Difference between revisions of "ApCoCoA-1:CharP.GBasisF128"
From ApCoCoAWiki
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<item>@return The Groebner Basis of the given ideal.</item> | <item>@return The Groebner Basis of the given ideal.</item> | ||
</itemize> | </itemize> | ||
| + | |||
| + | <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); | ||
| + | Char2.GBasisF128(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 + 64x, x^2, xy] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | |||
</description> | </description> | ||
<seealso> | <seealso> | ||
Revision as of 13:07, 13 July 2009
Char2.GBasisF128
Computing a Groebner Basis of a given ideal in F_128.
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 F_128 = (Z/(2))[x]/(x^7 + x + 1 ).
@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.
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); Char2.GBasisF128(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 + 64x, x^2, xy] -------------------------------
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields
