87.2 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 mode_declare (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)