[GAP Forum] Re: Complex numbers (again) and Lie closure

Knut Kasimir oova1980 at yahoo.de
Tue Apr 1 09:52:46 BST 2008

Dear Willem,

thank you very much for your answer.
I think I should be able to work with matrices whose entries are algebraic over Q. As I see it (being not a mathematician and a GAP newbie), the problem then reduces to create a number field and do my desired operations on it.

Best wishes,

Von: "degraaf at science.unitn.it" <degraaf at science.unitn.it>
An: forum at gap-system.org
CC: oova1980 at yahoo.de
Gesendet: Mittwoch, den 26. März 2008, 09:47:45 Uhr
Betreff: Re: Complex numbers (again) and Lie closure

Dear Knut,

You asked the following:

> What I want to do with GAP is the following: Given a set of complex  
> square matrices, find out if they form a vectorspace under repeated  
> commutation, i.e. a Lie algebra. In other words, do these given  
> matrices generate a Lie algebra under repeated commutation?

The problem here is that you need some exact representation of the complex
numbers that you use. (Just a floating point representation does not work.)
If the entries of your matrices are algebraic over Q, then you can represent
them as entries in a number field. Otherwise I don't see how your problem
could be solved.

Best wishes,

Willem de Graaf

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