formal degree of an algebraic extension
set of RootOfs of type algext
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.
The RootOfs in the following example are dependent, and the formal algebraic degree is bigger than the actual degree, which is 4:
The set of RootOfs in the following example is not closed under sub-RootOfs, and Degree does not return the correct formal degree, which is 4:
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