## 150 Reputation

2 years, 140 days

## A bug of Minpoly?...

Maple

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?

## How can I see all the functions availabl...

Maple

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 and IsFrobeniusPermGrou...

Maple 2022

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

## Bug of IsTransitive?...

Maple

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

## How to compute the Galois group of reduc...

Maple

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

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