Difference between revisions of "ApCoCoA-1:CharP.GBasisF1024"
From ApCoCoAWiki
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<command> | <command> | ||
<title>Char2.GBasisF1024</title> | <title>Char2.GBasisF1024</title> | ||
| − | <short_description> | + | <short_description>Computing a Groebner basis of a given ideal in <formula>\mathbb{F}_{1024}</formula>.</short_description> |
<syntax> | <syntax> | ||
| − | + | Char2.GBasisF1024(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></par> | ||
| + | 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>. | ||
| − | + | <itemize> | |
| − | + | <item>@param <em>Ideal</em> An Ideal in a Ring over Z, where the elements 0,..., 1023 represent the field's elements. 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 | ||
| + | <item>@return A 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.GBasisF128</see> |
| − | <see> | + | <see>Char2.GBasisF256</see> |
| − | <see> | + | <see>Char2.GBasisF512</see> |
| − | <see> | + | <see>Char2.GBasisF2048</see> |
| − | <see> | + | <see>Char2.GBasisF4096</see> |
| − | <see> | + | <see>Char2.GBasisModSquares</see> |
</seealso> | </seealso> | ||
| − | |||
<key>char2.GBasisF1024</key> | <key>char2.GBasisF1024</key> | ||
| + | <key>GBasisF1024</key> | ||
<wiki-category>Package_char2</wiki-category> | <wiki-category>Package_char2</wiki-category> | ||
</command> | </command> | ||
Revision as of 16:16, 22 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.
<par></par>
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 field's elements. 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
