The type(expr, abstract_rootof) function returns true if expr is the abstract collection of all the roots of an expression that uses a RootOf data structure. Otherwise, false is returned.

This function recognizes two forms of roots.

RootOf(expr) where expr is an algebraic expression

RootOf(expr, label = L) where expr is an algebraic expression, and L is any expression

If extra arguments are included in the call to type(expr, abstract_rootof), they are ignored.

$\mathrm{type}\left(\mathrm{RootOf}\left(x^2-4x+71\right)\,\mathrm{abstract\_rootof}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{RootOf}\left(x^2-4x+71\,\mathrm{index}=1\right)\,\mathrm{abstract\_rootof}\right)$

$\mathrm{false}$

$\mathrm{type}\left(\mathrm{RootOf}\left(x^2-4x+7\,\mathrm{label}=A\right)\,\mathrm{abstract\_rootof}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{RootOf}\left(x^2-4x+7\,2.+1.732050808\mathrm{I}\right)\,\mathrm{abstract\_rootof}\right)$

$\mathrm{false}$