On Wednesday, March 22, 2017 at 3:19:14 PM UTC-7, [email protected] wrote:
>
> Oh , didn't know this piece of info.
>>
> This thing took me time more than it would have if I implemented it
> myself, and I was intending to xD
> What I get from your answer is that if I put binary list inside k it
> returns the field.
> sage: k([0,1,1]) # where most significant bit is on the right
> a^2 + a
>
> thank you very much, I most probably would have never known this by my
> own, didn't see it any where in the docs.
> May be I just don't look good enough
>
It's a reasonable thing to try if you think of elements in k as represented
by polynomials in a. A polynomial in sage can be constructed by calling the
polynomial ring with the list of coefficients. It's sort-of documented in
GF(2^8)._element_constructor:
Free module elements over "prime_subfield()" are interpreted
'little endian':
sage: k = GF(2**8, 'a')
sage: e = k.vector_space().gen(1); e
(0, 1, 0, 0, 0, 0, 0, 0)
sage: k(e)
a
but as you can see the constructor is a bit more liberal than just that.
It's "discoverable" in the sense that it's reasonable to hope that it works
once you know how sage works, but it doesn't seem to be documented
literally.
As to the fact that you need to look at the binary representation: Both
integers and polynomials over GF(2) are naturally represented as
bitstrings. The indentification of these is what underlies Givaro's
"integer_representation".
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