Difference between revisions of "ApCoCoA-1:CharP.GBasisF128"
From ApCoCoAWiki
(Added ApCoCoAServer note) |
|||
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>Char2.GBasisF128</title> | <title>Char2.GBasisF128</title> | ||
| − | <short_description> | + | <short_description>Computing a Groebner Basis of a given ideal in <formula>\mathbb{F}_{128}</formula>.</short_description> |
<syntax> | <syntax> | ||
| − | + | Char2.GBasisF128(Ideal:IDEAL):LIST | |
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | + | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | |
| − | + | <par/> | |
| − | This command computes a Groebner basis in the field <formula> \mathbb{F}_{128} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^7 + x + 1 )} | + | This command computes a Groebner basis in the field <formula> \mathbb{F}_{128} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^7 + x + 1 )}</formula>. |
| − | |||
| − | |||
| − | |||
| − | |||
| + | <itemize> | ||
| + | <item>@param <em>Ideal</em> An Ideal in a Ring over Z, where the elements 0,..., 127 represent the field's elements. For short, the binary representation of the number represents the coefficient vector if 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> | ||
| + | <item>@return The Groebner Basis of the given ideal.</item> | ||
| + | </itemize> | ||
</description> | </description> | ||
<seealso> | <seealso> | ||
<see>GBasis</see> | <see>GBasis</see> | ||
| − | <see> | + | <see>Char2.GBasisF2</see> |
| − | <see> | + | <see>Char2.GBasisF4</see> |
| − | <see> | + | <see>Char2.GBasisF8</see> |
| − | <see> | + | <see>Char2.GBasisF16</see> |
| − | <see> | + | <see>Char2.GBasisF32</see> |
| − | <see> | + | <see>Char2.GBasisF64</see> |
| − | <see> | + | <see>Char2.GBasisF256</see> |
| − | <see> | + | <see>Char2.GBasisF512</see> |
| − | <see> | + | <see>Char2.GBasisF1024</see> |
| − | <see> | + | <see>Char2.GBasisF2048</see> |
| − | <see> | + | <see>Char2.GBasisF4096</see> |
| − | <see> | + | <see>Char2.GBasisModSquares</see> |
| − | |||
</seealso> | </seealso> | ||
| − | |||
<key>char2.GBasisF128</key> | <key>char2.GBasisF128</key> | ||
| + | <key>GBasisF128</key> | ||
<wiki-category>Package_char2</wiki-category> | <wiki-category>Package_char2</wiki-category> | ||
</command> | </command> | ||
Revision as of 16:23, 22 April 2009
Char2.GBasisF128
Computing a Groebner Basis of a given ideal in <formula>\mathbb{F}_{128}</formula>.
Syntax
Char2.GBasisF128(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}_{128} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^7 + x + 1 )}</formula>.
@param Ideal An Ideal in a Ring over Z, where the elements 0,..., 127 represent the field's elements. For short, the binary representation of the number represents the coefficient vector if 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 The Groebner Basis of the given ideal.
See also
