Difference between revisions of "ApCoCoA-1:CharP.GBasisF256"
| Line 1: | Line 1: | ||
<command> | <command> | ||
| − | <title> | + | <title>CharP.GBasisF256</title> |
<short_description>Computing a Groebner Basis of a given ideal in <tt>F_256</tt>.</short_description> | <short_description>Computing a Groebner Basis of a given ideal in <tt>F_256</tt>.</short_description> | ||
<syntax> | <syntax> | ||
| − | + | CharP.GBasisF256(Ideal:IDEAL):LIST | |
</syntax> | </syntax> | ||
<description> | <description> | ||
| Line 28: | Line 28: | ||
------------------------------- | ------------------------------- | ||
I:=Ideal(x-y^2,x^2+xy,y^3); | I:=Ideal(x-y^2,x^2+xy,y^3); | ||
| − | + | CharP.GBasisF256(I); | |
-- WARNING: Coeffs are not in a field | -- WARNING: Coeffs are not in a field | ||
-- GBasis-related computations could fail to terminate or be wrong | -- GBasis-related computations could fail to terminate or be wrong | ||
| Line 43: | Line 43: | ||
<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
<see>Introduction to Groebner Basis in CoCoA</see> | <see>Introduction to Groebner Basis in CoCoA</see> | ||
| − | <see> | + | <see>CharP.GBasisF2</see> |
| − | <see> | + | <see>CharP.GBasisF4</see> |
| − | <see> | + | <see>CharP.GBasisF8</see> |
| − | <see> | + | <see>CharP.GBasisF16</see> |
| − | <see> | + | <see>CharP.GBasisF32</see> |
| − | <see> | + | <see>CharP.GBasisF64</see> |
| − | <see> | + | <see>CharP.GBasisF128</see> |
| − | <see> | + | <see>CharP.GBasisF512</see> |
| − | <see> | + | <see>CharP.GBasisF1024</see> |
| − | <see> | + | <see>CharP.GBasisF2048</see> |
| − | <see> | + | <see>CharP.GBasisModSquares</see> |
<see>Representation of finite fields</see> | <see>Representation of finite fields</see> | ||
</seealso> | </seealso> | ||
| Line 64: | Line 64: | ||
<key>GBasisF256</key> | <key>GBasisF256</key> | ||
| − | <key> | + | <key>charP.GBasisF256</key> |
<key>finite field</key> | <key>finite field</key> | ||
| − | <wiki-category> | + | <wiki-category>Package_charP</wiki-category> |
</command> | </command> | ||
Revision as of 15:12, 6 December 2010
CharP.GBasisF256
Computing a Groebner Basis of a given ideal in F_256.
Syntax
CharP.GBasisF256(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 F_256 = (Z/(2))[x]/(x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1).
@param Ideal An Ideal in a Ring over Z, where the elements 0,...,255 represent the elements of the field F_256. 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 A Groebner Basis of the given ideal.
Example
Use R::=QQ[x,y,z]; I:=Ideal(x-y^2,x^2+xy,y^3); GBasis(I); [x^2 + xy, -y^2 + x, -xy] ------------------------------- Use Z::=ZZ[x,y,z]; -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong ------------------------------- I:=Ideal(x-y^2,x^2+xy,y^3); CharP.GBasisF256(I); -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [y^2 + 144x, x^2, xy] -------------------------------
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields
