Maxima Function
atvalue (expr, [x_1 = a_1, ..., x_m = a_m], c)
atvalue(expr,x_1=a_1,c)
Assigns the value c to expr at the point x = a
.
Typically boundary values are established by this mechanism.
expr is a function evaluation,
f(x_1, ..., x_m)
,
or a derivative,
diff (f(x_1, ..., x_m), x_1, n_1, ..., x_n, n_m)
in which the function arguments explicitly appear. n_i is the order of differentiation with respect to x_i.
The point at which the atvalue is established is given by the list of equations
[x_1 = a_1, ..., x_m = a_m]
.
If there is a single variable x_1,
the sole equation may be given without enclosing it in a list.
printprops ([f_1, f_2, ...], atvalue)
displays the atvalues of
the functions f_1, f_2, ...
as specified by calls to atvalue
.
printprops (f, atvalue)
displays the atvalues of one function f.
printprops (all, atvalue)
displays the atvalues of all functions for which atvalues are defined.
The symbols @1
, @2
, ... represent the
variables x_1, x_2, ... when atvalues are displayed.
atvalue
evaluates its arguments.
atvalue
returns c, the atvalue.
Examples:
(%i1) atvalue (f(x,y), [x = 0, y = 1], a^2); 2 (%o1) a (%i2) atvalue ('diff (f(x,y), x), x = 0, 1 + y); (%o2) @2 + 1 (%i3) printprops (all, atvalue); ! d ! --- (f(@1, @2))! = @2 + 1 d@1 ! !@1 = 0 2 f(0, 1) = a (%o3) done (%i4) diff (4*f(x,y)^2 - u(x,y)^2, x); d d (%o4) 8 f(x, y) (-- (f(x, y))) - 2 u(x, y) (-- (u(x, y))) dx dx (%i5) at (%, [x = 0, y = 1]); ! 2 d ! (%o5) 16 a - 2 u(0, 1) (-- (u(x, y))! ) dx ! !x = 0, y = 1