When I use evala(Minpoly(sqrt(3) + sqrt(2), x)), then I get a right answer: x^4 - 10*x^2 + 1

But when I want to get the minimal polynomial of cos((2*Pi)/7) by evala(Minpoly(cos((2*Pi)/7), x)), I will get a result:

x - cos((2*Pi)/7)

It clearly does not follow the definition of a minimal polynomial. Is it a bug of Minpoly or I have missed something?

We can see a list of functions for a package in the documentation, for example the package GroupTheory:

Is there a code based way to see all the functions in this package?

IsFrobeniusGroup(SmallGroup(20, 3)) will get true, but IsFrobeniusPermGroup(SmallGroup(20, 3)) will get false. What happen? As the documentation, it will get same result:

The two definitions are equivalent in the following sense.  If G is a Frobenius permutation group, then G is Frobenius as an abstract group

When I use IdentifySmallGroup(DihedralGroup(4)), I will get result 8,3. Then I know DihedralGroup(4) is SmallGroup(8, 3) actually. But I will get different result when I use it in IsTransitive:

IsTransitive(DihedralGroup(4), [1, 2, 3, 4])

true

IsTransitive(SmallGroup(8, 3), [1, 2, 3, 4])

false

If a polynomial is irreducible, you can use GroupTheory:-GaloisGroup or galois to compute its polynomial, for example:

G := GroupTheory:-GaloisGroup(x^5 - x + 1, x)

But what if polynomials are reducible? Such as x^5-x+15. How to compute its Galois group by maple? There are some examples to check at the end of this article