate (sinh(x)/(...

ev(%,nouns);

Calculate

ev-linsolve

jednacine: [x+y=30, 2...

promenljive: [x,y];

odziv: linsolve(jedna...

Calculate

ev-simp-sqrt

simp;

c1:(sqrt(5)+5)/10;

c2:(sqrt(5) - 5)/10;

Calculate

ev-fullratsimp-linsolve-print-rhs

cartera:linsolve([del...

[delta,B]:[rhs(carter...

ValorCartera:delta*S+...

Calculate

ev-linsolve

jednacine: [x+y=30, 2...

resenje: linsolve(jed...

z = x*y;

Calculate

ev-matrix-numer-plot2d-sqrt
plot2d(f(x),[x,-10,10]);

M:matrix([2],[5],[-3]);

v(x):=x*M;

f(x):=ev(sqrt(v(x)[1]...

Calculate

ev-float-solve

MN:49;

sN=(1500-1450)/1500;

MK=MN*3.1;

Calculate

ev-numer-pi-solve

Fg:G*me*mm/rm^2;

Fz:mm*rm*(w^2);

eq: Fg=Fz;

Calculate

ev

ev((-3+3*y^2)^2);

Calculate