MakeMonic expresses a RootOf in terms of a monic RootOf. It pulls the leading coefficient of the defining polynomial out of the RootOf and into the denominator.

MakeMonic only works on indexed, labeled, or one-argument RootOfs. For RootOfs with a numerical approximation or a range as selector, MakeMonic returns the input unchanged.

Nested RootOfs that are indexed, labeled, or one-argument, are handled recursively.

If r is not a RootOf or not of type algext, it is returned unchanged.

For indexed RootOfs, the leading coefficient is pulled out only if its signum is $1$ or $\mathrm{-1}$.

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(\mathrm{RootOf}\left(y{x}^3-1\,x\right)\right)$

$\frac{\mathrm{RootOf}\left({\mathrm{\_Z}}^3-y^2\right)}{y}$

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(1+\mathrm{RootOf}\left(y{x}^3-1\,x\right)\right)$

$1+\mathrm{RootOf}\left(y{\mathrm{\_Z}}^3-1\right)$

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(\mathrm{RootOf}\left(2\sin \left(x\right)-1\right)\right)$

$\mathrm{RootOf}\left(2\sin \left(\mathrm{\_Z}\right)-1\right)$

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(\mathrm{RootOf}\left(y{x}^3-1\,x\,\mathrm{index}=1\right)\right)$

$\mathrm{RootOf}\left(y{\mathrm{\_Z}}^3-1\,\mathrm{index}=1\right)$

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(\mathrm{RootOf}\left(y{x}^3-1\&comma;x\&comma;\mathrm{index}=1\right)\right)\mathbf{assuming}0<y$

$\frac{\mathrm{RootOf}\left({\mathrm{\_Z}}^3-y^2\&comma;\mathrm{index}=1\right)}{y}$

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(\mathrm{RootOf}\left(y{x}^3-1\&comma;x\&comma;\mathrm{index}=1\right)\right)\mathbf{assuming}y<0$

$-\frac{\mathrm{RootOf}\left({\mathrm{\_Z}}^3+y^2\&comma;\mathrm{index}=1\right)}{y}$

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(\mathrm{RootOf}\left(5y^2-\mathrm{RootOf}\left(3x^2+1\&comma;\mathrm{index}=1\right)\&comma;\mathrm{index}=1\right)\right)$

$\frac{\mathrm{RootOf}\left({\mathrm{\_Z}}^2-15\mathrm{RootOf}\left({\mathrm{\_Z}}^2+3\&comma;\mathrm{index}=1\right)\&comma;\mathrm{index}=1\right)}{15}$

$\mathrm{RootOf}\left(\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\right){\mathrm{\_Z}}^2-2\right)$

$\mathrm{RootOf}\left({\mathrm{\_Z}}^2-\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\right)\right)$

$f≔\mathrm{RootOf}\left(\mathrm{RootOf}\left(x^2-x\right)y^2-2\right)$

$f≔\mathrm{RootOf}\left(\mathrm{RootOf}\left({\mathrm{\_Z}}^2-\mathrm{\_Z}\right){\mathrm{\_Z}}^2-2\right)$

$\mathrm{Algebraic}:-\mathrm{MakeMonic}\left(f\right)$

$\frac{\mathrm{RootOf}\left({\mathrm{\_Z}}^2-2\mathrm{RootOf}\left({\mathrm{\_Z}}^2-\mathrm{\_Z}\right)\right)}{\mathrm{RootOf}\left({\mathrm{\_Z}}^2-\mathrm{\_Z}\right)}$