## 150 Reputation

2 years, 216 days

## How do you get a polynomial that satisfi...

Maple 2022

If I want to get an irreducible polynomial with root sqrt(5) and minimum degree, I can use:

```with(PolynomialTools):
MinimalPolynomial(sqrt(5), x)```

But what if I want this irreducible polynomial of the minimum degree to have roots in both sqrt(2), sqrt(3), and sqrt(5)? How do I get this polynomial?

ps: The coefficients are all integers

## How to restore the PermutationGroup from...

Maple

After this code:

`g1 := PermutationGroup({[[1, 2]], [[1, 2, 3], [4, 5]]})`

g1:=<(1, 2), (1, 2, 3)(4, 5)>

I can get a string "<(1, 2), (1, 2, 3)(4, 5)>". Could I use the string to restore the PermutationGroup with an elegant method?

## How to set the image size of DrawSubgrou...

Maple 2022
```lis := SearchSmallGroups('order' = 10 .. 100, 'soluble'):
seq(DrawSubgroupLattice(SmallGroup(g), 'highlight' = CompositionSeries(SmallGroup(g))), g in lis[10 .. 20])```

I want to see if these red nodes are present in each layer and connected at each level, so I need to detect a large number of images. But if I put them in the same row, these images will be very small and I have to zoom in one by one with the mouse to see them. How can I set the size of these images?

ps：I'm currently using my eyes to determine if these red nodes are present at each layer and connected at each level, and I'd be happy if there was code to do this

## Why RightCosets so speed?...

Maple
```with(GroupTheory):

st := time();
RightCosets(SymmetricGroup(10), SymmetricGroup(11));
time() - st;
```

0.047

Note `GroupOrder(SymmetricGroup(11))` is 39916800. It is a very large group. This seems unimaginable to me. Can I know how maple does it?

## The NormalSeries of maple is different w...

Maple 2022

As we know, when every Gi is normal in G, then the series is called a normal series:

`cs := CompositionSeries(DihedralGroup(8))`

We can draw it:

`DrawSubgroupLattice(DihedralGroup(8), labels = ids, highlight = cs)`

And all Gi is normal in G:

`IsNormal~(cs, DihedralGroup(8))`

[true, true, true, true, true]

But why `type(cs, 'NormalSeries')` will get `false`.. It is a bug or do I have a misunderstanding?

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