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