with(GroupTheory);
G := GaloisGroup(x^5 + 20*x + 32, x);

I just can get a result like:

GroupTheory:-GaloisGroup(x^5 + 20*x + 32, x)

But how do I know exactly what group it is? Actually I know the galois group is D₅, But can we use maple to get this information?

ds := DerivedSeries(PermutationGroup({[[2, 3, 5, 4]], [[1, 2, 3, 4, 5]]}))

will get a series group like:

How to get the group by the red line point out? Then I can use GroupOrder to get the order of it. I note GroupOrder[ds[2]] don't work

I am a Mathematica user actually. And I can know x^(1/(x + 1/x)) + y^(1/(y + 1/y)) == E is closed by the code:

ContourPlot[x^(1/(x + 1/x)) + y^(1/(y + 1/y)) == E, {x, 0, 7}, {y, 0, 7}]

But Mathematica cannot calculate this integral Integrate[1,Element[{x,y},ImplicitRegion[x^(1/(x+1/x))+y^(1/(y+1/y))>=E,{{x,0,7},{y,0,7}}]]]. It just can give a numerical solution by NIntegrate, This makes me depressed. So I try to calculate it by Maple. After I read some documentation of maple, I don't know how to use a implicit function to expression a region to do integral in MultiInt. So I ask here to help. Anybody can tell me how to write this code in Maple?