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
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
diff) in <expr>.
expand causes expansion.
expand (<m>, <n>) causes expansion, setting the values of
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
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
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 is an atom declared to be an evaluation flag (see
A to be bound to
true during the evaluation of <expr>.
V: expression (or alternately
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, a function name, has been declared to be an evaluation function (see
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
* 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
%t2 are equations) such as that returned by
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>)).
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
float switches are not both
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
5. For each instance of
eval in the arguments, steps (3) and (4) are repeated.
(%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 to see them.
(%o1) true (%i2)