ApCoCoA-1:CharP.GBasisF2048
Char2.GBasisF2048
computing a gbasis of a given ideal in <formula>\mathbb{F}_{2048}</formula>
Syntax
$char2.GBasisF2048(Ideal):List
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use
it/them.
This command computes a Groebner basis in the field <formula> \mathbb{F}_{2048} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^{11} +x^3 + x^5 +x + 1)}</formula>. It uses the ApCoCoA Server and the ApCoCoALib's class RingF2048.
The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 2047 represent the field's elements. Details on this representation can be found here. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g.
<formula> 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0</formula>
So the number <formula>11</formula> corresponds to the polynomial <formula>x^3 + x + 1</formula>.
See also
