[GAP Forum] subspace spanned by random subset (of finite field over subfield)

[fvanhove at cage.ugent.be]

Hello,

thank you very much for the clear response and the examples.

I had another question about this: finite fields, seen both as fields  
and as vector spaces.
I wanted to take a non-zero element of the bigger field, consider the  
cyclic subgroup generated by it, and let it act on the cosets of the  
multiplicative group (so in a sense, I want to consider Singer cycles,  
which are apparently not yet implemented)
Curiously, however, there seems to be no command to obtain the  
multiplicative group of a Galois field?

Kind regards,
Frédéric


Quoting Max Horn <max at quendi.de>:

> Hello again,
>
> there were (at least) two mistakes in my email:
>
> 1) This
>
>> Dear
>
> should of course have been
>
>  "Dear Frédéric"
>
> Sorry! Secondly, as Stefan Kohl pointed out,
>
> [...]
>
>>
>> Decomposing w^5 with respect to this basis:
>
> Here, I meant w^6 (and that is what the example code below does).
>
>
> Cheers,
> Max
>
>>
>> gap> Coefficients(Basis(W), w^6);
>> [ Z(3)^0, Z(3)^0, Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ]
>>
>> We verify this:
>>
>> gap> w^0 + w - w^2 + w^4 = w^6;
>> true
>>
>>
>> Hope that helps,
>> Max
>>
>>>
>>> Thanks in advance,
>>> Kind regards,
>>> Frédéric
>>>
>>>
>>>
>>>
>>>
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