69.2 Package absimp

The absimp package contains pattern-matching rules that extend the built-in simplification rules for the abs and signum functions. absimp respects relations established with the built-in assume function and by declarations such as modedeclare (m, even, n, odd) for even or odd integers.

absimp defines unitramp and unitstep functions in terms of abs and signum.

load("absimp") loads this package. demo(absimp) shows a demonstration of this package.

Examples:

(%i1) load ("absimp")$
(%i2) (abs (x))^2;
                                       2
(%o2)                                 x
(%i3) diff (abs (x), x);
                                      x
(%o3)                               ------
                                    abs(x)
(%i4) cosh (abs (x));
(%o4)                               cosh(x)