The convert/signum function converts all abs functions appearing in the expression to signum.

The convert/abs function converts all signum functions appearing in the expression to abs.

The signum(x) calling sequence is defined as abs(x)/conjugate(x) if x is not 0, and undefined if x is 0.

$\mathrm{convert}\left(\mathrm{signum}\left(x\right)\,\mathrm{abs}\right)$

$\frac{x}{\left|x\right|}$

$\mathrm{assume}\left(x\,\mathrm{real}\right)$

$\mathrm{convert}\left(\mathrm{abs}\left(x\right)\,\mathrm{signum}\right)$

$\frac{\mathrm{x~}}{\mathrm{signum}\left(\mathrm{x~}\right)}$