Difference between revisions of "ApCoCoA-1:CharP.GBasisF512"
From ApCoCoAWiki
m (ApCoCoA:Char2.GBasisF512 moved to ApCoCoA:CharP.GBasisF512) |
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<command> | <command> | ||
| − | <title> | + | <title>CharP.GBasisF512</title> |
<short_description>Computing a Groebner Basis of a given ideal in <tt>F_512</tt>.</short_description> | <short_description>Computing a Groebner Basis of a given ideal in <tt>F_512</tt>.</short_description> | ||
<syntax> | <syntax> | ||
| − | + | CharP.GBasisF512(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.GBasisF512(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.GBasisF256</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>GBasisF512</key> | <key>GBasisF512</key> | ||
| − | <key> | + | <key>charP.GBasisF512</key> |
<key>finite field</key> | <key>finite field</key> | ||
| − | <wiki-category> | + | <wiki-category>Package_charP</wiki-category> |
</command> | </command> | ||
Revision as of 15:16, 6 December 2010
CharP.GBasisF512
Computing a Groebner Basis of a given ideal in F_512.
Syntax
CharP.GBasisF512(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_512 = (Z/(2))[x]/(x^9 + x +1).
@param Ideal An Ideal in a Ring over Z, where the elements 0,...,511 represent the elements of the field. 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.GBasisF512(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 + 256x, x^2, xy] -------------------------------
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields
