Given a set of RootOfs defining an algebraic extension, Degree determines the formal algebraic degree of that extension.

The formal algebraic degree of a non-nested RootOf is the degree of its first argument with respect to the variable _Z, i.e., the degree of its defining polynomial.

The formal algebraic degree of a set of RootOfs is the product of the degrees of all the defining polynomials.

This procedure assumes that all sub-RootOfs of a RootOf in S are elements of S as well.

If all RootOfs in S are independent, then the formal algebraic degree is equal to the actual degree of the field extension defined by the RootOfs in S over the ground field.

$\mathrm{Algebraic}\left[\mathrm{Degree}\right]\left(\left\{\mathrm{RootOf}\left(x^2-2\,\mathrm{index}=1\right)\,\mathrm{RootOf}\left(y^2-\mathrm{RootOf}\left(x^2-2\,\mathrm{index}=1\right)\,\mathrm{index}=1\right)\right\}\right)$

$4$

$\mathrm{Algebraic}\left[\mathrm{Degree}\right]\left(\varnothing \right)$

$1$

$\mathrm{Algebraic}\left[\mathrm{Degree}\right]\left(\left\{\mathrm{RootOf}\left(x^2-2\,\mathrm{index}=1\right)\,\mathrm{RootOf}\left(x^2-3\,\mathrm{index}=1\right)\,\mathrm{RootOf}\left(x^2-6\,\mathrm{index}=1\right)\right\}\right)$

$8$

$\mathrm{Algebraic}\left[\mathrm{Degree}\right]\left(\left\{\mathrm{RootOf}\left(y^2-\mathrm{RootOf}\left(x^2-2\,\mathrm{index}=1\right)\,\mathrm{index}=1\right)\right\}\right)$

$2$