> < ^ Date: Mon, 25 Feb 2002 14:40:32 +0100 (MET)
> < ^ From: Jan Draisma <Jan.Draisma@unibas.ch >
> < ^ Subject: Re: A matrix group

Dear Gap-forum, and Nicola,

```I would express the algebraic numbers occuring in your example in a
suitable cyclotomic field (see E and CF in the manual); in your case
CF(20) should do; for instance, cos(t) and sin(t) should be sg like
this:
c1:=(-E(5)^2-E(5)^3)/2;
s1:=(-E(5)^2+E(5)^3)/(2*E(4));
Then define A and S, and simply call Size(Group([A,S])).
```

Best wishes,

Jan

Dear GAP forum,

I'd like to generate a group using two elements A and S: G = <A,S>. I
don't know if this group is finite. Someone can help me?

```S = diag(1,1,-1,-1)

A =
[0,                 0,             cos(s),     -sin(s)]
[-sin(t),         cos(t),             0,             0]
[cos(t),         sin(t),             0,             0]
[0,                 0,             sin(s),     cos(s)]
```

with

```cos(t) := 1/4 + 1/4 sqrt(5)

sin(t) := 1/4 sqrt(2) sqrt(5 - sqrt(5))

cos(s):= 3/4 - 1/4 sqrt(5)

sin(s):= 1/4 sqrt(2 + 6 sqrt(5))
```

Thank you, Nicola.

Miles-Receive-Header: reply

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