[GAP Forum] How to work in the two-element field F_2 in GAP.

[Sandeep Murthy]

Hi,

It seems you are passing 0 and 1 literally to create
the default field, in which case you will get the field
of rationals, in which of course 1 + 1 = 2 <> 0.

You can't refer to the zero and one of GF(2) literally by
0 and 1.  The zero is denoted by 0*Z(2), the one by Z(2)^0 (or
also just by Z(2)).  So the default field you want will
be obtained by

DefaultField( 0*Z(2), Z(2) )

FOr convenience you could just do

o := 0*Z(2); e := Z(2);

and then do your operations.

Sandeep.



Jianrong Li wrote:
> Dear Sandeep,
>
> Thank you very much. But how to make the default field to be GF(2)? I
> use the command GF(2), and try 1+1, but it returns 2.
>
> With best wishes,
> Jianrong.
>
>
>
> 2012/12/31 Sandeep Murthy <sandeepr.murthy at gmail.com
> <mailto:sandeepr.murthy at gmail.com>>
>
>     Hi,
>
>     Creating finite fields is described in section 59.3 of
>     the GAP reference manual.
>
>     GaloisField(2) (also GF(2)) will get you the field of
>     two elements 0,1.
>
>     Sandeep.
>
>
>     Jianrong Li wrote:
>
>         Dear Forum,
>
>         I want to work over the field F_2 with only two elements 0, 1.
>         1+1=0.
>
>         I have matrices with entries 0, 1. The multiplication of the
>         matrices are
>         over F_2.
>
>         I would like to define the default field as F_2. How could I do
>         that in GAP?
>
>         I tried DefaultField(Z(2)). But it seems that this doesn't work.
>
>         Thank you very much.
>
>         Best wishes,
>         Jianrong.
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