Converts an expression containing Heaviside, abs, signum, or `if` to a piecewise function. If the expression has the form $`\mathrm{if}`\left(...\right)$, the $\mathrm{if}$ must be replaced by If to avoid evaluation. If the expression contains more than one name, the argument var specifies the variable with respect to which the function is piecewise.

convert/piecewise can be used to compute the normal form of an expression involving piecewise, Heaviside, abs, signum, min, or max with respect to the variable var.

When converting Heaviside to piecewise you can perform the conversion taking Heaviside(0) = 1. For that purpose set the Environment Variable _EnvUseHeavisideAsUnitStep to true; see the last example.

$\mathrm{convert}\left(x\mathrm{Heaviside}\left(x\right)\,\mathrm{piecewise}\,x\right)$

$\left\{\begin{array}{cc}0& x<0\\ \mathrm{undefined}& x=0\\ x& 0<x\end{array}\right.$

$\mathrm{convert}\left(x\mathrm{Heaviside}\left(x\right)\&comma;\mathrm{piecewise}\&comma;x\right)$

$\left\{\begin{array}{cc}0& x<0\\ \mathrm{undefined}& x=0\\ x& 0<x\end{array}\right.$

$\mathrm{convert}\left(\mathrm{Heaviside}\left(x\right)+x\mathrm{Heaviside}\left(x-1\right)\&comma;\mathrm{piecewise}\&comma;x\right)$

$\left\{\begin{array}{cc}0& x<0\\ \mathrm{undefined}& x=0\\ 1& x<1\\ \mathrm{undefined}& x=1\\ 1+x& 1<x\end{array}\right.$

$\mathrm{convert}\left(\mathrm{abs}\left(1-\mathrm{abs}\left(x\right)\right)\&comma;\mathrm{piecewise}\right)$

$\left\{\begin{array}{cc}-1-x& x\le \mathrm{-1}\\ 1+x& x<0\\ 1-x& x<1\\ x-1& 1\le x\end{array}\right.$

$\mathrm{convert}\left(\mathrm{signum}\left(x\right)\&comma;\mathrm{piecewise}\right)$

$\left\{\begin{array}{cc}\mathrm{-1}& x<0\\ 0& x=0\\ 1& 0<x\end{array}\right.$

$\mathrm{\_Envsignum0}≔12$

$\mathrm{\_Envsignum0}≔12$

$\mathrm{convert}\left(\mathrm{signum}\left(x\right)\&comma;\mathrm{piecewise}\right)$

$\left\{\begin{array}{cc}\mathrm{-1}& x<0\\ 12& x=0\\ 1& 0<x\end{array}\right.$

$\mathrm{convert}\left(\mathrm{If}\left(x<1\&comma;xx\&comma;x<2\&comma;2x+2\&comma;x<3\&comma;3+x\right)\&comma;\mathrm{piecewise}\right)$

$\left\{\begin{array}{cc}{x}^2& x<1\\ 2x+2& x<2\\ 3+x& x<3\\ 0& 3\le x\end{array}\right.$

$\mathrm{\_EnvUseHeavisideAsUnitStep}≔\mathrm{true}$

$\mathrm{\_EnvUseHeavisideAsUnitStep}≔\mathrm{true}$

$\mathrm{convert}\left(\mathrm{Heaviside}\left(x\right)\&comma;\mathrm{piecewise}\right)$

$\left\{\begin{array}{cc}0& x<0\\ 1& 0\le x\end{array}\right.$