Difference between revisions of "ApCoCoA-1:CharP.GBasisF1024"
| Line 11: | Line 11: | ||
<itemize> | <itemize> | ||
| − | <item>@param <em>Ideal</em> An Ideal in a Ring over Z, where the elements 0,..., 1023 represent the field | + | <item>@param <em>Ideal</em> An Ideal in a Ring over Z, where the elements 0,...,1023 represent the elements of the finite field. For short, the binary representation of the number represents the coefficient vector of the polynomial in the field, e.g. 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0. So the number 11 corresponds to the polynomial x^3 + x + 1.</item> |
| − | So the number 11 corresponds to the polynomial x^3 + x + 1.</item> | ||
<item>@return A Groebner Basis of the given ideal.</item> | <item>@return A Groebner Basis of the given ideal.</item> | ||
| Line 31: | Line 30: | ||
<see>Char2.GBasisF4096</see> | <see>Char2.GBasisF4096</see> | ||
<see>Char2.GBasisModSquares</see> | <see>Char2.GBasisModSquares</see> | ||
| − | + | <see>Representation of finite fields</see> | |
</seealso> | </seealso> | ||
<key>char2.GBasisF1024</key> | <key>char2.GBasisF1024</key> | ||
Revision as of 14:14, 23 April 2009
Char2.GBasisF1024
Computing a Groebner basis of a given ideal in <formula>\mathbb{F}_{1024}</formula>.
Syntax
Char2.GBasisF1024(Ideal: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}_{1024} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^{10} + x^3 + x^2 + x + 1)}</formula>.
@param Ideal An Ideal in a Ring over Z, where the elements 0,...,1023 represent the elements of the finite field. For short, the binary representation of the number represents the coefficient vector of the polynomial in the field, e.g. 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0. So the number 11 corresponds to the polynomial x^3 + x + 1.
@return A Groebner Basis of the given ideal.
See also
Representation of finite fields
