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Atvalue

Function: atvalue (<expr>, [<x_1> = <a_1>, ..., <x_m> = <a_m>], <c>)

Function: 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

(%o1)                                true
(%i2)