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

degraaf at science.unitn.it degraaf at science.unitn.it
Wed Mar 26 08:47:45 GMT 2008

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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